ASSESSING SPECTRAL SHAPE-BASED INTENSITY MEASURES FOR SIMPLIFIED FRAGILITY ANALYSIS OF MID-RISE REINFORCED CONCRETE BUILDINGS

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1 ECED 205 Conferene: Erthquke Risk nd Engineering towrds Resilient World 9-0 July 205, Cmbridge UK AEING PECTRAL HAPE-BAED INTENITY MEAURE FOR IMPLIFIED FRAGILITY ANALYI OF MID-RIE REINFORCED CONCRETE BUILDING tylinos MINA Crmine GALAO 2 nd Tizin ROETTO 3 Abstrt: The objetive of this study is to identify n optiml intensity mesure (IM) for onditioning probbilisti seismi demnds of se-study reinfored onrete (RC) frme buildings, representtive of mid-rise RC building lsses in the Mediterrnen region. The predition is performed vi sttistil reltionship between multiple IMs (prtiulrly dvned slr prmeters ounting for spetrl shpe over rnge of periods) nd vrious displement-bsed engineering demnd prmeters (EDPs). uh sttistil reltionships re built on dt obtined from nlysis of the frmes subjeted to over nine hundred ground motion reords by employing n innovtive pity spetrum method, introdued in the pper, whih uses inelsti response spetr derived from tul erthquke elerogrms to estimte seismi demnd nd derive frgility urves. The outomes of the present work re in good greement with previous investigtions onduted by other reserhers on seleting optiml IMs for prediting struturl response by using full nonliner dynmi nlyses for different struturl typologies. Introdution Reent erthqukes in Mule, Chile (200), Tohoku, Jpn (20) nd Christhurh, New Zelnd (20) hve resulted in extensive onentrtion of dmge nd signifint losses in existing, low seismi designed, reinfored onrete (RC) struture nd prtiulrly mid-rise buildings for both residentil nd ommeril oupny. The limited vilbility of historil dmge dt ssoited with most seismi prone res mkes the derivtion of nlytil frgility funtions (D Ayl et l. 204) n essentil omponent of seismi risk ssessment. In prtiulr, nonliner dynmi nlysis (NLDA) represents the tool for ssessing inelsti struturl response with reltively low unertinty, urtely pturing filure modes. Aprt from the undoubted dvntges of using NLDA, the required omputtionl resoures nd high ost (in terms of time onsumption), preludes this pproh when nlysing lrge popultions or portfolios of buildings, for exmple for tstrophe modeling purposes. In ontrst, severl vrints of pity spetrum methods bsed on inrementl dynmi nlysis (IDA) nd stti push-over nlyses hve been proposed. These pity ssessment methods, suh s the N2 method (Fjfr, 2000), nd the reently proposed FRACA (introdued in the following setion) mong others, often rely on simplifying ssumptions in ssessing both the struturl pity nd the seismi demnd. In prtiulr, FRACA uses suites of sled nd/or unsled ground motion reords (simply GMs hereinfter) nd delivers immeditely the frgility funtion of the onsidered struture. Nonetheless, the effet of seleting nd implementing different ombintions of intensity mesure (IMs) nd engineering demnd prmeters (EDPs) in simplified frgility nlysis hs not been ppropritely investigted. Thus, one fes the question of how suitble the dopted IM is for representing GM unertinty. To this im, the development of frgility funtions requires the hoie of n IM whih is suitble to predit the response of the system with the smllest stter ( effiieny ) nd providing signifint mount of informtion ( suffiieny ) to predit the responses quntities involved in the performne objetives (e.g., Jlyer et l., 202). In ddition, mny reserhers hve investigted other IM EngD tudent, University College London, London, UK, s.mins@ul..uk 2 Leturer, University College London, London, UK,.glsso@ul..uk 3 Professor, University College London, London, UK, t.rossetto@ul..uk

