AN ENERGY-BASED SEISMIC RESPONSE EVALUATION OF SIMPLE STRUCTURAL SYSTEMS WITH SIMULATED GROUND MOTIONS

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1 4th ntrnational Confrnc on Earthquak Enginring and Sismology Octobr 217 ANADOLU UNVERSTY Eskishir/TURKEY AN ENERGY-BASED SESMC RESPONSE EVALUATON OF SMPLE STRUCTURAL SYSTEMS WTH SMULATED GROUND MOTONS S. Karimzadh 1, V. Ozsarac 2, A. Askan 3, and M.A. Erbrik 3 1 Post-Doctoral Rsarchr, Civil Eng. Dpartmnt, Middl East Tchnical Univrsity, Ankara, Turky ABSTRACT: 2 Graduat Studnt, Civil Eng. Dpartmnt, Middl East Tchnical Univrsity, Ankara, Turky 3 Prof., Civil Eng. Dpartmnt, Middl East Tchnical Univrsity, Ankara, Turky shaghkn@gmail.com n rcnt yars, thr has bn a strong intrst on nrgy-basd dsign and assssmnt mthods for structural systms. Th undrlying rsarch has bn mostly prformd using ral ground motion rcords takn from xisting arthquaks worldwid. Rsults may involv bias du to lack of homognity of th availabl ground motion datast in trms of magnituds, sourc to sit distancs or soil conditions. n this study, a larg st of ground motion rcords ar simulatd within a paramtric xrcis to invstigat th ffct of diffrnt intnsity masurs on th nrgy-basd rspons of simpl SDOF structurs. To gnrat simulatd rcords, stochastic finit-fault mthodology which is ffctiv in simulating a wid rang of frquncis including thos that influnc th built nvironmnt is usd. Th simulations ar prformd on activ faults around Duzc city cntr locatd on th wstrn sgmnts of North Anatolian Fault zon in Turky. Th simulatd rcords covr a wid rang of momnt magnitud, sourc-to-sit distancs and soil conditions. To assss th rspons statistics on SDOF modls, tim history analyss with simulatd rcords ar prformd. nput nrgy, damping nrgy and hystrtic nrgy ar considrd as th main output paramtrs. Th rsults of this study rval that nrgy is a mor stabl paramtr than th othr rspons paramtrs such as displacmnt and forc. Howvr, it is important to dissipat th stimatd input nrgy through damping and inlastic action. Finally, it is blivd that conducting paramtric sismic analysis basd on simulatd rcords yild ralistic rsults sinc ths rcords provid variability in sismic dmand. KEYWORDS: Enrgy-basd rspons, singl-dgr-of-frdom modls, tim history analysis, stochastic finitfault mthod, simulatd ground motions. 1. NTRODUCTON n arthquak nginring, nrgy-basd analysis and dsign approachs hav bn studid sinc th pionring work of Housnr (1956). That study gav inspiration to many rsarchrs, who mad significant contributions to this rsarch ara (Zahrah and Hall, 1984; Akiyama, 1985; McCab and Hall, 1989; Uang and Brtro, 199) dvlopd th fundamntal framwork of nrgy-basd mthodology. n th last two dcads, many rsarchrs studid th charactristics of nrgy rlatd paramtrs in a dtaild mannr (Dcanini and Mollaioli, 1998; Chai and Fajfar, 2; Bnavnt-Climnt t al., 22; Surahman, 27; Amiri t al., 28). Th rlatd rsarch was oftn carrid out by using actual ground motion rcords takn from many diffrnt arthquaks all ovr th world. Howvr, it is gnrally not possibl to construct homognous ground motion databass with wll-distributd ground motion paramtrs. An altrnativ approach is th us of simulatd ground motion rcord sts for obtaining nrgy rspons functions within th full rang of sismic intnsity paramtrs. Th objctiv of this study is to invstigat th influnc of diffrnt intnsity masurs on th nrgy-basd rspons of singl-dgr-of-frdom (SDOF) systms. For this purpos, a larg st of simulatd ground motion

