Experimental Verification of Variable-Frequency Rocking Bearings for Near-fault Seismic Isolation

Transcription

1 Expeimentl Veiiction o Vile-Fequency Rocking Beings o Ne-ult Seismic Isoltion Lyn-Ywn Lu Deptment o Constuction Engineeing Ntionl Kohsiung Fist Univesity o Science nd Technology, Kohsiung, Tiwn Tzu-Ying Lee Deptment o Civil Engineeing, Ntionl Centl Univesity, Toyun County, Tiwn. Chi-Chie Hsu Ntionl Kohsiung Fist Univesity o Science nd Technology, Kohsiung, Tiwn SUMMARY A ne-ult ethquke usully possesses long-peiod pulse-like component tht my esult in n excessive isolto displcement in conventionl isoltion system, nd consequently it will incese seismic isk o led to n ovesized isolto design. To llevite this polem, vile-equency ocking-type eing (VFRB) is poposed in this study. The poposed ocking eing hs ocking suce with vile cuvtue, nd y popely selecting the geomety o the ocking suce, the isoltion stiness nd equency o the poposed ocking eing ecome the unctions o the eing displcement. In ode to expeimentlly veiy its esiility, ull-scle steel me isolted y pototype VFRB eings ws tested y using shking tle test in this study. The ocking suce o the pototype eings wee deined y six-ode polynomil unction, so they hve eltively highe initil stiness ollowed y sotening ehvio. This mechnicl popety enle the VFRB isoltion system to eectively suppess the excessive isolto displcement induced y pulse-like ne-ult ethquke, while etins esonle isoltion eiciency. The test dt show vey good geement with the simulted ones. Moeove, the expeimentl esults demonstte tht the VFRB-isolted me exhiits the desied ehvio in ne-ult ethquke, nd thus conims the pplicility o VFRB isoltos o ne-ult seismic isoltion. Keywods: ocking eing, vile stiness, vile equency, ne-ult isoltion. 1. INTRODUCTION Dieent om tditionl seismic esistnce techniques, the notion o seismic isoltion is to implement sot isoltion lye unde the potected stuctue, so the stuctue cn e uncoupled om gound excittions (Neim nd Kelly 1999). A seismic stuctue with n isoltion system is usully designed to e long-peiod system with ixed isoltion equency nd dmping tio. This long-peiod etue inevitly induces low-equency esonnt-like esponse when the isoltion system is sujected to gound motion contining stong long-peiod components. Mny studies hve conimed tht due to the long-peiod etue se-isolted stuctue will incu excessive isolto displcement in ne-ult ethqukes with long-peiod pulse component (Jngid nd Kelly 1; Lu et l. ; Povidkis 8). Consequently, this will led to n ovesized isolto design o incese the isk o isoltion pounding eect. To vet this polem, some eseches hve suggested using isoltion systems with vile mechnicl popeties, so the isoltion systems will not hve esonnt equency nd my e dptive to wide nge o ethqukes with dieent chcteistics (Ngjih nd Nsimhn 6; Lu et l. 11). As pt o esech eots o vile isoltion systems, the ojective o this study is to develop nd test new type o isoltos clled vile-equency ocking eings (VFRB), which hve vile isoltion stiness nd equency tht cn meet the desied design speciictions. In this ppe, the theoy nd omuls tht descie the mechnicl popeties o genel VFRB will e eviewed. Then, shking tle tests will e conducted to veiy the developed VFRB theoy, nd the isoltion peomnce o the pototype VFRB will e evluted y using the test dt. Additionlly, in

