Introduction to a Robust Period-independent Ground Motion Selection and Scaling Method

Transcription

1 Introducton to a Robust Perod-ndependent Ground Moton Selecton and Scalng Method M. Dehghan, R. Tremblay École Polytechnque de Montréal SUMMARY: A new approach for ground moton selecton and scalng for structural analyss s proposed and elaborated. In the proposed approach, ground moton records are selected based on the hazard deaggregaton data and then refned accordng to the observed trends n ntensty, frequency content, and duraton. scalng s done at a frequency bandwdth n whch most of sesmc energy s concentrated. Effects of the proposed method on the sesmc demand parameters are studed usng nonlnear tme-hstory analyses on nelastc sngle-degree-offreedom systems. The robustness of the proposed approach s demonstrated through a comparatve study. Keywords: Domnant sesmc event, Ground moton parameters, INTRODUCTION Tme-hstory analyss has become an essental tool for performance-based sesmc desgn and evaluaton. One of the mportant steps nvolved n ths process s the ground moton selecton and scalng whch could substantally affect the outcomes and the desgn-rehabltaton decsons. Choosng an approprate number of ground moton records and the selecton of a practcal effectve method of scalng the chosen records to a gven level of sesmc hazard are stll challengng decsons, despte the large amount of research that has been conducted on these ssues. In fact, there s no general consensus n the earthquake engneerng communty on a proper way of handlng these problems (NIST, ). One man reason s related to the ground moton randomness, and the complex dynamc response of structures beng subjected to ths aleatory nput energy. The wde varablty n the structural sesmc demands observed when usng dfferent avalable selecton and scalng methods s a strong motvaton for developng a robust, yet smple ground moton selecton and scalng approach whch results n a stable central tendency and small scatter when assessng structural sesmc demand. Ths would lead to a hgher degree of confdence n demand predcton and a more defnte margn of safety aganst unfavourable structural responses. In ths study, a robust ground moton selecton and scalng method s proposed and explaned n detal. Statstcal robustness of ths method s examned throughout nonlnear tme hstory analyses. RECORD SELECTION. Domnant events The proposed record selecton method starts from deaggregaton of sesmc hazard for a gven locaton. Sesmc hazard deaggregaton s a technque to decompose the contrbuton of dfferent earthquakes to a gven level of sesmc ntensty nto clustered bns of magntudes and ste-to-source dstances, wth relatve contrbuton of each bn to the ntensty. Ths technque has been dentfed as a probablstcally consstent way for fndng domnant earthquake magntudes and ste-to-source dstances (Bazzurro and Cornell, 999). Deaggregaton of the % n 5 years probablty of exceedance of spectral acceleratons for Vctora, Brtsh Columba, at perods of. and. second are shown n Fg..a and b.

2 Contrbuton to Hazard, 8 4 S a (.) =.378 g Modal bn: 7 km Mean bn: 4 km a) b) Contrbuton to Hazard, S a (.) =.7 g Modal bn: 7 km Mean bn: 5 km Fgure.. Sesmc hazard deaggregaton for spectral acceleratons for Vctora, BC at T of: a). s; b). s. In ths study, hazard deaggregaton results are provded by the Geologcal Survey of Canada (Halchuk et al., 7). The followng steps are proposed to fnd the domnant-event scenaros at a gven locaton and to select the event-compatble records:. Event bns data (M, R and the contrbuton thereof) for spectral acceleratons at all avalable perods are combned and sorted n descendng order based on relatve contrbutons;. For the repettve event bns wth the same M and R values, the one wth the hghest contrbuton s kept and the remanng ones are dscarded; 3. Only the frst n bns are stored, based on ther relatve contrbutons, and the remanng ones are dscarded, where n s the number of requred records for tme-hstory analyss; 4. Domnant event bns can be ether (these 4 optons correspond to scenaros S to S4 examned n the comparatve study of secton 4 of ths paper): a. the frst bns wth cumulatve contrbuton exceedng 5% of the total contrbuton of the n bns wth the number of records for a bn beng based on the relatve contrbuton of that bn to the total contrbuton of the remanng