EFEFCTS OF GROUND MOTION UNCERTAINTY ON PREDICTING THE RESPONSE OF AN EXISTING RC FRAME STRUCTURE

Transcription

1 13 th World Conference on Erthquke Engineering Vncouver, B.C., Cnd August 1-6, 2004 Pper No EFEFCTS OF GROUND MOTION UNCERTAINTY ON PREDICTING THE RESPONSE OF AN EXISTING RC FRAME STRUCTURE Ftemeh JALAYER 1, Jmes L. BECK 2, Keith A. PORTER 3 nd John F. HALL 4 SUMMARY Estimtion of structurl response my be significntly ffected by the representtion of seismic ground motion uncertinty. A complete probbilistic presenttion of ground motion cn be constructed by specifying stochstic model tht depends on seismic source prmeters. Alterntively, the ground motion uncertinty cn be represented by dopting prmeters known s the intensity mesures (IM), nd using ttenution reltionships to relte the IM to seismic source prmeters. The uncertinty in the prediction of structurl response cn be expressed in terms of the probbility of exceeding given vlue of the structurl response. In this study, the uncertinty in the ground motion is represented in these two lterntive wys: () full probbilistic representtion using n dvnced simultion technique known s subset simultion (Au [4]) bsed on stochstic ground motion model conditionl on mgnitude nd distnce proposed by Atkinson nd Silv (Atkinson [3]), nd, (b) by dopting spectrl ccelertion t the smll mplitude fundmentl period s the intensity mesure. In lterntive (b), suite of ground motion recordings re used to represent ground motion chrcteristics not lredy cptured by the IM. The ttenution reltion relting the IM to the seismic source prmeters is obtined by two lterntive pproches: (i) by simulting stochstic ground motions nd pplying them to n elstic SDOF system nd (ii) by using the empiricl regression eqution of Abrhmson nd Silv (1997). The lterntive pproches re compred bsed on their prediction of the uncertinty in structurl response. Another comprison is done between the following two cses: (1) by predicting the structurl response following lterntive (b) nd using suite of rel ground motion recordings nd (2) by predicting the structurl response following lterntive (b) nd using suite of synthetic records. The suite of synthetic records re generted ccording to the sme stochstic model used in lterntive () for given mgnitude nd distnce; this provides common bsis for comprisons. In order to emulte selection of suite of rel records from bin, lterntive () nd cse (2) of lterntive (b) described bove re repeted using suite of synthetic records generted for mgnitude nd distnce s uncertin vribles belonging to designted bin. An existing 7-story reinforced concrete structure is used s cse-study. The structurl model (Jlyer [9]) includes stiffness nd strength degrdtion. 1 George W. Housner Reserch Fellow, Cliforni Institute of Technology 2 Professor, Cliforni Institute of Technology 3 George W. Housner Senior Reserch Fellow, Cliforni Institute of Technology 4 Professor, Cliforni Institute of Technology

2 INTRODUCTION One of the min ttributes distinguishing performnce-bsed erthquke engineering from trditionl erthquke engineering is the definition of quntifible performnce objectives. The performnce objectives re quntified usully bsed on life-cycle cost considertions, which encompss vrious prmeters ffecting structurl performnce, such s, structurl, non-structurl or contents dmge, nd humn csulties. Aprt from being rre events nd hving lrge consequences, erthqukes lso hve lrge uncertinty ssocited with them. There re lterntive wys to represent this uncertinty for design nd ssessment of structures. Most of the current seismic design procedures (FEMA 356 [7], ATC-40 [2]) tke into ccount the uncertinty in the ground motion implicitly by defining design erthqukes with prescribed probbilities of being exceeded in given time period. In the recent yers, specificlly fter the 1994 Northridge Erthquke, considerble reserch effort hs been focused on defining probbilistic performnce objectives tht blnce desirble structurl performnce nd life cycle costs (Wen, [13]). A performnce objective cn be expressed in terms of the probbility of exceeding specified limit stte defined in terms of life cycle cost or some other structurl performnce prmeter. Probbilistic performnce objectives, by definition, tke into considertion the uncertinty in the ground motion. However, there re lterntive wys for representing ground motion uncertinty. One wy to represent ground motion uncertinty is by dopting prmeter (or vector of prmeters) known s the intensity mesure (IM) in order to represent the uncertinty in the ground motion. The dopted IM is lso used to scle suite of ground motion recordings (round ~20-30) in order to cpture ground motion uncertinty not cptured by the IM itself. The dvntge of such representtion of ground motion, which hs been proposed for existing performnce-bsed design procedures, is tht is tkes into ccount the uncertinty in the ground motion in two stges, nmely, the ground motion level nd structurl response level, in more-or-less un-coupled mnner. The other dvntge of this IM-bsed pproch is tht it cn be devised with firly smll number of structurl nlyses (if structurl model uncertinty is ignored). This dvntge, however, cn lso be interpreted s wekness of such representtion; since it cnnot provide full probbilistic representtion of the ground motion with such smll number of ground recordings. Moreover, the mount of its devition from true probbilistic representtion of the ground motion cnnot be quntified. The lterntive wy to represent the uncertinty in the ground motion is by complete probbilistic representtion of the ground motion. In wy, this representtion is the limiting cse of the IM-bsed one, in tht the ground motion time history cn be thought of s vector IM with stochstic components. This probbilistic representtion is bsed on stochstic ground motion model conditionl on seismic source prmeters. The min dvntge of this representtion is tht it provides full probbilistic representtion of ground motion nd hence of structurl response. However, it requires considerble number of structurl nlyses. The number of required structurl nlyses cn be significntly reduced by using efficient simultion routines such s subset simultion (Au [4], [5]) or very efficient importnce smpling method clled ISEE (Au [6]). The min wekness of this method lies in its dependence on stochstic ground motion model to provide relistic description of the chrcteristics of the ground motions expected to hppen. This pper summrizes preliminry effort for benchmrking the lterntive representtions of ground motion for scenrio erthquke (i.e., fixed M nd r) with regrd to their prediction of structurl response. More specificlly, the performnce objective is expressed in terms of the probbility tht designted structurl response prmeter (here, mximum inter-story drift rtio) exceeds specified vlue. In order to provide common bsis for compring the two different representtions, the stochstic ground motions re lso employed in the IM-bsed pproch. This llows for compring the two representtions seprte from the differences between rel nd synthetic ground motion recordings. In order to emulte selection of suite of rel recordings from bin representing scenrio erthquke,

