RELATIONSHIP BETWEEN DESIGN RESPONSE SPECTRA FOR RARE AND FREQUENT EARTHQUAKE LEVELS

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1 th Wold Confeence on Ethquke Engineeing ncouve, B.C., Cnd ugust -6, 00 Ppe No. 9 ELIONHIP BEWEEN EIGN EPONE PEC O E N EQUEN EHQUKE LEEL Yingmin LI Cheng HI Ming LI Ling HN UMMY It is known tht uilding stuctues should e designed to hve diffeent pefomnce unde diffeent ethquke levels. hee o fou levels, such s fequent, occsionl nd e levels, e usully defined y the codes fo seismic design in most counties. n impotnt thing tht hs een ignoed up to now is tht the shpes of design esponse spect fo diffeent ethquke levels e not unifom ccoding to the ttenution lws of gound motions. Employing the thee pmetes model, pek gound cceletion, pek gound velocity nd pek gound displcement, of design esponse spect, the eltionship etween design esponse spect fo e nd fequent ethquke levels is deived theoeticlly. he eltions etween pmetes defining the shpe of esponse spect e then evluted quntittively y intoducing the typicl ttenution lws of pek vlues of gound motions nd esponse spect in Chin. Bsed on the design esponse spect fo the fequent level defined in the Code fo eismic esign of Buildings of Chin [], the design esponse spect fo the e level e suggested. he esults show tht the design spect fo e level should hve moe long-peiod components thn these fo fequent level. It is convenient tht the chcteistic peiods of spect fo e level my e djusted to e 0.05sec longe thn those fo fequent level in the sme site. INOUCION o seismic design, the shpes of design esponse spect fo the diffeent ethquke levels e usully tken s follows in most codes, ( ) ( ) ( ) ( ) whee ( ), ( ) nd ( ), ( ) () () denote cceletion design spectum nd cceletion mplifiction fcto design spectum fo e nd fequent ethquke level. he supescipts nd efe to the e nd fequent ethquke levels espectively. is popotion fcto, which e 6.5, 5.65, his wok ws sponsoed y Ntionl Ntul cience oundtion of Chin unde Gnt No College of Civil Engineeing, Chongqing Univesity, Chongqing, 0005, Chin eptment of cience nd echnology, Ministy of Constuction, Beijing, 0085, Chin

2 .75 fo seismic fotifiction intensity Ⅶ,Ⅷ,Ⅸ in the code of Chin. Unfotuntely, the ssumption mentioned ove is not esonle. istly, ccoding to ttenution lw of gound motions, the shpe of esponse spectum hs get eltions with mgnitude nd epicentl distnce. he design spect fo lge mgnitude nd f distnce hve moe long-peiod components thn tht fo smll mgnitude nd ne distnce, which e ignoed in eqution () nd (). econdly, the vlues in ech peiod of spect fo e level e multiplied y sme fcto tht is independent with peiods fom those of spect fo fequent level, which leds to diffeent design stndds fo stuctues with diffeent peiods. he esults of seismic hzd nlysis given y Conell [] indicte tht exceednce poilities of pek cceletion, pek.6. velocity nd pek displcement e line with, nd. Hu [] pointed out tht hzd of cceletion decesed moe thn tht of displcement if thee pmetes,, e mgnified y unifom tio. It is known tht in shot, middle nd long peiod sections of esponse spect e espectively contolled y,, nd. If the vlue coesponding to ech peiod of design esponse spect fo the fequent level is mgnified y the sme tio, the stuctues with long peiods designed ccodingly hve gete hzd thn those with shot peiods. Genelly, the significnce ctegoy of the stuctues with long peiods, such s tll uildings nd high-ise stuctues, is gete thn tht of the stuctues with shot peiods. om the viewpoint of hzd esistnt, ethquke ction o seismic fotifiction mesues should e incesed fo the stuctues with long peiods. o those stuctues, even if the significnce ctegoy is sme to the stuctues with shot peiods o stonge seismic fotifiction mesues e dopted, the ethquke ction stndd should not e lowe ccoding to eqution () nd (). iffeent design esponse spect fo the e nd fequent ethquke levels hve een dopted in the code of Chin, GB In this ppe, the eltionship etween the design esponse spect fo the e nd fequent ethquke levels e studied ccoding to theoeticl deivtion nd quntittive evlution. HEOEICL EIION BE ON HEE PMEE MOEL o seismic design, the e nd fequent ethquke levels men diffeent exceednce poilities of ethquke ctions. he vlues fo diffeent peiods of design esponse spect should coespond to the sme exceednce P poilities. he design esponse spect tht esult fom seismic hzd nlysis with intensive egionl chctes e inpplicle. t the sme time, it is not possile to give the sttistic eltionship etween design esponse spect fo e nd fequent ethquke levels. ccoding to stnddiztion out design esponse spect suggested y Newmk[], pseudo-cceletion esponse spect P cn e detemined y thee pmetes,, nd s shown in igue.he model my e fomulized s follows P ( ) v v π / () d d (π / ) whee, nd denote sttistic vege mplifiction fctos fo highe (out -0Hz), middle v d pseudo-cceletion esponse spect P v mplifiction e d (out 0.-Hz) nd lowe (out -0Hz) fequency sections espectively. nd e peiod limit vlues. nd e peiods fo inflection points nd usully clled s chcteistic peiods, given y continuous conditions, which cn e expessed s d igue. hee-pmete model