bns,.e., more records wll be selected from the bns wth hgher relatve contrbutons; b. the frst n/ bns, whch means that two records wll be selected from each bn; c. all n bns, wth only one record beng selected from each bn; or d. the frst bns up to a cumulatve contrbuton of 5%, wth equal number of records beng selected from each bn,.e., same chance for every event. The proposed algorthm s meant to ensure that no possble event wth a sgnfcant contrbuton wll be overlooked and a wde range of frequency content, duraton and ntensty levels wll be obtaned wth the selected records. The wde range ensures that nter-event varablty s ncluded n the process and potentally damagng events are consdered, regardless of ther magntude and dstance. Event bnbased record selecton s consstent wth the probablstc approach of sesmc hazard calculaton, as events wth the same magntude and dstance n the approach result n the same rate of exceedance for a gven level of ntensty.. Intal record selecton Magntude and dstance of each domnant-event bn s expanded based on the resoluton of the clustered deaggregaton data used. In ths study, dm =.5 and dr = km. For each bn, ths expanded range of magntude and dstance was then appled as a selecton crtera to all avalable records n the PEER database (PEER, ). Events were only selected from recordng staton located on very dense sol and soft rock stes (3 V s3 7 m/s). s wth poor cut-off frequency were excluded from the ntal selecton process. It s beleved that after a certan magntude level, the magntude saturaton level, some ground moton characterstcs such as frequency content and duraton are no longer magntude dependent (Rathje, 4). Fgure.a and b show the sesmologcal

3 and emprcal predcton models for the mean perod of acceleraton sgnal as a robust frequency content parameter (see secton.3. for the defntons). These models ndcate that the mean perod of acceleraton becomes ndependent of magntude for M 7.5 whle remans lnearly dstance dependent over the whole range consdered. Ths trend was used when records for M7 bns were beng selected. To nclude ths effect, smply the upper bound of magntude n the bns wth the largest M7 could be relaxed. The process of the ntal selecton was performed for all event bns of the prevously defned scenaros. The numbers of ntally selected records for domnant-event bns were as hgh as n the case of moderate magntude-moderate dstance bns (M.5 at 5 km). Trend of Mean Perod [ = 8 bar, = 3. km/s, =.35, Q = 3, n =.] a) b) Emprcal Model for Predcton of Mean Perod on Soft Rock No Forward Drectvty effect ncluded Mean Perod, T m, s.8..4 Mean Perod, T m, s Dstance, km Magntude, M w 8.4 Closet Dstance, km Magntude, M w 8 Fgure.. Predcton models for mean perod of acceleraton sgnal: a) sesmologcal; b) emprcal.3 Selecton refnement As the ntal selecton crtera, sesmologcal metadata such as magntude, dstance, and sol profle are often used to fnd event-compatble records from the avalable databases such as PEER. When the search crtera are only lmted to the mentoned metadata, a large number of event-compatble records may be found. Due to the requred computaton capactes t may not be practcal to use all of these records n the tme-hstory analyss. Therefore a systematc approach s requred to refne and condense the ntally selected records to the requred numbers. Random refnement s often suggested n most of the ground moton selecton schemes such as ATC-58 (Haselton, 9). Ths may lead to a hgh scatter n the computed demand because all of the selected records are gven the same chance, regardless of ther damagng potental. Instead of random refnement, records can be ranked based on the trends n damagng potental related parameters. In ths way, records close to the central tendency of damage-related parameters wll be selected and the records wth exceptonal characterstcs wll be dscarded. Generally, damagng potental of earthquake records are attrbuted to three major classes of sgnal parameters: ) ampltude (ntensty); ) frequency content; and 3) strong shakng duraton (Kramer, 99)..3. Ampltude-related parameters In general, ampltude-related parameters can be calculated from: a) tme-doman sgnal propertes such as peak ground acceleraton (PGA) or velocty (PGV); or b) spectral-doman parameters such as acceleraton ntensty spectrum, ASI, (ntegral of the acceleraton spectrum). A revew of the