3 structurl response predictions re repeted using suite of synthetic records generted when mgnitude nd distnce re uncertin vribles from designted mgnitude-distnce bin. An existing seven story hotel locted in Vn Nuys, Cliforni, is used s cse-study. It is modeled s reinforced concrete structure with degrding behvior in the nonliner rnge. Mximum inter-story drift rtio denoted by, θ mx, is used s the designted structurl response prmeter; nd the spectrl ccelertion t the fundmentl period, S ( T 1 = 0.80 sec), is dopted s the ground motion intensity mesure. MODEL STRUCTURE: TRANSVERSE FRAME OF AN EXISTING BUILDING One of the trnsverse frmes in the hotel structure locted in Vn Nuys is selected for the structurl model (Figure 1). This building is n older reinforced concrete (RC) structure tht suffered sher filures in its columns during the 1994 Northridge Erthquke. The frme is modeled using DRAIN2D-UW, which is modified version of DRAIN2D produced t the University of Wisconsin (see Pincheir [11]). The structurl model tkes into ccount stiffness nd strength degrding behvior in the non-liner rnge for both flexure nd sher (see Jlyer, 2003 for more detils) Figure 1. Structurl Model SUBSET SIMULATION PROCEDURE- AN EFFICIENT SIMULATION TECHNIQUE Subset simultion (Au [4], [5]) is simultion procedure used for efficiently computing probbilities of rre events, such s the seismic risk for structurl system. Subset simultion is bsed on the ide tht smll probbilities cn be expressed s the product of lrger conditionl probbilities. This helps to brek the simultion of rre event into sequence of simultions of more frequent events tht re conditioned on filing successively incresing threshold levels. Subset simultion cn be preformed with significntly smller number of structurl nlyses compred to stndrd Monte Crlo simultion. Subset simultion technique cn be employed for ssessing the relibility of both liner nd non-liner dynmic systems. Vrious sources of uncertinty, such s the uncertinty in the input or modeling uncertinty cn be introduced into the relibility problem solved by subset simultion. This pper employs the subset simultion technique for both obtining probbilistic estimte of the structurl response nd lso tht of the dopted intensity mesure. It is ssumed tht the uncertinty in the input, here ground motion uncertinty, is the only source of uncertinty. However, s mentioned bove, this routine is generl with respect to the sources of uncertinty introduced into the ssessments. The stochstic ground motion model introduced by Atkinson nd Silv (Atkinson [3]) is employed in order to describe the seismic source chrcteristics for scenrio erthquke.