3 v d v π π, () Genelly, fo fequency section used in stuctues seismic design, the diffeence etween velocity esponse spect ) ( v nd pseudo-velocity esponse spect ) ( P v cn e ignoed. t the sme time, consideing highe fequency section (0, ) whose vlues e line with peiods nd wekening the stipultion tht the vlues should espectively e in invese popotion to nd in middle nd lowe fequency section, the whole cceletion design esponse spectum nd cceletion mplifiction fcto spectum my e estlished though thee s + 0 (5) + 0 (6) Consideing continuous conditions, then / /,, (7) whee,,, nd e constnts. he ttenution index of in the section (, ) is doule thn it in the section (, ). efining (,, ) nd (,, ) s design pek cceletion, pek velocity nd pek displcement fo e nd fequently levels espectively, fo the section (, ), following cn e deived (8) (9),, (0) whee i is the minimum of i nd i, i is the mximum of i nd i. o the eltionship etween e nd fequent ethquke levels tuns to the eltionship etween thee pek pmetes of e nd fequent ethquke levels. Eqution (8) to (0) indicte tht the tios of in the high, middle nd low fequency sections of the esponse spect espectively equl to the tios of pek cceletion, pek velocity nd pek displcement. Eqution () nd () cn only e used fo high fequency section of the esponse spect.

4 HEOEICL EIION BE ON ENUION LW O GOUN MOION Bsed on the esults of seismic hzd nlysis, usully the vlues of, nd e diffeent. iectly intoducing the eltion, lg Y I + () whee Y is pek vlue of gound motions such s,, nd. I is the fotifiction intensity. nd e constnts otined sttisticlly. ince the vlues of fo,, nd e identicl in eqution (), it is oviously tht, nd the shpes of cceletion design esponse spect fo e nd fequent ethquke levels will e unifom. o the eltion expessed y eqution () is not pcticle to detemine the shpes of cceletion design esponse spect fo diffeent ethquke levels. he eltionship etween design esponse spect fo e nd fequent ethquke levels cn e given sed on the ttenution lws of gound motions. Genelly, the ttenution lws of gound motions cn e expessed s [5] lgy Y + Y M + cy lg( + 0Y ( M )) + fy () 0Y ( M ) dy exp( ey M ) whee Y my e intensity I, the gound motions pek vlues (,, ) o espond spect. M, nd e espectively the mgnitude, the epicentl distnce nd the site viles. Y, Y, c Y, d Y, e Y nd f Y e the coefficients coespond to Y. 0Y (M) is the stution fcto which inceses with the mgnitude incesed. o the intensity I, 0Y (M) is constnt. he site chcte fo sme site doesn t chnge fo e nd fequent ethquke levels, so lg ( Y Y ) Y + cy Y () wheeδ Y lg( + 0Y (M ))-lg( + 0Y (M ). eivtion sed on ttenution lws of pek vlues When Y in eqution () e eplced y the gound motions pek vlues (,, ), it cn e ewitten s lg( ) + c lg( ) + c () lg( ) + c he inflection point peiods, nd e diffeent fo diffeent ethquke levels. Bsed on eqution (0), the tios of inflection point peiods fo e nd fequent ethquke levels cn e expessed s lg( ) ( ) + (, ) lg( ) [( ) + (, ) ] (5) lg( ) [( ) + (, )] whee (, ) c c. It is ovious tht << Y <<, () in eqution (5) cn e omitted. o eqution (5) ecomes ( ) ( ) ( ) ( ) ( ) ( ) lg lg (6) lg om the ove deivtions, conclusion cn e otined tht the shpes of the design esponse spect e diffeent fo diffeent levels, nd these diffeences cn e eflected ppoximtely though djusting inflection point peiods.