2 4th ntrnational Confrnc on Earthquak Enginring and Sismology Octobr 217 ANADOLU UNVERSTY Eskishir/TURKEY rcords ar mployd through a paramtric study. Th simulatd ground motion rcords ar obtaind using th stochastic finit-fault mthodology, which is fficint in simulating th frquncis of nginring intrst (Motazdian and Atkinson, 25). A st of ground motions is constructd through th simulations of potntial vnts within a slctd momnt magnitud rang, diffrnt sourc-to-sit distancs and soil conditions. Th simulations ar prformd on an activ fault around Duzc city cntr locatd on th Wstrn sctions of North Anatolian Fault zon in Turky. Thn, tim history analyss on SDOF systms ar conductd with simulatd rcords to obtain th rspons statistics. Th output paramtrs ar input nrgy, hystrtic nrgy and damping nrgy. 2. ENERGY EQUATON AND THE RELATED PARAMETERS Th quation of motion for a dampd SDOF systm is: mu cu fs( u) mug (1) whr m and c stand for th mass and viscous damping of th SDOF systm. u and u ar th acclration and vlocity trms, rspctivly. Th trm u g corrsponds to th input ground acclration. f s(u) dnots th rstoring forc as a function of th systm displacmnt u, which quals to f s=ku for linar lastic bhavior. n th cas of inlastic rspons, hystrtic rlationships dtrmin th f s(u). ntgrating both sids of Eq.1 with rspct to u lads to nrgy quilibrium quation as follows: m udu cudu fs( u) du mug du (2) u u u u whr th thr trms on th lft-hand sid of th formulation ar kintic nrgy (E k), damping nrgy (E ξ) and absorbd nrgy (E a), rspctivly. Absorbd nrgy is composd of two parts; th irrcovrabl hystrtic nrgy (E h), and th rcovrabl lastic strain nrgy (E s), whr Es f 2 s 2k. Th right-hand sid of Eq.2 is input nrgy (E i) which is a function of both ground motion and systm proprtis. Physically, E i is th nrgy impartd to th structural systm subjctd to a ground motion rcord. During th dynamic rspons, E i is tmporarily convrtd into E k and E s, which vanish at th nd of dynamic xcitation. At this instant, all input nrgy should b dissipatd by damping (through E ξ) and inlastic action (through E h). For lastic systms, damping is th only way of dissipating nrgy. Thr ar two altrnativ forms of nrgy quations with input and kintic nrgy trms (absolut and rlativ) according to Uang and Brtro (199). Still, both approachs rsult in th sam rsponss such as th rlativ displacmnt. Absolut nrgy quation corrsponds to th work don by th total bas shar at th foundation of th moving bas SDOF systm whil th rlativ nrgy quation rprsnts th work don by th static quivalnt rlativ forc (- mu g ) on th quivalnt fixd-bas SDOF systm. n this study, for all rspons analyss th rlativ nrgy approach is utilizd. 3. SMULATON OF A REGONAL GROUND MOTON SET Duzc which is locatd in th wstrn sgmnts of North Anatolian Fault zon, is slctd as our cas study. n this sction it is aimd to incras th variability in sismic dmand to b usd in structural analyss. Thrfor, a st of scnario vnts compatibl with rgional sismicity ar simulatd using stochastic finit fault mthodology basd on a dynamic cornr frquncy approach proposd by Motazdian and Atkinson (25). Ths tim sris ar simulatd for diffrnt magnitud rangs (Mw=6., 6.5 and 7.) considring local sourc, path and sit

3 4th ntrnational Confrnc on Earthquak Enginring and Sismology Octobr 217 ANADOLU UNVERSTY Eskishir/TURKEY conditions. A total of 37 nods insid of th Duzc rgion boundd by 3-32 Eastrn longituds, 4-41 Northrn latituds ar considrd for ground motion simulation. Th slctd nods ar locatd at sits with sit classs C and D according to NEHRP sit classification which ar rprsntd as S2 and S3, rspctivly in this study. Furthr dtails corrsponding to ground motion simulations in th study ara can b found in Karimzadh t al. (216) and Ugurhan t al. (21). t is notd that stochastic finit fault simulation mthod provids only on random horizontal componnt at ach station. To prform structural analyss, among th total 222 tim sris gnratd at th slctd 37 nods, 24 tim sris ar slctd. Ths rcords ar classifid with rspct to thir sourc to sit distancs (Joynr and Boor distanc: R JB), soil class and magnitud of th vnt as prsntd in Tabl 1. Figur 1 illustrats th variations of PGA and PGV with rspct to R JB for th slctd tim sris. t is sn that th maximum valus of PGA and PGV for th slctd rcords rach approximatly.8g and 8 cm/s, rspctivly. Tabl 1. Distribution of