4 ATKINSON AND SILVA (2000) STOCHASTIC GROUND MOTION MODEL A stochstic ground motion model my be used to describe the ground motion t the site for scenrio event with given mgnitude nd distnce from the site. This pper dopts the stochstic point-source ground motion model developed by Atkinson nd Silv (2000) for Cliforni ground motions recorded on rock sites. In order to generte ground motion time history to be employed in Monte Crlo simultion procedure, sequence of independent nd identiclly distributed stndrd Norml vribles (white noise) t discrete time intervls re modulted by n envelope function. The resulting modulted white noise sequence is trnsformed into the frequency domin using the discrete Fourier trnsform nd then multiplied by the rdition spectrum defined by the ground motion model. This results in spectrum tht on verge grees with the rdition spectrum defined by the ground motion model. Finlly, the inverse Fourier trnsform is used to bring the resulting spectrum bck into the time domin. It should lso be noted tht mplifictions for soil site is considered by pplying empiricl soil fctors provided by Abrhmson nd Silv (1997) (Abrhmson [1]) to the reltions derived for rock sites. EFFECT OF GROUND MOTION UNCERTAINTY ON PROBABILISTIC IM PREDICTION FOR A SCENARIO EARTHQUAKE A preliminry step for compring lterntive representtions of ground motion uncertinty is by benchmrking the predictions of the intensity mesure (IM) for scenrio erthquke with specified mgnitude nd distnce. In the IM-bsed representtion of ground motion, empiricl ttenution reltions re used to predict the men nd stndrd devition of the intensity mesure for given vlue of the mgnitude nd distnce. In the lterntive representtion, simultion techniques my be employed to provide full probbilistic distribution of the dopted intensity mesure for given mgnitude nd distnce bsed on stochstic ground motion model. In order to bridge between these two ground motion representtions, the full probbilistic pproch cn be used to obtin synthetic ttenution reltion bsed on the generted stochstic ground motion records. This cn be done by designting the IM itself s response prmeter nd obtining its probbilistic distribution for given scenrio event. This exercise is useful for providing common bsis for compring the two representtions. Empiricl Attenution Reltions The (dopted) intensity mesure cn be predicted for given mgnitude nd distnce using empiricl ttenution models tht re developed from dtbse of ground motion records. The reltion between IM nd ground motion prmeters, such s mgnitude nd distnce, cn be expressed in the following generic form: ln IM = f ( M, r) + ε σ ln IM M, r Eq. 1 Here, ln IM denotes the nturl logrithm of IM, M denotes moment mgnitude, nd r denotes distnce from the site. The functionl form f (.) predicts the men of ln IM for given mgnitude, distnce, style of fulting, nd soil condition of the site. This functionl form is determined using regression model to fit dtbse of rel ground motion recordings. σ ln IM M, r denotes the stndrd error of the regression for given mgnitude nd distnce. It is used to estimte the stndrd devition of ln IM for given mgnitude nd distnce. ε is the normlized prediction error (usully ssumed to be stndrd Norml vrible) denoting the number of stndrd devitions ln IM differs from its men estimte provided by the empiricl ttenution model.

5 Abrhmson nd Silv (1997) Empiricl Attenution Reltion In this pper, the spectrl ccelertion t the smll-mplitude fundmentl period of the structure, T 1 = 0.80 sec, denoted by S ( T 1 ) or simply S, is dopted s the intensity mesure (IM). The empiricl response spectrl ttenution reltions developed by Abrhmson [1] for shllow crustl erthqukes re used for representing the uncertinty in the spectrl ccelertion for given scenrio erthquke. The spectrl ccelertion is described by log-norml distribution. The prmeters of this distribution, nmely, men nd stndrd devition, re predicted by the ttenution reltion. Figure 2 illustrtes (solid line) the probbility of exceeding given vlue of spectrl ccelertion clculted from the Abrhmson nd Silv (1997) ttenution reltion t period of T = 0.75 sec, the closest listed vlue to the fundmentl period of the model structure, for strike-slip erthquke event with, M = 7, r = 20 km, recorded on deep soil. Synthetic Attenution Reltion Bsed on Atkinson nd Silv (2000) Model An lterntive wy to develop n ttenution reltion for given scenrio event is to derive it from the stochstic ground motion model using n efficient simultion technique (here, subset simultion) in order to obtin probbility distribution for the spectrl response of n elstic SDOF system. In this pper, the resulting probbility distribution for S is lso referred to s the synthetic ttenution reltion; in order to distinguish it from the empiricl ttenution reltion. Figure 2 illustrtes (dshed line) the probbility of exceeding given vlue of S obtined using subset simultion technique with 2300 smples nd the Atkinson nd Silv (2000) stochstic ground motion model. This plot gives the probbility distribution for the spectrl response of n elstic SDOF system with 5% dmping t T = 0.80 sec for scenrio event with M = 7 nd r = 20 km recorded on deep soil. 1 Probbility of Exceeding Spectrl Accelertion for Scenrio Erthquke, M=7, r=20km, Deep Soil Probbility of Exceeding S (T 1 ) Abrhmson nd Silv (1997) Attenution Reltion SS, Atkinson nd Silv (2000) Stochstic Model S (T 1 =0.80 sec) [g] Figure 2- Effect of the Alterntive Representtions of Ground Motion Uncertinty on the Prediction of the Spectrl Accelertion t the Fundmentl Period of the Structure