2 the tests, pticul ttention will e pid to the seismic esponse o the VFRB system sujected to ne-ult ethquke.. MECHANICAL PROPERTIES OF A VARIABLE-FREQUENCY ROCKING BEARING (VFRB).1. Restoing oce o the VFRB Fig. 1 shows the poposed ocking eing instlled unde stuctue ooting. As shown in the igue, the ocking eing hs n ticul (ll-nd-socket) joint on the top nd ocking suce with se plte on the lowe pt. The ticul joint is connected to the supe-stuctue though mounting plte, while the se plte is mounted on the gound o the oundtion o the stuctue. In n ethquke, the ocking suce o the eing will ock ck-nd-oth on the se plte, thus the tnsmitted gound motion onto the supe-stuctue cn e mitigted. The ocking suce, which is usully xilly symmetic, must e concved nd my hve vile cuvtue. Aticul joint Bse plte Rocking suce Figue 1. Photo o pototype vile-equency ocking eing. In this susection, the omul desciing the oce-displcement eltion o genel VFRB eing will e given. Fig. shows the ee-ody-digm o the ocking eing. In Fig., thee e two coodinte systems: x-y nd X-Y coodintes. The x-y system is ixed coodintes, while the X-Y system is moving coodintes tht is ttched to the eing nd will ock long with the eing. Also shown in Fig., the ocking eing hs two mjo design pmetes: the eing height h nd the geometic unction G) o the ocking suce. Fo the convenience, the unction G) is usully expessed in tems o the X-Y coodintes, i.e., Y=G). y x P Y U B M h Rocking suce unction Y=G) O X A N F (Fixed cood.) x Gound X (Moving cood.) Figue. Fee ody digm o the ocking eing.

3 In Fig., thee e ou oces nd one moment pplying on the eing: P is the veticl lod; N is the noml oce pplied on the contct point A o the ocking suce; F is the iction oce pplied on point A; U denotes the hoizontl she oce tht intects etween the eing nd the supe-stuctue; M epesents the moment cused y iction in the ticul joint. Note tht the she U is equivlent to the hoizontl seismic oce tnsmitted to the supe-stuctue. The she U o the ocking eing cn e deived y tking the moment equiliium eqution out the contct point A. The deived totl she U cn e witten in the ollowing om U u u (.1) The tems u nd u in Eqn..1 epesent the estoing oce nd the iction oce components in the totl she U, espectively. u is contiuted y the iction moment M in the eing, while u depends on the geomety o the eing s ocking suce. The detil deivtion o u nd u wee given in the eeence (Lu et. l. 9). While the deived u will e discussed lte, the estoing oce u cn e witten explicitly s u P u, whee h G ) G ) X u (.) h G ) X G ) In the ove equtions, X is the X-coodinte o the contct point A in X-Y coodinte system (see Fig. ), nd G) denotes the ist deivtive o G) out vile X. Note tht in Eqn.., u u / P epesents the nomlized estoing oce with espect to the eing s veticl lod P. Eqn.. demonsttes tht the estoing oce u o the ocking eing is unction o X, G) nd h, nd is popotionl to the veticl lod P. Note tht s shown in Fig., X is not the se displcement o the supestuctue. The se displcement (o isolto displcement) should e deined s the hoizontl displcement o point B denoted y x in Fig.. Point B is the cente o the ticul joint. Futhemoe, ecuse the hoizontl displcement o point B is equl to the x-coodinte o point B in the x-y coodinte system, it cn e deived tht h G( X ) G ) X X x 1 G ) dx (.3) 1 G ) Investigting Eqns.. nd.3, one should elize tht it is diicult to diectly expess the estoing oce u s n explicit unction o the isolto displcement x. Howeve, the eltionship etween u nd x does exist nd cn e estlished though the intemedite vile X... Restoing oce o the ocking eing As mentioned peviously, the iction moment M in the ticul joint o the eing cuses the equivlent hoizontl iction component u shown in Eqn..1. At ny time instnt, the mgnitude o u will ely on the cuent sttus o the eing motion, which hs two possile motion sttes, i.e., ocking nd sticking (non-ocking) sttes. In the ocking stte, the mgnitude o u will e equl to its mximum vlue denoted y u, mx ; while in the stick stte, u depends on the pesent dynmic esponse o the isolted stuctue nd its mgnitude should not exceed u, mx. Theeoe, u cn e expessed s whee u u,mx (o sticking stte) u u,mx (o sticking stte) (.)