most popular ampltude-related parameters was recently performed by (Ye et al., ). Generally, acceleraton- and velocty-based parameters are well-correlated wth the extent of damage n stff and flexble structures, respectvely..3. Frequency content-related parameters Frequency content can be specfed by means of: a) tme-doman parameters such as rato of PGV to PGA; b) frequency-doman parameters such as mean perod, T m,.e., the centre of gravty of the acceleraton power spectrum between.5 and Hz (Rathje, 4); or c) spectral-doman parameters such as predomnant spectral acceleraton (T psa ) or velocty (T psv ),.e., perods at peak spectral ordnates. The effectveness of the varous frequency content-related parameters s revewed n (Kumar et al., ). Besdes central tendency of frequences, frequency band-wdth s often requred to express the frequency content n a more precse way. Power spectrum moments have been shown to

4 be effectve tools to specfy the frequency band-wdth of ground moton sgnals (Kramer, 99). A study conducted on 548 horzontal records avalable n the PEER database shows that the mean perod has the hghest average nter-correlaton coeffcent wth the other frequency content-related parameters. It s noteworthy that ths parameter has 8% lnear correlaton wth a much smpler parameter, π PGV/PGA..3.3 Duraton-related parameters The duraton n whch a tme-doman ntensty parameter s hgher than a relatve or absolute threshold (e.g., 5% of PGA) has been wdely used to defne most of the duraton-related parameters. The reader s referred to (Hancock and Bommer, ) for a comprehensve revew of the duraton-related parameters. In spte of the extensve research done to fnd the most damage-related ground moton parameters, there s no sngle unque parameter whch could be sutable for all types of structures regardless of ther dynamc propertes (Ye et al., ). Ths may mply that nstead of lookng for the best parameter of each class,.e., the one wth the hghest correlaton wth damage, t would be better to fnd the parameter whch has the hghest nter-correlaton wth the other parameters n the same class. Ths parameter s referred to heren as the best estmator. Ths ensures that when the value of the best estmator s hgh, other parameters are lkely to be hgh as well. Studes have shown that among dfferent correlaton methods, rank correlaton can be more approprate when the relaton between varables s nonlnear. Ranked-correlaton (Spearman correlaton coeffcent) s defned as the lnear correlaton coeffcent between the ranked varables: ρ x xy y x x y y (.) where x and y are the rank of varables X and Y. Fg..3 shows the colour-coded tables of 5 ampltude-related and 7 frequency content-related parameters calculated for a set of records. In ths table, darker colours represent hgher values. The best estmator of ampltude and frequency content are located n the column under the name of SMV (sustaned maxmum velocty, the 3 rd hghest velocty cycle) and T m (mean perod), respectvely. The table s sorted by the values n the best estmator s column n ascendng order. Concentraton of darker colours n the top rows of the table ndcates that most of the parameters have hgh value when the best estmator s hgh. PGA PGV PGD a rms v rms d rms CAV ASI VSI SMA SMV EDA Aras SED I c PGV/PGA T m T c T pa T psa T psv S a (.)/S a (.) Fgure.3. Colour-coded table of normalzed ampltude- and frequency content-related parameters The proposed record refnement procedure can be summarzed n the followng steps:. The requred number of records from a gven bn, m, s set;. Ground moton sgnal propertes are calculated for the three classes of damage-related

5 parameters: a. ampltude-related, ncludng: PGA, PGV, PGD, a rms, v rms, d rms, CAV, ASI, VSI, SMA, SMV, EDA, Aras, SED, I c, etc; b. frequency content-related, ncludng: π PGV/PGA, T m, T psa, T psv, S a (.)