2 seletion riteri, relted for exmple to hzrd omputbility, profiieny, nd prtility. This pper ims to ) introdue FRACA, n effetive tool for simplified seismi frgility nlysis nd, 2) shed light in ompring different IM/EDP ombintions for the frgility nlysis of mid-rise RC buildings by FRACA. FRACA In the urrent study, the simplified pity ssessment methodology, nd relted omputer odes, known s FRACA (FRAgility through CApity petrum ssessment) is implemented in order to determine the performne points (PPs) of se-study strutures for different GM inputs. FRACA is bsed on the displement-bsed proedure, originlly proposed by Rossetto nd Elnshi (2005). The step by step proedure followed by the methodology is summrized below (Figure ):. Conversion of pushover urve (fore-displement spe) for the onsidered struture to n equivlent single degree of freedom (DoF) -bsed pity urve (elertiondisplement response spetrum, ADR formt) tking into onsidertion the floor msses nd the inter-story displements (Figure ). 2. Ideliztion of the pity urve. The user n hoose different idelized models, yielding point, ultimte point nd hrdening options (Rossetto et l., 204 nd Figure ). 3. Disretiztion of the pity urve to series of heking points ssoited with vrious pre- nd post-yield periods. The number of pre- nd post-periods n be seleted by the user (Figure b). 4. Computtion of elsti response spetrum from the inputted GMs. The elsti demnd is lulted for periods up to the yielding period T y (Figure ). 5. Clultion of the inelsti demnd of the equivlent DoF for the seleted post-yield periods (Figure d). 6. Determintion of PP t the intersetion of the pity with the demnd urve (Figure d). The orresponding EDP vlues re then obtined from the bk-lultion of PP to the fore-displement formt. It is noteworthy to mention tht unlike other pity spetrum methods, FRACA does not rely on redution ftors or indies to determine the inelsti spetrum from the elsti one. Insted, it rries out, for eh trget dutility nd period, simplified dynmi nlysis on the idelized nonliner DoF model orresponding to the pity urve. This feture lso hs the dvntge of permitting the use of vrious GM reords tht generte unsmoothed spetr s opposed to stndrdized design spetr. Therefore, the reord-to-reord vribility n be diretly introdued nd the resulting loud of performne points leds to frgility urves tht ount for the nturl vribility in the seismi demnd. In prtiulr, the omputed EDPs orresponding to different sled/unsled seismi demnd inputs, in onjuntion with user defined dmge sttes re used for the genertion of nlytil frgility urves. This method is reommended in the reently published GEM Guidelines for Anlytil Vulnerbility Estimtion, (D Ayl et l. 204), where further detils re lso provided. Considered intensity mesures In order to quntify the GM fetures tht influene the nonliner response of the strutures of interest, severl types of IMs re tested. Conventionl IMs nmely pek ground elertion (PGA), pek ground veloity (PGV), pek ground displement (PGD), nd spetrl (pseudo) elertion t the initil fundmentl period (for dmping rtio of 5%), re the most ommonly used IMs nd re onsidered here. In generl, PGA nd T poorly predit the struturl response of mid- to high-rise moment resisting frmes (MRFs), lthough the ltter IM suffiiently ptures the elsti behviour of first-mode dominted DoF systems, espeilly in the se of low to moderte fundmentl periods. However, the behviour of 2

3 highly nonliner strutures or strutures dominted by higher-mode periods (less thn T ) re not very well represented by utilizing T due to the lk of informtion on the spetrl shpe provided by this IM. Therefore, it is beoming essentil to implement dvned IMs tht ount for the elongted periods nd/or onsider nonliner demnd dependent struturl prmeters. Figure. Min steps of FRACA for the derivtion of the Performne Point using triliner ideliztion model. More speifilly, the first dvned slr IM onsidered is (proposed by Cordov et l., 2000), whih utilizes spetrl shpe informtion (period elongtion), nd is expressed s: T T T where nd α re oeffiients ssumed to be = 2 nd α = 0.5 respetively, bsed on the librtion rried out by the uthors in the originl study. Bojórquez nd Iervolino (20) lso proposed the dvned slr IM,, whih is bsed on T nd the prmeter N p, defined s: IN p T N p where α is prmeter to be librted nd N p is defined s: I N p () (2) N p, vg T,..., T T N N i T T i N (3) 3