4 u,mx 1 G' ) P (.5) h G ( X ) X G ' ) whee nd epesent the mteil iction coeicient nd the dius o the ticul joint, espectively. Eqn..5 indictes tht the mximum iction oce u, mx is lso unction o X -coodinte. The complete deivtion o Eqn..5 is given in the ticle y Lu et. l. (9)..3. Tngentil isoltion stiness nd isoltion equency The tngentil stiness k (o clled instntneous stiness) o the poposed eing, which is deined s the te o chnge o the estoing oce, cn e computed y tking the deivtive o u with espect to the se displcement x, i.e., du du ) / dx Pu ) k ) (.6) dx dx ) / dx x ) In the lst eqution, u deined in Eqn.. hs een pplied. Eqn..6 implies tht the isoltion stiness is not constnt ut unction o the se displcement x, since X X ( x ). Futhemoe, y using Eqn..6, the tngentil isoltion equency cn e computed y the ollowing eqution k ) P u ) g u ) ) (.7) M M x ) x ) whee M is the mss o the supe-stuctue. Notly, in Eqn..7 it is ssumed tht the supestuctue ehves like igid ody, nd the veticl lod P due to the stuctul weight cn e expessed s P M g. Fom Eqn..7, it is evident tht isoltion equency o the eing is not constnt, ut is n implicit unction o the se displcement x nd the geometic unction G), since u is unction o G) (see Eqn..). It is o this eson tht the poposed eing is clled the vile-equency ocking eing. Eqn..7 lso demonsttes tht the isoltion equency o the PRB is completely independent om the stuctul mss M. By popely selecting the geometic unction G) o the ocking suce, the isolted system my possess voule dynmic chcteistics in dieent se displcement. 3. DEFINING THE ROCKING SURFACE BY A POLYNOMIAL FUNCTION In the shking tle tests o this study, the geometic unction G) o the pototype VFRB eings is deined y the ollowing sixth-ode polynomil unction G 6 X c X c X c (3.1) 1 3 X whee c 1, c nd c 3 e the thee constnt coeicients. The ove polynomil unction is n even unction, which is symmetic out the Y-xis nd psses though the oigin o the X-Y coodintes. Since the shpe o such eing is deined y polynomil, the eing is clled Polynomil Rocking Being (PRB) heete. Futhemoe, te G X is sustituted om Eqn..8 in Eqns.. nd.5, oth the estoing oce u nd mximum iction oce u, mx o the PRB ecome unctions o thee polynomil coeicients, c 1, c nd c 3. The selection o these thee coeicients is n impotnt tsk in designing the PRB, since they detemine the mechnicl popeties o the PRB. Lu et l. (11) studied sliding isoltos with vile cuvtue (SIVC) whose stiness is lso unction o the isolto displcement. Thei esults indicte tht n SIVC with eltively highe initil