th slctd rcord st with rspct to soil class, distanc and magnitud Distanc, R JB Soil Typ S2 (Soft Rock) S3(Stiff Soil) (km) Magnitud Mw=6. Mw=6.5 Mw=7. Mw=6. Mw=6.5 Mw= Numbr of Rcords > S3 S2 8 6 S3 S2 PGA(g).4.2 PGV(cm/s) R JB (km) Figur 1. Variation of PGA and PGV with rspct to R JB for th slctd rcords 4. DYNAMC ANALYSES OF SDOF SYSTEMS Th aim of this study is to obtain spctral variations of nrgy-basd paramtrs for SDOF systms with varying priods subjctd to th slctd st of simulatd ground motions as providd in Tabl 1. To xamin th influnc of ground motion paramtrs including magnitud, sourc to sit distanc and soil class on lastic input nrgy ( E ), in th first stag of analysis, linar lastic SDOF modls ar mployd. n th scond stag, to invstigat th rlationship btwn lastic ( E ) and inlastic input nrgis ( E ) as wll as th ratio btwn hystrtic nrgy ( E H ) and inlastic input nrgy ( E ), inlastic SDOF modls ar utilizd. To fulfill this objctiv, lastoplastic and stiffnss dgrading (i.. Clough Johnston modl) hystrsis modls ar mployd. For all stags, th damping ratio ( ) is takn as =2%, 5% and 8%. Th strngth ratio ( ), which is dtrmind as th yild strngth dividd by th wight, is assumd to tak valus of =.1,.2,.3 and ANALYSS RESULTS R JB (km) n this study, th rlationships btwn lastic input nrgy, ratio of inlastic to lastic input nrgy and ratio of

4 4th ntrnational Confrnc on Earthquak Enginring and Sismology Octobr 217 ANADOLU UNVERSTY Eskishir/TURKEY hystrtic nrgy to inlastic input nrgy with th abovmntiond ground motion paramtrs ar invstigatd. Th ratio of inlastic to lastic input nrgy ( R E ) and ratio of hystrtic nrgy to inlastic input nrgy ( R H ) ar dtrmind, rspctivly as follows: R E E E (3) RH EH E (4) Figur 2.a shows lastic input nrgy spctra for rcords of vnt with M w=7 rcordd at <R JB<5 km. nvstigatd paramtrs ar sit class (S2 and S3) and damping ratio ( =2, 5 and 8%). t is obsrvd that input nrgy for S3 is slightly highr than input nrgy for S2 for priods lss than.4 whil th nrgy valus for S2 and S3 convrg up to th priod of.5 sconds. Aftr T=.5 sconds, input nrgy for S3 class again bcoms largr than input nrgy for S2 class up to th priod of 3.5 sconds. This obsrvation indicats that as th sit conditions gt softr (or wakr), input nrgy incrass. This obsrvation is consistnt with similar analyss which mploys ral ground motion rcords. Aftr th priod of 3.5 sconds for both soil classs input nrgis convrgs. Th spctral shap of lastic input nrgy is also in agrmnt with prvious studis (Akiyama, 1985; Dcanini and Mollaioli, 1998; Bnavnt-Climnt t al., 22; Amiri t al., 28). For dsign purposs, prvious studis rcommndd ithr a bilinar or a trilinar shap to rprsnt lastic input nrgy spctra. Th trnd in this study sms to b much closr to a trilinar shap with an initial ascnding rgion, a constant-valud platau and a dscnding rgion. Damping dos not sm to hav a pronouncd ffct on E. t only rducs th pak rsponss with a maximum diffrnc of 2% at T=1.5s. Figur 2.b rprsnts lastic input nrgy amplification by considring th ratio of E for softr sit class (i.. S3) to E for hardr sit class (i.. S2). Th nrgy amplification is obsrvd to tak valus around 3 for T>.75 sconds. Th nrgy amplification gradually dcrass for priods gratr than 2.5 sconds. E i (cm2 /s 2 ) S3 - =2% S3 - =5% S3 - =8% S2 - =2% S2 - =5% S2 - =8% Ei amplification =2% =5% =8% Figur 2. Elastic input nrgy spctra for diffrnt sit classs and damping ratios; input nrgy amplification du to diffrnt sit conditions Figur 3.a shows lastic input nrgy spctra for rcords with < R JB<5 km and =5%. nvstigatd paramtrs ar sit class (S2 and S3) and magnitud (M w=6, 6.5 and 7). t is obsrvd that magnitud has a significant ffct on E. For M w=7, nrgy impartd to structur bcoms vry larg whn compard to input nrgy for both M w=6 and 6.5. Figur 3.b yilds E amplification du to magnitud by comparing th nrgy valus for M w=7 with valus for M w=6. For both soil classs, th trnd for ratio of impartd nrgy from M w=7. ovr Mw=6. is similar up to th priod of 2.5 sconds whr it varis in btwn 4 to 1. Thn, it bcoms constant for S3 whil for S2 it incrass rapidly up to 2 folds at T=4 sconds. This obsrvation may b attributd to th fact that at longr priods th sourc ffcts govrn mor than th sit ffcts, particularly for th nrgy amplification of Mw=7 to