4 where TN orresponds to the mximum period of interest nd lys within rnge of 2 nd 2.5T, s suggested by the uthors. In this study T N vlue is obtined diretly from the FRACA nlysis (Cse study setion). Ten different vlues, from 0. to, for the - prmeter re onsidered here in order to identify the optiml vlue for, to follow. Cse study strutures Two regulr RC 4-storey, 4-by bre frmes, representing different vulnerbility lsses bsed on the design odes used for their onstrution, re seleted to illustrte the evlution of the studied IMs. peifilly, the two seleted se-study strutures shre the sme geometry (by widths nd story heights) but hrterized by different mteril properties, elements geometry nd reinforement detiling. The first frme is designed to only sustin grvity lods following the Royl Deree n of 939 tht regulted the design of RC buildings in Itly up to 97, herefter Pre-Code building; the seond frme is designed ording to the ltest Itlin seismi ode (or NIBC08; C.LL.PP. 2008), following the High Dutility Clss (DCH) rules, herefter peil-code building. Further informtion regrding the design of those two buildings is vilble in De Lu et l. (2009). Inter-story heights, spn of eh by nd ross-setions dimensions for the two se-study building re reported in Figure 2. The onsidered frmes re regulr (both in pln nd in elevtion); the dimensions in brkets refer to the Pre-Code building (ll bems hve the sme rosssetions in both ses). Figure 2. Elevtion dimensions nd members ross-setions of the se-study buildings. The two se-study frmes re modeled using the eismotrut finite element softwre ( two seprte sets of onventionl stti PO methods re seleted for the nlysis of the bovementioned frmes. Inrementl lterl lods re pplied in different lod phses t the side nodes t eh floor level. The lterl lod inrements re distributed uniformly or following n inverse tringulr pttern (uniform PO nd tringulr PO), orresponding to floor msses nd story heights respetively. Tble summrizes the dynmi informtion ssoited with eh of the tested buildings required to ompute different IMs, nmely struturl nlysis method, fundmentl period T (bsed on eismostrut nd FRACA estimtions, denoted s T *) s well s elongted period T N. T * is derived from the stiffness of the idelized pity urve used in FRACA, while the 4

5 elongted period T N orresponds to the ultimte point of the pity urve ssoited to eh building-po nlysis method. Figures 3 (left pnel) presents the stti PO urves (tringulr PO for illustrtive purposes) for the se-study buildings. The urves re reported in terms of top entre of mss displement divided by the totl height of the struture (i.e., the roof drift rtio, RDR) long the horizontl xis of the digrm nd bse sher divided by the building seismi weight (i.e., the bse sher oeffiient) long the vertil xis. It is noted tht highly nonliner behviour is observed over ertin RDR thresholds for the studied strutures. Figure 3 (right pnel) shows the performne points in the ADR spe omputed by FRACA (n Elsti Perfetly Plsti ideliztion model is employed) by using the GMs reords desribed in the following setion. Building Pre-Code peil-code Tble. Dynmi properties for eh se-study struture. T PO T * (s) (s) T N (s) TRI UNI TRI UNI Figure 3. tti PO urves for the se-study buildings (left) nd performne points generted by FRACA (right). Ground motion dtbse The IMBAD dtbse (eleted Input Motions for displement-bsed Assessment nd Design; merzini et l., 204), used here, onsists of 467 reords, eh inluding the two horizontl (X-Y) nd one vertil (Z) omponents (40 reordings), generted by 30 seismi events (inluding minshoks nd ftershoks) tht ourred worldwide. These elerogrms re ssembled from vrious ground motion dtbses derived for different regions of the world following the seletion riteri ddressed below:. hllow rustl erthqukes worldwide with moment mgnitude (M) rnging from 5 to 7.3 nd epientrl distne R 35 km. This ensures to provide strong ground motion reords of engineering relevne for most of the design onditions of interest tht n be used without introduing lrge sling ftors. 2. Good qulity t long periods, so tht only reords for whih the high-pss ut-off frequeny used by the dt provider is below 0.5 Hz re onsidered. Therefore, most reords re from digitl instruments (bout 80%), while from nlogue instruments only those reords with good signl to noise rtios t long periods, typilly from lrge mgnitude erthqukes, re retined. 3. Avilbility of site lss informtion bsed on quntittive riteri. 5