5 stiness ollowed y sotening mechnicl ehvio (decesing stiness) is peele o ne-ult seismic isoltion, ecuse it is le to eectively suppess the excessive isolto displcement induced y sevee long-peiod ethquke without signiicntly incesing the supestuctue cceletion. To deine the estoing oce u s unction o the isolto displcement x, they lso suggested ith-ode polynomil unction with speciic coeicient vlues o u. Bsed on the unction u suggested y Lu et l. (11), the vlues o the coeicients c 1, c nd c 3 o the PRB used in the pesent study e chosen s listed in Tle 1. As esult, Fig. 3 shows the nomlized estoing oce ( u / P ) nd the isoltion peiod T ( / ) s unctions o the eing displcement x. Fig. 3() shows tht the PRB hs eltively highe initil stiness t x, ut the stiness switly deceses s x inceses, until x eches the citicl displcement o.8m, eyond which the eing stiness inceses long with x. Moeove, Fig. 3() shows tht the PRB hs n initil isoltion peiod o out 1 second t x, which is shote thn the commonly used isoltion peiods, ut the isoltion peiod T is switly polonged to moe thn 7 seconds t x. 8 m, eyond which T is shotened due to the incesed isoltion stiness. Tle 1. Pmetes o pototype PRB isoltos used in the test. Geometic Pmete Vlue Mteil pmete Popety c (1/m 5 ) Bll socket Bss Polynomil coeicient o c ocking suce 5.1 (1/m 3 ) Spheicl hed Steel c (1/m) Rocking suce Steel Being height h.187 m Bse plte Rue Rdius o ll hed. m Mteil iction coe..3 Hoizontl Foce / Weight Bse Displcement (m) Peiod (s) Bse Displcement (m) () Nomlized estoing oce () Isoltion peiod Figue 3. Mechnicl popeties o the pototype PRB eings. PRB eing Mss locks Acceleomete Displcement senso Shking tle Figue. Mechnicl popeties o the pototype PRB eings.. HYSTERETIC PROPERTY TEST OF THE PROTOTYPE PRB SYSTEM In ode to veiy expeimentlly the genel theoy o the VFRB discussed in the pevious sections, two types o shking tle tests wee conducted: (1) hysteetic popety test o the PRB system, nd () seismic test o PRB isolted stuctue. Tle 1 lists ll the constituent mteils nd pmetic vlues o the pototype PRB eings used in the tests. Figue depicts the setup o the ist test, which involved ou PRB eings mounted unde the ou cones o igid oject o totl weight

6 out W=1.kN. Becuse the pupose o this test is simply to oseve whethe the hysteetic popety o the tested PRB system ollows the deived omuls, the dynmic eect o the supestuctue ws eliminted y using the igid mss locks s the isolted oject. In the test, sinusoidl hoizontl excittion o equency 1 Hz nd mplitude.1g ws imposed on the tested PRB system. The cceletion nd displcement o the isoltion system wee ll ecoded y n cceleomete nd displcement senso, s shown in Fig.. Bsed on the mesued dt, Fig. 5 compes the expeimentl nd theoeticl hysteesis loops o the ovell PRB isoltion system. The totl she oces o oth loops hve een nomlized with espect to the veticl lod. Notly, the expeimentl she oce in Fig. 5() is otined indiectly y multiplying the cceletion o the isolted oject with its mss. On the othe hnd, the theoeticl oce plotted in Fig. 5() is simulted y using Eqns..1,. nd. with the pmetes listed in Tle 1. Figue 5 shows tht the expeimentl hysteesis loop mtches the theoeticl one vey well, nd the pototype PRB system hs the desied mechnicl popeties. It lso indictes tht the omuls deived in Section e le to simulte the hysteetic ehvio o VFRB isoltion system. In the next section, these omuls will e pplied to simulte the seismic esponses o steel stuctue isolted y the pototype PRB system, so thei ppliction to moe elistic cse cn e uthe veiied..3 Nomlized hysteesis loop Nomlized Hysteesis Loop.. She oce/axil oce She oce/axil oce Displcement(m) () Expeimentl Displcement (m) () Theoeticl Figue 5. Compison o nomlized hysteesis loops o the pototype PRB system. 5. SEISMIC TEST OF A PRB-ISOLATED STRUCTURE 5.1. Test setup Figue 6 shows the setup o the second shking tle test tht involves ull-scle one-stoy steel me isolted y the pototype PRB eings mounted unde ech column o the me. While the popeties o the eings hve een listed in Tle 1, Tle summizes the stuctul pmetes o the steel me. The steel me is 3m high nd hs the plne dimension o 3m x m (length y width). The totl mss o the me is out 1.8 metic tons. The esults o system identiiction test show tht the steel me hs undmentl equency (ixed se) o out.17 Hz nd dmping tio o.1%. To investigte the isoltion peomnce o the PRB-isolted me in dieent ethqukes, two types o histoic gound motions with vey dieent chcteistics wee consideed s the excittions in the test. Imposed on the isolted me long its longe 3m side, the two gound motions e: (1) the El Cento ethquke o 19, which is used to epesent gound excittion tht is widely used in ethquke engineeing esech to epesents typicl -ield ethquke in this study. () The Impeil Vlley ethquke (El Cento Ay 6), which ws ecoded y sttion ne tectonic ult in 1979, nd is used to epesent ne-ult ethquke in this study.