6 Observtions It cn be observed from Figure 2 tht the probbility distribution for S bsed on the empiricl ttenution reltion (the solid line) spns over wider rnge of spectrl ccelertion vlues compred to the one provided by the synthetic ttenution reltion (the dshed line). In order to compre the two curves more quntittively, lognorml probbility distribution (thin solid line) with medin (0.33g) nd stndrd devition of ln S (0.26) equl to the synthetic ttenution reltion (dshed line) is lso plotted. It cn be observed tht the lognorml distribution describes perfectly the synthetic ttenution reltion. Since the empiricl ttenution reltion itself is described by lognorml distribution with medin equl to 0.34g nd stndrd devition of the logrithm equl to 0.56, one cn compre the empiricl nd synthetic ttenution reltions by compring the medin nd the stndrd devition of the logrithm of the corresponding lognorml probbility distributions. It is observed tht the medin spectrl ccelertions from the synthetic nd empiricl ttenution reltions re very close to ech other, but the stndrd devition of ln S ccording to the empiricl ttenution reltion is more thn twice tht of the synthetic reltion. EFFECT OF GROUND MOTION UNCERTAINTY REPRESENTATION ON PROBABILISTIC STRUCTURAL RESPONSE PREDICTION FOR A SCENARIO EARTHQUAKE In the previous section, lterntive ground motion representtions nd their effect on probbilistic predictions of the intensity mesure S were studied. In similr mnner, this section looks into the effect of ground motion uncertinty representtion on prediction of structurl response. The discussions re divided into four ctegories. The first ctegory describes structurl response predictions using lest squres estimte of structurl response versus spectrl ccelertion bsed on the dt provided by few (e.g., 20) non-liner dynmic nlyses of structure subjected to suite of rel ground motion records. In this ctegory, spectrl ccelertion is relted to ground motion prmeters by n empiricl ttenution reltion. The second ctegory describes response predictions using simultion procedure (subset simultion) bsed on stochstic ground motion model. The third ctegory describes response predictions similr to the first ctegory but using non-liner dynmic response to synthetic records nd lso using synthetic ttenution reltion to relte the spectrl ccelertion to ground motion prmeters. The third ctegory of ground motion representtions, which is rrely used in prctice, serves s bridge between the two lterntive representtions of ground motion nd fcilittes the comprisons. The lst ctegory is dedicted to structurl response predictions using synthetic ground motion records s in the second nd third ctegory but generted from designted mgnitude-distnce bin. This is n effort to emulte the rel ground motion selection from mgnitude-distnce bin representing scenrio erthquke. Predicting Structurl Response Using IM nd Existing Ground Motion Records to Represent Ground Motion Uncertinty In this pproch, the spectrl ccelertion for scenrio erthquke is predicted by the empiricl ttenution reltion of Abrhmson nd Silv The next step is to predict the structurl response uncertinty for the rnge of possible vlues of the spectrl ccelertion. It hs been demonstrted (Jlyer [9]) tht severl non-liner dynmic nlysis procedures cn be used to predict the structurl response uncertinty conditionl on S over rnge of spectrl ccelertion vlues. One such procedure employs liner regression to dt pirs consisting of the logrithm of the structurl response nd logrithm of spectrl ccelertion for suite of rel ground motion recordings. Figure 3 illustrtes mximum inter-story drift rtios obtined by performing non-liner dynmic nlyses on suite of 20 rel ground motion records selected from Pcific Erthquke Engineering Reserch Center (PEER [12]) dtbse nd plotted versus the corresponding spectrl ccelertion vlues for the records. These