5 4th ntrnational Confrnc on Earthquak Enginring and Sismology Octobr 217 ANADOLU UNVERSTY Eskishir/TURKEY Mw=6. E i (cm2 /s 2 ) S3 - M=6 S3 - M=6.5 S3 - M=7 S2 - M=6 S2 - M=6.5 S2 - M=7 Ei amplification S2 S Figur 3. Elastic input nrgy spctra for diffrnt sit classs and magnituds; input nrgy amplification du to diffrnt magnituds Figur 4 prsnts lastic input nrgy spctra for rcords with M w=7. and =5%. nvstigatd paramtrs ar sit class (S2 and S3) and distanc (< R JB<5, 5< R JB<1, 1< R JB<2, R JB>2). t is obsrvd that for both soil classs input nrgy dcrass as JB distanc incrass. Thrfor, lastic input nrgy bcoms critical for closr distancs spcially lss than 1 km. Elastic input nrgy incrass at priods longr than 2.5 sconds for soil class S2 and Mw=7. for distancs ar lss than 5 km. This obsrvation is consistnt with th anticipatd nar-fild ffcts. E i (cm2 /s 2 ) R JB 5 5 R JB 1 1 R JB 2 2 R JB E i (cm2 /s 2 ) R JB 5 5 R JB 1 1 R JB 2 2 R JB Figur 4. Elastic input nrgy spctra for distanc intrvals and soil class S2; S3 Figur 5.a illustrats th variation of R E (dfind in Eq.3) for S2 and S3 classs by using two diffrnt hystrsis modls (i.. lasto-plastic and Clough Johnston modls). For SDOF systms, it is assumd that =.1 and =5%. n Figur 5, th ratio taks larg valus in th vry short priod rang with a sharp dscnding trnd. At T=.3 sconds, th curvs bgin to mrg around th valu of 1. Thr sms to b no ffct of ithr sit class or hystrsis modl on th spctral variation of R E. Hnc, it can b statd that xcpt th short priod rgion, th paramtr R E is vry stabl. This obsrvation is consistnt with dsign cods: For dsign purposs, this ratio can b assumd to b 1. for modrat and long priod rangs, which in turn mans lastic and inlastic input nrgis ar qual to ach othr. n th short priod rang, or for vry rigid structurs, inlastic nrgy dmand sms to b vry high. That is why gnrally forc-basd dsign stratgy, which nsurs lastic bhaviour, is usd for ths structurs. Figur 5.b shows th variation of R H (dfind in Eq.4) for S2 and S3 classs and two considrd hystrsis modls ( =.1, =5%). Th ratio dcrass with approximatly a constant slop for ach soil typ as th priod of structur incrass. Th only xcption is th ratio for both soil typs whil using Clough modl whr a sharp incras is obsrvd up to th priod of.75 sconds. Th ffct of sit conditions is also prsnt in all priod rangs. t is

6 4th ntrnational Confrnc on Earthquak Enginring and Sismology Octobr 217 ANADOLU UNVERSTY Eskishir/TURKEY obsrvd that for priods lss than.75 sconds, th ratio of hystrsis nrgy ovr input nrgy for S3 is slightly largr than that for S2 whil using Clough modl. n contrast, for priods gratr than.75 sconds, soil typ S3 provids largr R H compard to S2 for this modl. Th sam obsrvation is valid for lasto-plastic modl with a transitional priod of.5 sconds. Th ffct of hystrsis modl is obsrvd for th whol priod rangs whil Clough modl provids largr hystrsis to input nrgy ratio with a maximum of 3 prcnt diffrnc at vry short priods. 