/S a (.), etc; c. duraton-related parameters, ncludng: D 5-95, D 5-75, D Bracketed, D Unform, etc.; 3. Inter-correlaton between the parameters of each class s calculated by ether lnear correlaton coeffcents (Pearson correlaton) or, preferably, rank correlaton coeffcents (Spearman correlaton); 4. For each class of sgnal parameters, the one wth the hghest average nter-correlaton rato s defned as the best estmator for that class of damage-related parameter; 5. Devaton of the best estmator of each record from the expected value of the best estmator, ϵ, s calculated for all of the records wthn the bn: a. when the best estmator s normally dstrbuted: ϵ = (x μ X )/σ X b. when the best estmator s log-normally dstrbuted: ϵ = (ln(x ) μ lnx )/σ lnx where x s the value of the best estmator for the th record n the bn, μ X and σ X are the mean and standard devaton of the best estmator for all of the records respectvely, and μ lnx and σ lnx are the mean and standard devaton of the natural logarthm of the best estmator for all of the records respectvely;. For every record, average of ϵ s obtaned, ϵ,avg ; 7. s are ranked based on the ϵ,avg, wth the record wth the mnmum ϵ,avg beng ranked no. ; and 8. Ranked records are sorted n an ascendng order and the frst m records are selected. Typcal outcome of ths process s shown n Fg..4. In ths example, records belongng to the bn of M.5 at 5 km were refned to records. The best estmators were SMV, T ma and D Bracketed. The propertes of the selected records are crcled n the plots on the rght-hand sde of the fgure. Relatve Frequency Dstrbuton of the Best Estmator for the Ampltude-related GM Property 5% Mean =. 38% Medan =.9 COV = 4% 5% 3% % Sustaned Maxmum Velocty (SMV), cm/s Dstrbuton of the Best Estmator for the Frequency Content-related GM Property 5% Mean =.58 9% Medan =.54 COV = 49% 3% Relatve Frequency Relatve Frequency % %.5.5 Mean Perod of Acceleraton (T ma ), s Dstrbuton of the Best Estmator for the Duraton-related GM Property 5% Mean =.97 9% Medan =.5 COV = 39% 3% % % Bracketed Duraton (D Bracket ), s SMV, cm/s T ma, s D Bracket, s Scatter of Ampltude-related GM Property All GMs Selected GMs Scatter of Frequency Content-related GM Property Scatter of Duraton-related GM Property s All GMs Selected GMs All GMs Selected GMs Fgure.4. Dstrbuton of the best estmators and outcomes of the proposed refnement process.

6 3 RECORD SCALING 3. Conventonal scalng methods Ground moton records selected for tme-hstory analyses are often requred to be scaled to a predefned level of sesmc hazard or ntensty. The man reason for scalng s that the exceedance rate of the ntensty of an as-recorded ground moton (e.g., spectral acceleraton at a gven perod) does not match the target hazard level. Generally, ths can be done n tme or frequency doman. The latter approach changes the frequency content of a gven record whle the former lnearly adjusts the ampltude of the record wthout dstortng ts frequency content. A mathematcally consstent way of tme-doman scalng s to match the spectral acceleraton of a record [S a (T )] to the ordnate of the target spectrum at the fundamental perod of the buldng under study [S a (T )]. SF MFP S a ( T ) S a ( T ) ( 3.) Ths assures that the buldng wll experence an acceleraton level consstent wth the ntended level of hazard f the buldng remans essentally elastc and vbrates manly n ts frst mode. Ths may not be the case n most earthquake engneerng applcatons as ths method does not guarantee a targetconsstent level of hazard n the elongated perods as a result of yeldng or n the hgher modes of vbraton. Drawbacks of the scalng at the fundamental perod can be shown f a relatvely hgh frequency record s beng scaled for a flexble buldng or vce versa. Fgure 3. shows a comparson between the scaled spectra of such a records and a typcal target spectrum. The ground motons were selected from the same event (994 M.9 Northrdge) and have been recorded on the same type of sol profle (V s3 = and 45 m/s) at almost the same closest dstance from the fault rupture ( and 3 km). The hgh and low frequency records are from component 7 Monte Ndo Fre Staton and Playa Del Rey - Saran staton, respectvely. Hgh frequency record was matched at T =.8 s correspondng to the fundamental perod of a 9-storey bucklng-restraned braced frame (BRBF) and the low frequency one s scaled at T =. s whch s the fundamental perod of a 3 storey BRBF. In Fg. 3., the taller, more flexble buldng wll experence excessve acceleraton n ts hgher modes (e.g., T =.7 or.4 s) whereas the shorter, stffer buldng wll undergo sgnfcant acceleraton f ts fundamental perod shfts toward the longer values (e.g., T =. s). Nonlnear tme-hstory analyss shows that ths unntended level of hazard wll result n an overestmated nter-storey drft rato (4% for the flexble buldng and 3% for the stff buldng). a) 8 b) Vctora Hazard