7 records re ll free field recordings on deep soil (soil type D by the Geo-mtrix definition, PEER [12]). In order to pproximtely represent the ground motion corresponding to scenrio event with mgnitude 7 nd distnce 20 km, the records re chosen from bin of ground motions records with moment mgnitude between 6.5 nd 7.5 nd closest distnce to the site between 10 to 30 kilometers. Structurl Response Prediction Adopting Spectrl Acclertion s IM for Scenrio Erthquke with M=7, r=20 km 20 Rel Ground Motion Records with 6.5 < M < < r < S t T 1 =0.80 seconds [g] 10 1 = b = σ ln(θmx ) S = θ mx =*S b Mximum Story Drift Angle, θ mx Figure 3. Predicting Structurl Response (Mximum Inter-story Drift Angle) for Suite of Rel Ground Motion Records The dt-pirs plotted in Figure 3, re used to provide conditionl probbilistic description of mximum inter-story drift rtio, denoted by θ mx, given the spectrl ccelertion S t the fundmentl period of the structure (i.e., the dopted intensity mesure). This hs been done by lest-squres fitting of line to these points in logrithmic scle (see Luco [10], Jlyer [8]), which is equivlent to fitting power-lw b function, θ mx = S, to these points in rithmetic scle. This functionl form predicts the conditionl men of the logrithm of mximum inter-story drift rtio for given spectrl ccelertion vlue. Assuming tht mximum inter-story drift rtio θ mx cn be described by lognorml vrible with constnt stndrd devition (i.e., not function of spectrl ccelertion), one my use the stndrd error of the regression to estimte the conditionl stndrd devition of the logrithm of mximum inter-story drift for given spectrl ccelertion ( σ ln( θ mx ) S = ). The probbility of θ mx not exceeding vlue x, conditionl on S is therefore given by: ln x ln b ln S P[ θ mx x S ] = Φ( ) Eq. 2 σ ln( θmx ) S where Φ is the cumultive distribution function for stndrd Norml vrible nd the prmeters in Eqution 2 re given in Figure 3. The uncertinty in the prediction of structurl response for given scenrio erthquke cn be described by the probbility of exceeding given vlue of mximum inter-story drift ngle, x, which cn be evluted numericlly using the Totl Probbility Theorem:

8 P[ θ mx > x M, r] = 1 P[ θ mx x S ] p( S M, r) ds Eq. 3 0 This integrtion combines the lognorml distribution function p( S M, r) provided by the empiricl ttenution reltion, which predicts the spectrl ccelertion for given scenrio erthquke, nd the conditionl lognorml distribution of response given spectrl ccelertion described in Eqution 2. Figure 5 illustrtes the probbility of exceeding mximum inter-story drift rtio (solid line) for scenrio erthquke of mgnitude 7 nd distnce to site equl to 20 km tht is clculted s described. It should be noted tht the number of non-liner dynmic nlyses used to produce this result is equl to 20, which is the number of ground motion records used for structurl response predictions. The probbility vlues in Figure 5 (verticl xis) re shown in the logrithmic scle in order to better illustrte the rnge of probbility vlues smller thn 0.1, which is the rnge of interest in structurl relibility problems. Predicting the Complete Probbility Distribution of Structurl Response Using Subset Simultion with Stochstic Ground Motion Model The probbility of exceeding mximum inter-story drift rtio cn lso be clculted using n efficient simultion procedure such s Subset Simultion. Figure 5 illustrtes (dshed line) this probbility for scenrio erthquke of mgnitude 7 nd distnce to site equl to 20 km tht is clculted using the subset simultion procedure. The stochstic ground motion records generted by the simultion routine re constructed using the Atkinson nd Silv (2000) stochstic ground motion model modified for soil site. It should be noted tht the uncertinty in the prediction of structurl response in this cse is described directly bsed on complete probbilistic description of ground motion for scenrio erthquke nd does not require the intensity mesure s n intermediry vrible. The number of non-liner dynmic nlyses performed in this subset simultion procedure were equl to 1400 (this predicts the probbilities with coefficient of vrition round 30%). It cn be observed from Figure 5 tht, for the probbility vlues smller thn round 0.5, the IM-bsed pproch over-estimtes the probbility of exceeding mximum inter-story drift compred to the subset simultion result. However the medin drift vlues (i.e., drift vlue corresponding to probbility of exceednce equl to 0.50) predicted by the two lterntive pproches re very close. Predicting Structurl Response Using IM nd Stochstic Ground Motion Recordings In order to better understnd the observed differences between lterntive ground motion representtions on structurl response prediction, the probbility of exceeding vrious mximum inter-story drift rtios cn be clculted by using records generted from the stochstic ground motion model in the IM-bsed method. The procedure for clculting the probbility of exceeding mximum inter-story drift is similr to the one described in the first ctegory of response predictions. However, it is different in tht it uses the synthetic ttenution reltion (plotted in Figure 2) for predicting the intensity mesure; nd lso tht it uses suite of synthetic records to predict the structurl response given the intensity mesure. Figure 4 illustrtes mximum inter-story drift ngle vlues obtined by performing non-liner dynmic nlyses on suite of 20 synthetic ground motion records generted using the Atkinson nd Silv ground motion model for scenrio erthquke of mgnitude 7 nd distnce to site equl to 20 km. the prmeters for Eqution 2 in this cse re given in Figure 4. It cn be observed from the figure tht spectrl ccelertion vlues re less scttered compred to the similr plot for the rel ground motion records. This is consistent with the plots in Figure 2 where the rnge of probble spectrl ccelertion vlues for the synthetic records is nrrower thn tht of the rel records. Since spectrl ccelertion is the independent vrible of the regression, the prmeter estimtions using liner regression re ssocited with more uncertinty compred to the rel ground motion records. Lter on, wy to improve the liner regression prmeter predictions bsed on synthetic records is described.