5 4 S3 - Elastoplastic =.1 S3 - Clough =.1 S2 - Elastoplastic =.1 S2 - Clough = S3 - Elastoplastic =.1 S3 - Clough =.1 S2 - Elastoplastic =.1 S2 - Clough =.1 E i /E i 3 2 E h /E i Figur 5. Spctral variation of R E; R H for diffrnt sit classs and hystrsis modls Figur 6 prsnts th variation of inlastic input nrgy for lasto-plastic modl and two altrnativ soil classs using diffrnt strngth factors. Figur 6.a rvals that for priods lss than.3 sconds as strngth factor incrass, inlastic nrgy slightly dcrass, and vic vrsa for priods largr than.3 sconds. For soil class S2, th ffct of strngth factor is mor dominant within a priod band of [.3, 1.2 s]. Whn th inlastic input nrgy corrsponding to soil class S3 is of concrn, it is sn that th maximum ffct of using diffrnt strngth factors is obsrvd for priods in btwn.6 to 2.8 sconds (Figur 6.b). n addition, in ths priod rang, as th valu of strngth factor riss, th valu of inlastic input nrgy incrass. n contrast, for priods lss than.6 sconds, an incras in strngth factor rsults in a rduction of inlastic nrgy. Ovrall, th rsults for diffrnt soil classs dmonstrat that softr soil conditions (S3) provid largr inlastic nrgy compard to stiffr soil conditions (S2) =.1 =.2 =.3 = =.1 =.2 =.3 =.4 E i (cm 2 /s 2 ) 15 1 E i (cm 2 /s 2 ) Figur 6. nlastic input nrgy spctra for lasto-plastic modl using diffrnt strngth factors for S2; S3 6. CONCLUSONS This study focuss on th valuation of nrgy-rlatd paramtrs, particularly input nrgy, by considring th dynamic analysis of lastic and inlastic SDOF systms subjctd to a simulatd ground motion datast. Similar prvious studis wr prformd using ral ground motion rcords. Howvr, th conclusions of thos studis wr not fully gnralizd ithr du to scarcity of data (spcially for larg magnitud and short distancs) or th larg scattr du to slction of rcords from diffrnt arthquaks. This study tris to ovrcom ths issus by simulating ground motion rcords that covr th whol possibl rang of rgional valus for major sismological

7 4th ntrnational Confrnc on Earthquak Enginring and Sismology Octobr 217 ANADOLU UNVERSTY Eskishir/TURKEY paramtrs such as magnitud, sit class and distanc. A paramtric study is conductd to obsrv th charactristics of lastic and inlastic input nrgis and th prcntag of hystrtic nrgy that should b dissipatd through inlastic action. Th rsults of this study sm to augmnt th rsults of prvious studis whil thy ar consistnt with th physical conclusions. Th numrical obsrvations hrin ncourag th us of simulatd ground motions to dvlop simpl and practical nrgy-basd dsign and valuation procdurs for structural systms. REFERENCES Housnr, G.W. (1956). Limit Dsign of Structurs to Rsist Earthquaks. Procdings, First World Confrnc on Earthquak Enginring, Vol : pp Zahrah, T.F. and Hall, W.J. (1984). Earthquak nrgy absorption in SDOF structurs, Journal of Structural Enginring-ASCE 11:8, McCab, S.L. and Hall, W.J. (1989). Assssmnt of sismic structural damag, Journal of Structural Enginring- ASCE 115:9, Uang, C. and Brtro, V.V. (199). Evaluation of sismic nrgy in structurs, Earthquak Enginring and Structural Dynamics 19:1, Akiyama, H. (1985). Earthquak Rsistant Limit Stat Dsign for Buildings, Univrsity of Tokyo Prss, Tokyo, Japan. Dcanini, L.D. and Mollaioli, F. (1998). Formulation of lastic arthquak input nrgy spctra. Earthquak nginring and structural dynamics 27(12), Chai, Y.H. and Fajfar, P. (2). A procdur for stimating input nrgy spctra for sismic dsign. Journal of Earthquak Enginring 4(4), Bnavnt-Climnt, A., Pujads, L.G. and Lopz-Almansa, F. (22). Dsign nrgy input spctra for modrat sismicity rgions. Earthquak nginring and structural dynamics 31(5), Surahman, A. (27). Earthquak-rsistant structural dsign through nrgy dmand and capacity. Earthquak nginring and structural dynamics 36(14), Amiri, G.G., Darzi, G.A. and Amiri, J.V. (28). Dsign lastic input nrgy spctra from ranian arthquaks, Canadian Journal of Civil Enginring 35(6), Motazdian, D. and Atkinson, G. (25). Stochastic finit-fault modling basd on a dynamic cornr frquncy. Bulltin of th Sismological Socity of Amrica 95(3), Ugurhan, B., and Askan, A. (21). Stochastic strong ground motion simulation of th 12 Novmbr 1999 Duzc (Turky) arthquak using a dynamic cornr frquncy approach. Bulltin of th Sismological Socity of Amrica 1(4), Karimzadh S., Askan A. and Yakut A. (216). Nonlinar tim history analyss of multi-dgr of frdom structurs undr ral and synthtic rcords using stochastic finit-fault mthodology (CONHC). Chania, Crt, Jun 28-3.