5 eivtion sed on ttenution lws of esponse spect When Y in eqution () is eplced y the cceletion design esponse spectum ( ), it cn e ewitten s lg( ( ) ( )) ( ) + c ( ) ( ) (7) o the cceletion mplifiction fcto esponse spectum, it cn e otined tht lg ( ( )) ( ) M (, ) + (8) In which, the vlues of () e influenced y peiod. o the eos cused y omitting () e diffeent fo diffeent. Bsed on these tios ( ), which coesponding to diffeent, the tios fo the diffeent fequent sections of design espond spect should e futhe djusted in seismic design. he vlues of vying with e shown in igue, the esults sed on the ttenution model given y Huo [6]. s shown in igue, the vlues in lines with mks e clculted y eqution (8), the vlues in lines without mks e clculted y eqution (8) with () omitted. he eos cused y omitting () incese with the incese of It s cle tht () shouldn t e ignoed with the incese of. igue. lues of vying with in noth Chin QUNIIE ELUION BE ON YPICL ENUION LW O EPONE PEC IN CHIN Employing the eltionship commonly used in Chin [5] le. lues ofδ M nd / I M.9lg (9) Intensity Ⅶ Ⅷ Ⅸ nd definingδii -I, ΔMM -M, then Δ I.6.9. I.6.9lg( ) (0) / / / /.5 Clely, is coeltive with. le shows the Δ M / / /.5 / vlues of M nd ccoding to diffeent intensity Ⅶ, Δ M Ⅷ,Ⅸ. is detemined ccoding to eltive sttisticl dt in / /.5 / /.5 Chin. I depend on the e nd fequent ethquke levels. Δ M Given y the ppoximte eltion lglg I-0.0, I cn e / / /.5 evluted s shown in le. igue shows the vlues of k Δ M (k / ) effected y nd ccoding to the ttenution lws of gound motions in noth Chin.

6 igue. lues of k effected y nd in noth Chin igue () nd () show tht coefficient k vies with. igue (c) to (f) show tht coefficient k vies with M. In shot, the vition of the mgnitude mkes gete effect on inflection point peiods thn the vition of the epicentl distnce dose. he soil site is ffected less y M nd thn the ock site. om igue () nd (), the following cn e otined, () he tendency tht k vies with the incese of is line ppoximtely; () When nd e invile, k inceses with the incese of M; nd () k ecomes smlle with the incese of. his tendency ecomes moe ovious fo the long xis diection, lge nd the soil site. But these vile vlues don t exceed 0..

7 om igue (e) to (f), the following cn e otined, () k deceses with the incese of ; () When nd M e invile, k deceses with the incese of ; nd () k ecomes lge with the incese of M. Consideing nd togethe, the vlues of k e clculted though intepoltion method. Bsed on le nd the given vlue 0. 9, the tios of inflection point peiods fo e nd fequent ethquke levels e clculted y eqution (0) s shown in le. le. he tios of inflection point peiods ctegoies Intensity ock oil ock oil ock oil ock oil Ⅶ Ⅷ Ⅸ CONCLUION om the ove nlysis, it s cle tht the shpes of the design esponse spect e diffeent fo diffeent ethquke levels. In high, middle nd low fequency sections of esponse spect, the tios etween cceletions fo e nd fequent ethquke levels espectively equl to the tios of pek cceletions, pek velocities nd pek displcements. hese tios cn e eched though djusting inflection point peiods. ou ltentives e pesented in le. Consideing the continuity of codes nd the fesiility fo enginees, it is suggested tht the existing α mx of e ethquke level emins unchnged nd the chcteistic peiod g ( ) my e djusted ccoding to the fist ctegoy in le. o intensity Ⅶ, g g ; o intensity Ⅷ nd Ⅸ, site of ctegoy Ⅰ, g. g, othe sites, g. g. futhe simplified epesenttion cn e g g fo intensity Ⅷ nd Ⅸ, which e dopted in the Code fo eismic esign of Buildings of Chin(GB500-00). he following should e pointed out, () It s fesile to study the eltionship etween design esponse spect fo e nd fequent ethquke levels sed on the ttenution lws of gound motions; () he conclusions e genel ecuse the ttenution lws e univesl; () he design esponse spect cn e extended to the longe peiod section in the simil method; nd () his eltionship etween the design esponse spect fo e nd fequent ethquke levels shouldn t e dopted in design esponse spect fo the diffeent intensity es. CKNOWLEGEMEN his wok ws sponsoed y Ntionl Ntul cience oundtion of Chin unde Gnt No EEENCE. GB500-00, Code fo eismic esign of Buildings. (in Chinese) Beijing: Chin chitectue & Building Pess, 00.. Conell C. Engineeing seismic isk nlysis. Bulletin of the eismologicl ociety of meic. 968, 58(5): Hu Yuxin. Ethquke Engineeing. (in Chinese) Beijing: eismic Pess, 988.

8 . Newmk NM, Hll WJ. eismic design citei fo nucle ecto fcilities. Poceedings of the th Wold Confeence on Ethquke Engineeing, ntigo, Chile, II (B-): 7-50, Li Yingmin. Modeling of stong gound motions fo engineeing pupose. (in Chinese) hesis fo docto degee, Chongqing Jinzhu Univesity, Chongqing, Chin, Huo Junong. ttenution lws of gound motions of ne sites. (in Chinese) hesis fo docto degee. Chin eismologicl Bueu, Heing, Chin, Li Yingmin, Bi holing, Li Ming. eltionship etween design esponse spect fo diffeent ethquke levels nd detemintion of design esponse spect fo e ethquke level. (in Chinese) Ethquke Enginee nd Enginee ition. 00, (6): 9-6.

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