9 Structurl Response Prediction Adopting Spectrl Accelertion s IM for Scenrio Erthquke with M=7 nd r=20km 10 0 = b = σ ln(θmx ) S = S t T 1 =0.80 seconds [g] Synthetic Records Generted using Atkinson nd Silv (2000) with M=7, r=20 Line Fitted to the Logrithm of Dt using Liner Lest Squres Method Mximum Story Drift Angle, θ mx Figure 4- Structurl Response (Mximum Inter-story Drift Angle) to Suite of Synthetic Ground motion Records 10 0 EDP Predictions Using Alerntive Representtions of Ground Motion, M=7, r=20, Deep Soil Probbility of Exceeding EDP for given Scenrio Event IM bsed, Stochstic Attenution AS 2000 Full Probbilistic, SS, Stochstic Ground Motion Model AS 2000 IM bsed, Empiricl Attenution AS Mximum Inter story Drift Rtio (EDP) Figure 5- Effect of the Representtion of Ground Motion Uncertinty on the Prediction of the Structurl Response The probbility of exceeding mximum inter-story drift (clculted by numericl integrtion s described in the first ctegory), for the scenrio erthquke of mgnitude 7 nd distnce to site of 20 km, is plotted (in dotted line) in Figure 5. It cn be observed tht the result of the IM-bsed pproch using synthetic records (dotted line) follows very closely the subset simultion result (dshed line). This is especilly interesting since the IM-bsed pproch cn be devised with significntly less number of nlyses compred to subset simultion. Since both pproches re bsed on synthetic records generted

10 for the sme scenrio event, the good greement observed between the results my be n indiction of spectrl ccelertion being suitble intensity mesure in this cse. However, s mentioned bove, the smll sctter in the spectrl ccelertion vlues in Figure 4 results in lrger uncertinty ssocited with the estimtion of the regression prmeters compred to the regression prmeter estimtions in Figure 2 for the rel ground motion records. Moreover, ny judgment mde with respect to the suitbility of the spectrl ccelertion s n intensity mesure (bsed on the synthetic ground motion records) is implicitly relted to the suitbility of the stochstic ground motion model for describing the future erthqukes occurring t the site. Predicting Structurl Response Using Synthetic Ground Motion Records Generted From Bin The differences observed in the predictions of structurl response using rel nd synthetic recordings for scenrio erthquke in Figure 5 my in prt be ttributed to the differences between rel ground motion selection nd synthetic ground motion genertion. Since the rel ground motion records re chosen from dtbse of erthqukes tht hve tken plce in the pst, it is virtully impossible to select suite of records with specified lrge mgnitude nd smll distnce. Therefore, rel ground motions representing scenrio erthquke re chosen from mgnitude-distnce bin covering rnge of mgnitude nd distnce close to those of the scenrio event of interest. In contrst, the suite of synthetic records cn be generted for scenrio erthquke with specified mgnitude nd distnce. In n ttempt to emulte the selection of rel ground motion records from designted mgnitude-distnce bin, synthetic records re generted in this subsection from bin of mgnitude between 6.5 nd 7.5 nd closest distnce between 10 km nd 30 km (sme bin definition s the rel records). In order to generte such records, it hs been ssumed tht the moment mgnitude hs Gutenberg-Richter [4] probbility distribution truncted on the two ends of the bin s mgnitude intervl. Also, it hs been ssumed tht the erthqukes occur equl likely in circulr re confined between the two ends of the bin s distnce intervl [4]. It should be noted tht in the IM-bsed pproch, the synthetic records generted from designted bin re only used in order to obtin the conditionl probbility distribution of mximum interstory drift rtion given spectrl ccelertion. Hence, the synthetic ttenution reltion is still obtined for the specified mgnitude nd distnce vlues. This is more consistent with the rel ttenution reltions tht re provided s function of mgnitude nd distnce. Figure 6 illustrtes the spectrl ccelertion nd mximum inter-story drift rtio pirs corresponding to 20 synthetic ground motion records generted s described bove from bin. The lest squres line fitted to the dt is lso plotted in the figure. Compring to Figure 4 where the synthetic records re generted for scenrio erthquke, the spectrl ccelertion vlues demonstrte lrger vribility similr to the rel dt cse in Figure 3. This not only renders the regression prmeter estimtions with less uncertinty compred to the dt in Figure 4 but it lso mkes the synthetic ground motion genertion more similr to rel ground motion selection. It should be noted tht this exercise is not necessrily vluble from prcticl point of view; it is rther n ttempt to increse the common ground for drwing comprisons between structurl response to rel nd synthetic ground motion records. Figure 7 illustrtes the probbility of exceeding mximum inter-story drift rtio obtined by following the lterntive pproches described in this pper. This figure is the sme s Figure 5 with regrd to the lterntive pproches used for clculting the probbility of exceeding mximum inter-story drift rtio. However, it differs from Figure 5 in tht the synthetic records re generted from mgnitude-distnce bin rther thn with specified mgnitude nd distnce. Hence, the solid line corresponding to IM-bsed pproch using rel ground motion records is the sme s Figure 5. It cn be observed tht the IM-bsed pproch using synthetic records (the dotted line) follows more closely the solid line. Also the subset simultion results (the dshed line) demonstrtes better greement with the solid line for smller probbility vlues, which is the rnge of interest in structurl relibility problems. In summry, it cn be observed tht incresing mgnitude-distnce smpling intervl results in comprtively wider probbility