6 Methodology In the present study, sttistil regression tehniques re implemented to determine the IM tht better predits eh onsidered EDPs. Hene, to determine the sttistil properties of the loud response, the liner lest squres is pplied on EDPs versus IMs pirs for the suite of GMs (unsled) in order to estimte the onditionl men nd stndrd devition of EDP given IM. The simple power-lw model in Eq. (4) is used here: b EDP IM (4) where nd b re the prmeters of the regression. The regression s stndrd devition (s) is ssumed to be onstnt with respet to IM over the rnge of IMs in the loud. The powerlw model illustrte in Eq. (4) n be simply re-written s shown below in Eq. (5), s liner expression of the nturl logrithm of the EDP nd the nturl logrithm of the IM: ln EDP ln blnim (5) The use of logrithmi trnsformtion indites tht the EDPs re ssumed to be onditionlly lognormlly distributed (onditionl upon the vlues of the IMs); this is ommon ssumption tht hs been onfirmed s resonble in mny pst studies. In the urrent study, the fous is lid on deformtion-bsed EDPs, whih re listed below:. pek (over time) inter-story drift rtio, s the lrgest differene between the lterl displements of two djent floors, divided by the height of the story (denoted s IDR i for story i-th); 2. mximum (over ll stories) pek interstorey drift rtio (denoted s MIDR); 3. rtio of the pek lterl roof displement to the building height (i.e., RDR). The bovementioned hve demonstrted to be well orrelted to both struturl nd nonstruturl dmge. Thus, they n be used to ompute lol or globl instbility of RC MRFs. Optiml IM seletion riteri As disussed in the introdution, the seleted IM hs signifint effet on the unertinty ssoited with the resultnt frgility urves. Therefore, the seletion of optiml IMs is of high importne within the entire risk ssessment proess nd onsequently, rised the need for defining quntittive nd qulittive seletion riteri in order to filitte this seletion. The most ommonly used riteri for the determintion of n optiml IM used in this study re briefly disussed below:. Effiieny: Effiieny is the most ommonly used quntittive riterion for the determintion of optiml IMs, nd is relted to the vrition of demnd estimtes for different vlues of the onsidered IM (e.g., Giovenle et l., 2004). peifilly, more effiient IMs result in redued dispersion of the medin EDP estimtes onditionl to given IM. As result, less nlysis runs re required to nrrow down the onfidene intervls. An effiient IM is the one tht provides the smllest vlue of the stndrd devition s from the regression nlysis. 2. uffiieny: An innovtive definition of suffiieny, in prtiulr reltive suffiieny, ws reently proposed by Jlyer et l. (202). In prtiulr, to investigte the reltive suffiieny of seond IM, i.e. IM 2, with respet to first one, i.e. IM, quntittive mesure my be employed. This mesure is derived on the bsis of informtion theory onepts nd quntifies the suitbility of one IM reltive to nother. peifilly, the reltive suffiieny mesure, denoted herein s I(EDP IM 2 IM ), is equl to the verge differene between the informtion gined bout the performne vrible EDP given IM nd IM 2 nd tht gined given IM only. Therefore, for eh loud nlysis performed, one n estimte this mesure using the equtions provided in Jlyer et l. (202). The 6

7 reltive suffiieny mesure is expressed in units of bits of informtion. If the reltive suffiieny mesure, I(EDP IM 2 IM ), is zero, this indites tht on verge the two IMs provide the sme mount of informtion bout the EDP. In other words, they re eqully suffiient. If the reltive suffiieny mesure is positive, this mens tht on verge IM 2 provides more informtion thn IM bout the EDP, so IM 2 is more suffiient thn IM. imilrly, if the reltive suffiieny mesure is negtive, IM 2 provides on verge less informtion thn IM nd so IM 2 is less suffiient thn IM. 3. Hzrd omputbility: Aording to the definition given by Giovenle et l. (2004), hzrd omputbility desribes the proess to obtin the erthquke hzrd for given IM. Numerous hzrd mps nd Ground Motion Predition Equtions (GMPE) exist for more ommonly used IMs, nmely PGA nd spetrl ordintes t given periods (representing sometimes restrited rnge of possible disrete periods), mking these IMs more fvourble from the hzrd omputbility perspetive; wheres, other IMs my require interpoltion or supplementry struturl or dynmi informtion, mking the omputtion of the hzrd more time-onsuming proess. Results nd disussion For ske of brevity, only the results for the se of tringulr PO lods nd MIDR re presented; the im is to show the proess to determine the optiml IM for the frgility nlysis of the prtiulr building lss. However, the sme methodology is pplied to ll the se-study buildings nd results of the nlysis, essentilly onsistent ross ll the sestudy buildings nd EDPs, re reported in Mins (204). As shown in Figure 3 (left pnel) the seleted struture behves highly nonlinerly over ertin RDR thresholds. As onsequene, the tul number of GM tht pushed the frme into the nonliner rnge is reltively smll but still sttistilly signifint. Therefore, the regression prmeters, b, s nd R 2 for eh EDP nd eh IM re estimted only onsidering the GM reords resulting in tul nonliner response. Figure 4 (left pnel) shows the obtined s vlues orresponding to MIDR vs IMs regression for both se-study building. With regrd to effiieny, the visul inspetion of Figure 4 onfirm tht deformtion-bsed EDPs pper to be better orrelted with the spetrl shpe prmeter performs I (the optiml -vlue n be identified from the figure); while N p better thn the other onventionl IMs nd losely mthes the estimtions. It is lso onfirmed tht PGA, s well s PGD, re poor preditors of the nonliner struturl response of mid- to high-rise moment resisting frmes (highest vlues of s). For the peil-code building, the spetrl shpe prmeter provide the highest vlues of s ompring to the other dvned IMs, but still outperforms ll onventionl slr IMs. A potentil improvement my be obtined by librting nd (in the se of ) for the speifi se-study strutures rther thn using the vlues suggested by other reserhers for different se-study strutures. The reltive suffiieny mesure for MIDR nd the ndidte IMs is shown in Figure 4 (right pnel) for both buildings. The referene IM is the one orresponding to the lowest s vlue from the regression (left pnel). The results in Figure 4 (right pnel) onfirm the results in terms of effiieny (left pnel). The IMs resulting in the highest effiieny re lso hrterized by the highest reltive suffiieny. Lst riterion for the determintion of n optiml intensity mesure is the hzrd omputbility. For the urrent riterion, onventionl IMs hve signifint dvntge over the dvned ones, s numerous GMPEs nd hzrd mps exist prtiulrly for PGA, PGV nd PGD, nd some spetrl ordintes for speifi rnges of periods. On the other hnd, it is still possible to derive GMPE for spetrl elertion bsed dvned IMs, s shown in Cordov et l. (2000) nd Bojórquez nd Iervolino (20). T 7