Spectrum Typcal Low Freq. 4 Typcal Hgh Freq. Spectral Acceleraton, g 3 4 Perod, s 3 4 Perod, s Fgure 3.. Excessve overshoot of nput sesmc energy when frequency content of record s neglected Ths may be avoded f the scalng s done over a range of perods centred to the fundamental perod of structures. Usually ths range has been suggested to start from.t (hgher modes) and end at.5t (elongated perod). It should be noted that the upper bound of ths perod range depends on the extent of damage, and the post-yeld stffness of the system. Elongated perod as hgh as 3.T has been reported n the lterature (NIST, ). One can take the rato of average spectral ordnates n ths range as the scale factor as suggested n (Atknson, 9, Baker, ): Spectral Velocty, cm/s 3

7 .5T SF ASE Sa ( T ) Sa ( T ) ( 3.).T.5T.T Scale factor also can be calculated by mnmzng the squared error between the target spectrum and the scaled spectrum of the record n the mentoned range [(S a (T ) SF S a (T )) ]. Ths scale factor can be obtaned by forcng the frst dervate of the squared error to be zero:.5t.5t SF MSE [ Sa ( T ) Sa ( T )] [ Sa ( T )] ( 3.3).T.T All these types of perod-dependent scalng need a predefned range of perods and none of them can completely avod the excessve overestmaton of the hazard wthn ths range. The fundamental perod s also subjected to the modellng assumptons. In addton, n the process of hazard calculaton all these perods are treated ndependently from each other. In other words, the probablty of exceedng at all these perods s not known and may not be possble to calculate. Recent studes proposed usng a condtoned mean of the scaled spectra to overcome ths problem (Baker, ). In ths method ground moton predcton equaton for a par of domnant M and R s converted to a condtonal mean spectrum based on the correlaton between spectral acceleraton ratos before and after fundamental perod. In fact, ths method replaces the unform hazard spectrum wth a condtoned spectrum whch typcally has less ntensty n perod range lower and hgher than the fundamental perod. Ths new spectrum s then used to fnd a set of records whch medan of ther scaled spectra s close to the condtoned spectrum. Ths method s meant to take nto account the more realstc spectral shape when records are beng scaled at the fundamental perod. 3. Least Movng Average scalng method Alternatvely, record scalng can be performed ndependently from the dynamc characterstcs of the structures under study. Ths means that a unque scale factor s used for all types of structures regardless of ther fundamental, hgher modes, and elongated perods. In fact, early generaton of scalng methods mostly reled on the normalzaton of record ampltudes by means of a specfc level of tme-doman ntensty measures such as PGA or PGV (Shome and Cornell, 998, Kurama and Farrow, 3). However, these ntensty measures can not be well-correlated wth expected damage n all types of structures. As a result, damage predcton s based to the measure of ntensty used for the record normalzaton. In addton, ste target desgn spectrum (e.g., unform hazard spectrum (UHS)) can be completely neglected when these methods are used. Instead of record normalzaton or matchng at the fundamental perod (or a range), t s suggested to scale at a perod range over whch the spectral shape of record s smlar to the target spectrum. Past studes have shown that by ths method, records are matched to the target n a frequency band-wdth where most of sesmc energy s concentrated. If the selected records cover a suffcent range of frequences (records wth dfferent frequency content), ths scalng method leads to spectral shape-consstent results. The method proposed heren s called Least Movng Average because t scans all the perod ranges of the spectrum and fnds a narrow perod band n whch the average of error between the target and record spectra s mnmum. The proposed ground moton scalng approach s summarzed n the followng steps:. The 5% damped target acceleraton spectrum (e.g., UHS) s defned for perod ponts, startng from. to second (perod ntervals expand exponentally);. The 5% damped acceleraton spectrum of record s calculated for all perod ponts, T ; 3. Spectral error ratos,.e., ratos between the target spectrum and the spectrum of the orgnal records, S ( T ) S ( T ), are computed for all perods; a a 4. Mnmum and maxmum nclusve averagng perods, T mn and T max, are set (e.g.,. and s), 5. Averagng band s defned, ether as a fxed or a varable band:

8 a. fxed band: averagng band wdth s constant for all the movng perods (e.g., ΔT =.5 s); b. varable band: averagng band wdth ncreases as the movng perod (T ) moves towards longer perods; for every movng perod, averagng band starts at αt and ends at βt (α =.5 and β =.5 are suggested);. The frst and the last movng perods, T and T end, are computed: a. for fxed band averagng: T = T mn + ΔT and T end = T max ΔT, b. for varable band averagng: T = T mn / α and T end = T max / β, 7. The type of average s selected; t can be ether: a. arthmetc movng average: S ( T ) S ( T a a ) ; n T b. geometrc movng average: exp ln Sa ( T ) Sa ( T ) ; nt 8. The scale factor s the mnmum of the movng averages. Results from the proposed method for typcal hgh and low frequency records are shown n Fg. 3.: hgh frequency records are matched to target at perods close to the mean perod of the sgnal, (T m ), whereas low frequency records are matched n the low frequency regon of the target spectrum. Spectral Acceleraton, S a Perod, s Unscaled Smoothed Spec Scaled Scalng Perod Mean Perod Spectral Acceleraton, S a Perod, s Unscaled Smoothed Spec Scaled Scalng Perod Mean Perod Fgure 3.. Scalng by Least Movng Average for typcal: a) hgh frequency; b) low frequency record 4 COMPARATIVE STUDY The effectveness of the proposed method was examned usng nonlnear tme analyses performed on a seres of nelastc sngle-degree-of-freedom (SDOF) systems. A seres of dedcated computer programs for record selecton and refnement, record scalng, and SDOF nelastc tme-hstory analyss were developed. Ths computer code was used to evaluate the possble mpacts of dfferent domnantevent scenaros, number of records, and record scalng methods on two demand ndces: ) peak ductlty; and ) cumulatve ductlty. Four domnant-event scenaros (S to S4), three number of records (, and 4 records), and three record scalng methods were nvestgated. 4. scalng Ground moton records were scaled usng three methods: ) matched at fundamental perod (Eqn. 3.); ) least squared error (Eqn. 3.3); and 3) least movng average. The average of acceleraton spectra s found to be nsenstve to the domnant-event scenaros and the number of records n Fg. 4.. The same behavour was observed for the mean plus one standard devaton of the acceleraton spectra and the maxmum of the acceleraton spectra was only slghtly affected by the domnant-event scenaro n the short perod range. These results ndcate that the proposed selecton and scalng method reduces the undesrable varatons n nput sesmc energy that s generally observed when changng the domnant events or the number of records.

9 Mean of Scaled Spectra for Scenaro # Mean of Scaled Spectra for Scenaro # Spectral Acceleraton, g Spectral Acceleraton, g.5 Vctora Desgn Spectrum Refned to GMs Refned to GMs Refned to 4 GMs 3 4 Perod, s Mean of Scaled Spectra for Scenaro # Vctora Desgn Spectrum Refned to GMs Refned to GMs Refned to 4 GMs 3 4 Perod, s Spectral Acceleraton, g Spectral Acceleraton, g.5 Vctora Desgn Spectrum Refned to GMs Refned to GMs Refned to 4 GMs 3 4 Perod, s Mean of Scaled Spectra for Scenaro # 4.5 Vctora Desgn Spectrum Refned to GMs Refned to 8 GMs Refned to 3 GMs 3 4 Perod, s Peak Ductlty, max Fgure 4.. Effects of dfferent scenaros and number of selected records on the average of scaled spectra Statstcs of Damage, scalng method: Not-scaled 8 a) b) Mean + Standard Devaton Mean Domnant-Event Scenaro Statstcs of Damage, scalng method: Mnmzed Square Error c) 8 d) Peak Ductlty, max 4 Halved () Basc () Doubled (4) No. of records 3 4 Domnant-Event Scenaro Fgure 4.. Statstcs of peak ductlty computed for dfferent selecton scenaros and scalng methods 4. SDOF analyss and results Statstcs of Damage, scalng method: Match at Fundamental Perod Domnant-Event Scenaro Statstcs of Damage, scalng method: Least Movng Average 8 The records selected for the prevously dscussed hazard scenaros were refned, scaled and appled to a seres of nelastc SDOFs desgned for % n 5 years sesmc hazard n Vctora, BC. The SDOFs had perods of.5,.,.5 and. s and were desgned wth a force reducton factor of 4.8. Inelastcty was smulated usng Bouc-Wen plastcty model (Ikhouane et al., 7). The model can reproduce smooth hysteress response ncludng Bauschnger effect, whch s approprate for modellng bucklng-restraned braces exhbtng stable, full, and symmetrc hysteress response wthout stffness and strength degradaton. Bouc-Wen model parameters were calbrated throughout optmzaton study conducted on the results of a full-scale bucklng-restraned brace test descrbed n (Tremblay et al., ). Vscous dampng rato was set to 3% of the crtcal dampng. In total, 3 Peak Ductlty, max Peak Ductlty, max Domnant-Event Scenaro