11 distribution for the structurl response, which seems to gree better with resulting probbility distribution using rel ground motion records. Structurl Response Prediction dopting Spectrl Accelertion s IM for Scenrio Erthquke with M=7, r=20 km 20 Synthetic Records with 6.5 < M < km < r < 30km S t T 1 =0.80 seconds [g] 10 1 = b = σ ln(θmx ) S = Mximum Story Drift Angle, θ mx Figure 6- Structurl Response (Mximum Inter-story Drift Angle) to Suite of Synthetic Ground motion Records Generted from Mgnitude-Distnce Bin Representing the Scenrio Erthquke M=7 nd r=20km. EDP Predictions Using Alerntive Representtions of Ground Motion < M < 7.5, 10km <r < 30km, Deep Soil Probbility of Exceeding EDP for given Scenrio Event IM bsed, Stochstic Attenution AS 2000 Full Probbilistic, SS, Stochstic Ground Motion Model AS 2000 IM bsed, Empiricl Attenution AS Mximum Inter story Drift Rtio (EDP) Figure 7- Effect of the Representtion of Ground Motion Uncertinty on the Prediction of the Structurl Response. The Synthetic Ground Motion Records re Generted from Mgnitude-Distnce Bin Representing Scenrio Erthquke with M=7 nd r=20km

12 Observtions It cn be observed from Figure 5 tht the structurl response predictions mde using the IM-bsed pproch nd the synthetic ground motions re very close to those mde using subset simultion nd the stochstic ground motion model. This demonstrtes tht the efficient IM-bsed pproch gives good pproximtion to the probbility distribution of mximum inter-story drift rtio. This result is especilly interesting if one tkes into ccount the number of simultions performed in the two methods, nmely, 20 nd 1400, respectively. Figure 5 lso demonstrtes difference between the results obtined using rel nd synthetic records. It cn be observed tht the rel nd synthetic records provide roughly the sme vlue for medin mximum inter-story drift rtio. However, the probbility distribution obtined using rel records is more widely distributed compred to the probbility distribution(s) obtined using synthetic records. The difference between probbility distributions becomes more pronounced in the til, i.e., smll probbility vlues. Aprt from the differences between rel nd synthetic records, one my ttribute the wider probbility distribution obtined using rel records to the fct tht these records re selected from mgnitudedistnce bin s opposed to hving fixed mgnitude nd distnce. Figure 7 demonstrtes the resulting probbility distributions of mximum inter-story drift rtio using synthetic records when the records re generted from bin defined in the sme wy s the rel records. It cn be observed tht the probbility distributions obtined using rel nd synthetic records show much better greement compred to Figure 5. The liner trend between the logrithm of mximum inter-story drift rtio versus the logrithm of spectrl ccelertion is more observble in Figure 6 when synthetic records re generted from bin compred to Figure 4 where they re generted with fixed mgnitude nd distnce. Since the vribility is lrger in the independent vrible of the liner regression (in this cse, spectrl ccelertion) in Figure 6, there is more confidence in the resulting prmeter estimtes. SUMMARY AND CONCLUSIONS The effect of lterntive ground motion uncertinty representtions on the prediction of structurl response for scenrio erthquke event is compred. The uncertinty in the ground motion cn be described by complete probbility distribution bsed on stochstic ground motion model. Alterntively, n intermediry vrible (or vector of vribles) known s the intensity mesure cn be dopted to describe the uncertinty in the ground motion. Response predictions bsed on the complete probbilistic model of the ground motion re mde using n efficient simultion technique known s Subset Simultion. The effect of ground motion representtion on the prediction of the intensity mesure itself for scenrio event hs lso been compred. This is equivlent to compring the dopted empiricl ttenution reltion to the synthetic ttenution reltion constructed by pplying subset simultion to liner oscilltor subjected to the synthetic ground motion records. Benchmrking response predictions bsed on the two lterntive representtions of ground motion uncertinty is lso useful in tht it provides criterion for judging nd compring how effective cndidte intensity mesure is. This is especilly useful in the selection of the most desirble intensity mesure for representing the uncertinty in the ground motion. It hs been observed tht the response predictions provided by the two lterntive representtions of ground motion uncertinty re very close when they both use stochstic ground motions. However, the prmeter estimtes provided by liner regression in the IM-bsed pproch using synthetic ground motions hve lrger uncertinty ssocited with them compred to when rel ground motions re used. Therefore, the sensitivity of response predictions to the liner regressions prmeters using stochstic