8 Figure 4. tndrd devition (dispersion) of residuls of MIRD for the onsidered IMs nd eh sestudy building (left); reltive suffiieny mesure for lterntive IMs with respet to the IM with the lowest dispersion for eh se-study building (right). Conlusion This pper summrizes the results of n investigtion iming t identifying the GM prmeters tht re better orrelted with displement-bsed response prmeters for simplified frgility nlysis of mid-rise RC buildings. The outomes of the present work re onsistent with previous investigtions onduted by the uthors nd other reserhers on seleting optiml IMs (slr or vetor-vlued) for prediting struturl response by using NLDA. In generl, the dvned IMs, properly librted for the speifi building typology, tht ount for the period elongtion nd demnd dependent struturl prmeters, omfortbly stisfy ll the seletion riteri, nd represent then optiml IMs for simplified frgility nlysis of mid-rise RC buildings REFERENCE Bojórquez E., nd Iervolino I. (20) petrl shpe proxies nd nonliner struturl response. oil Dynmis nd Erthquke Engineering, 3(7), C.LL.PP. (2008) DM 4 Gennio, Norme tenihe per le ostruzioni. Gzzett Uffiile dell Repubbli Itlin 29 (in Itlin). Cordov PP, Deierlein GG, Mehnny nd Cornell CA (2000) Development of two-prmeter seismi intensity mesure nd probbilisti ssessment proedure. Proeedings of the 2nd U Jpn Workshop on Performne-Bsed Erthquke Engineering for Reinfored Conrete Building trutures, pporo, Jpn, 3 eptember. D Ayl D, Meslem A, Vmvtsikos D, Porter K, Rossetto T, Crowley H nd ilv V (204) Guidelines for Anlytil Vulnerbility Assessment. Vulnerbility Globl Component projet. De Lu F, Elefnte L, Iervolino I nd Verderme GM (2009) trutture esistenti e di nuov progettzione: omportmento sismio onfront. tti di XIII Convegno Nzionle "L'Ingegneri ismi in Itli", Bologn, Itly (in Itlin). Fjfr P (999) Cpity spetrum method bsed on inelsti demnd spetr. Erthquke Engineering nd truturl Dynmis, 28(9), Giovenle P, Cornell CA nd Estev L (2004) Compring the dequy of lterntive ground motion intensity mesures for the estimtion of struturl responses. Erthquke Engineering nd truturl Dynmis, 33(8), Jlyer F, Bek JL nd Zrein F (202) Anlyzing the uffiieny of Alterntive lr nd Vetor Intensity Mesures of Ground hking Bsed on Informtion Theory. ACE Journl of Engineering Mehnis, 38(3),

9 Mins (204) eleting optiml intensity mesures for simplified frgility nlysis of mid-rise RC buildings. MRes Report, University College London, UK. Rossetto T nd Elnshi A (2005) A new nlytil proedure for the derivtion of displement-bsed vulnerbility urves for popultions of RC strutures. Engineering trutures, 27(3), Rossetto T, Gehl P, Mins, Nssirpour, Mbug J, Duffour P nd Dougls J (204) ensitivity nlysis of different pity pprohes to ssumptions in the modeling, pity nd demnd representtions. Proeedings of ACE-ICVRAM-IUMA onferene, Liverpool, UK, 3-6 July merzini C, Glsso C, Iervolino I nd Polui R (204) Ground motion reord seletion bsed on brodbnd spetrl omptibility. Erthquke petr, 30(4),