10 nonlnear tme-hstory cases were carred out. Fgure 4. shows the mean and mean plus one standard devaton of the peak ductlty of the analyzed SDOFs for dfferent number of records, scalng methods, and domnant-event scenaros. It can be seen that the mean of peak ductlty does not change when the basc number of records s doubled or halved. Mean s also stable regardless of the selected domnant-event scenaro. The least movng average scalng method (Fg. 4.d) shows the most robust statstcs. Varablty s lmted (COV 5%) and nsenstve to the domnant-event scenaro and the number of record used for analyss. The same trend was observed for the cumulatve ductlty. 5 CONCLUSIONS A practcal and statstcally robust ground moton selecton and scalng method s presented and ts effcency s qualfed throughout nonlnear tme-hstory analyses. The unntended consequences of the conventonal ground moton selecton and scalng methods are shown. Step-by-step nstructons for fndng the domnant events (from hazard deaggregaton data), refnement of the ntally selected records, and record scalng are provded. Spectral calculatons and tme-hstory analyses showed that the proposed method leads to stable expected values of the demand wth a lmted varablty. ACKNOWLEDGMENT The fnancal support provded by the Natural Scences and Engneerng Research Councl of Canada (NSERC) for the Canadan Sesmc Research Network (CSRN) s acknowledged. Scholarshp awarded to the frst author by Structural Steel Educaton Foundaton (SSEF) s also acknowledged. REFERENCES Atknson, G. (9). Earthquake tme hstores compatble wth the 5 Natonal buldng code of Canada unform hazard spectrum. Canadan Journal of Cvl Engneerng, 3:, 99-. Baker, J. W. (). Condtonal Mean Spectrum: Tool for Ground-Moton Selecton. Journal of Structural Engneerng, 37:3, Bazzurro, P. and Cornell, C. A. (999). Dsaggregaton of sesmc hazard. Bulletn of the Sesmologcal Socety of Amerca, 89:, 5-5. Halchuk, S., Adams, J. and Angln, F. (7). Revsed Deaggregaton of Sesmc Hazard for Selected Canadan Ctes. The Nnth Canadan Conference on Earthquake Engneerng. Hancock, J. and Bommer, J. J. (). A State-of-Knowledge Revew of the Influence of Strong-Moton Duraton on Structural Damage. Earthquake Spectra, :3, Haselton, C. B. 9. PEER 9/ - Evaluaton of Ground Moton Selecton and Modfcaton Methods: Predctng Medan Interstory Drft Response of Buldngs. Pacfc Earthquake Engneerng Research Center. Ikhouane, F., Mañosa, V. and Rodellar, J. (7). Dynamc propertes of the hysteretc Bouc-Wen model. Systems & Control Letters, 5:3, Kramer, S. L. (99). Geotechncal earthquake engneerng, Prentce Hall, Upper Saddle Rver, N.J. Kumar, M., Castro, J. M., Stafford, P. J. and Elghazoul, A. Y. (). Influence of the mean perod of ground moton on the nelastc dynamc response of sngle and mult degree of freedom systems. Earthquake Engneerng & Structural Dynamcs, 4:3, Kurama, Y. C. and Farrow, K. T. (3). Ground moton scalng methods for dfferent ste condtons and structure characterstcs. Earthquake Engneerng & Structural Dynamcs, 3:5, NIST. Selectng and Scalng Earthquake Ground Motons for Performng Response-Hstory Analyss. NEHRP Consultants Jont Venture. PEER. (). PEER Ground Moton Database - Beta [Onlne]. Pacfc Earthquake Engneerng Center. Avalable: [Accessed 7/3/]. Rathje, E. (4). Emprcal Relatonshps for Frequency Content Parameters of Earthquake Ground Motons. Earthquake Spectra, :, 9. Shome, N. and Cornell, A. C. (998). Normalzaton and Scalng Accelerograms for Nonlnear Structural Analyss. th U.S. Natonal Conference on Earthquake Engneerng, -. Tremblay, R., Bolduc, P., Nevlle, R. and DeVall, R. (). Sesmc testng and performance of bucklngrestraned bracng systems. Canadan Journal of Cvl Engneerng, 33:, Ye, L., Ma, Q., Mao, Z., Guan, H. and Zhuge, Y. (). Numercal and comparatve study of earthquake ntensty ndces n sesmc analyss. The Structural Desgn of Tall and Specal Buldngs.