13 ground motions needs to be studied. The response predictions using rel ground motion records (IMbsed pproch) nd those provided using synthetic ground motion records (IM-bsed pproch nd subset simultion) gree on the estimted medin mximum inter-story drift rtio (i.e., vlue corresponding to probbility of exceednce equl to 0.50). However, the predictions re significntly different for smll probbility vlues. The shpe of the probbility distribution of response obtined using rel records is wider compred to those predicted using synthetic records. This cn be in prt ttributed to the difference between synthetic record genertion nd rel ground motion selection. Being limited to the dtbse of recorded ground motions, it is difficult to select suite of ground motions with specified lrge mgnitude nd smll distnce. Therefore, these records re selected from mgnitude-distnce bin tht is constructed within designted intervls round mgnitude nd distnce of the scenrio erthquke. In contrst, mgnitude nd distnce re fixed for the synthetic records generted for scenrio erthquke. This cn led to less vribility in spectrl ccelertion vlues nd hence in structurl response in the cse of synthetic records s compred to rel records. It would hve been more desirble to be ble to select rel records with the specified mgnitude nd distnce nd to compre the resulting structurl response prediction to those using synthetic records. However, in lieu of creting such selection, synthetic ground motion records re generted in mnner tht mimics rel ground motion selection from bin of records. The response predictions obtined using the new set of synthetic ground motion show better greement with response prediction using rel records. The next logicl step will be to benchmrk the structurl response predictions, obtined by the lterntive pproches described in this pper, considering ll the possible erthquke scenrios t the site. It is lso extremely importnt to ensure tht the stochstic ground motion model is ble to predict the ground motions expected to occur t the site. Therefore, the future comprisons need to include lterntive stochstic ground motion models. Finlly, the benchmrking of the lterntive representtions of ground motion uncertinty needs to be performed with respect to vribles defining the performnce objectives, such s expected repir cost in the structure. ACKNOWLEDGEMENT This work ws supported in prt by the Erthquke Engineering Reserch Centers Progrm of the Ntionl Science Foundtion under Awrd Number EEC through the Pcific Erthquke Engineering Reserch Center (PEER). This support is grtefully cknowledged. Any opinions, findings nd conclusions or recommendtions expressed in this mteril re those of the uthors nd do not necessrily reflect those of the Ntionl Science Foundtion. REFERENCES 1. Abrhmson, N. A.; Silv, W. J., Empiricl response spectrl ttenution reltions for shllow crustl erthqukes, Seismologicl Reserch Letters, 68, 1, Jn.-Feb. 1997, pges ATC-40, Methodology for seismic evlution nd retrofit of existing concrete buildings, Applied Technology Council, Redwood City, CA, Atkinson, G.M., nd, Silv, W., Stochstic modeling of Cliforni ground motions, Bulletin of the Seismic Society of Americ 2000, 90 (2), Au, S. K., Beck, J.L., Subset simultion nd its ppliction to seismic risk bsed on dynmic nlysis, Journl of Engineering Mechnics, August, Au, S. K., Beck, J.L., Estimtion of smll filure probbilities in high dimensions by subset simultion, Probbilistic Engineering Mechnics, 16, , Au, S.K., Beck, J.L., First excursion probbilities for liner systems by very efficient importnce smpling, Probbilistic Engineering Mechnics 2001, 16,

14 7. FEMA 356, Pre-stndrd nd Commentry for the Seismic Rehbilittion of Buildings, Federl Emergency Mngement Agency, Wshington, DC, (2000). 8. Jlyer, F., nd, Cornell, C. A., A Technicl Frmework for Probbility-bsed Demnd nd Cpcity Fctor Design (DCFD) Seismic Formts. PEER Report 2003/ Jlyer, F., Direct Probbilistic Seismic Anlysis: Implementing Non-liner Dynmic Assessments, Ph.D. Thesis, Deprtment of Civil nd Environmentl Engineering, Stnford, CA, Luco, Nicols nd Cornell, C. A., Structure-specific sclr intensity mesures for ner-source nd ordinry erthquke ground motions, Submitted for Publiction: Erthquke Spectr, April Pincheir, Jose A., Dotiwl, Fridun S. nd D'Souz, Jonthn T., Seismic nlysis of older reinforced concrete columns, Erthquke Spectr, 15, 2, My 1999, pges PEER strong motion dtbse, Wen, Y.K., Relibility nd performnce-bsed design, Structurl Sfety 2001, 23.