7 Tle. Stuctul pmetes o the steel me used in the test. Popety Vlue Popety Vlue Mteil H-shped steel Ntul equency s.17 Hz Stuctul dimension 3 m 3m m Dmping tio s.1 % Top-loo mss m s 5.91 tons Stuctul stiness k s 199 kn/m Bse-loo mss m 6.91 tons Dmping coeicient c s 3.38 kn-s/m Steel me Mss lock Lod cell PRB eing Figue 6. Test setup o the PRB-isolted steel me. Displcement (m) Sim. Exp. Isolto Displcement Acceletion (m/s ) Sim. Exp. Supestuctue Acceletion () Isolto displcement () Stuctul cceletion Figue 7. Compison o expeimentl nd theoeticl esponses o the PRB isolted me unde hmonic excittion (equency=1hz; mplitude=1.7m/s). 5.. Compison o expeimentl nd theoeticl esponses To veiy the PRB theoy discussed peviously, Fig. 7 compes the expeimentl nd simulted esponses o the PRB-isolted me unde hmonic excittion, which hs equency o 1 Hz nd mplitude o 1.7 m/s. In the simulted esults o Fig. 7, the pmetic vlues given in Tles 1 nd

8 e used o the PRB nd stuctul systems, espectively. Additionlly, the xil lod P o the PRB system is tken to e the totl weight o the isolted me nd emins constnt. Figs. 7() nd 7() show tht the simulted isolto displcement nd stuctul cceletion mtch vey well with the mesued ones. This indictes tht the theoy nd numeicl method discussed in the pevious sections e pplicle o the nlysis o the dynmic esponse o PRB-isolted stuctul system. Additionlly, it lso conims tht the test dt mesued y the sensos e elile..8.6 PRB FPS PRB FPS Displcement (m) () Isolto displcement Acceletion (m/s ) () Stuctul cceletion Figue 8. Compison o the PRB nd FPS esponses unde the -ield ethquke (El Cento; PGA=.6m/s). Displcement (m) PRB FPS Acceletion (m/s ) PRB FPS () Isolto displcement () Stuctul cceletion Figue 9. Compison o the PRB nd FPS esponses unde the ne-ult ethquke (Impeil Vlley; PGA=.1m/s) Compison o isoltion esponses o PRB nd FPS To evlute the isoltion eiciency o the PRB, in this susection, the mesued time-histoy esponses o the PRB-isolted me is comped to the simulted esponses o the sme me isolted y conventionl iction isoltos, in this cse FPS isoltos. Fo i compison, the simulted FPS-isolted me will she the sme stuctul pmetes listed in Tle, nd lso use the sme gound excittions mesued om the shking tle test. Futhemoe, in the simultion, typicl isoltion peiod o two seconds ws dopted o the FPS system, while the iction coeicient o the FPS is tken to e FPS =.7, which is the sme s the initil equivlent iction coeicient o the PRB (see Fig. 5). Figue 8 compes the time-histoy esponses o the steel me with the PRB nd FPS systems, when oth systems e suject to the El Cento ethquke (the -ield ethquke) with PGA=.6 m/s, while Fig. 9 compes the esponses o the Impeil Vlley ethquke (the ne-ult ethquke) with PGA=.1 m/s. Figue 8 shows tht in the -ield ethquke the PRB nd FPS hve oughly equl pek isolto displcements, ut the PRB induces slightly highe supestuctue cceletion. On the othe hnd, in the ne-ult ethquke, Figue 9 demonsttes tht

9 the PRB eectively suppesses out 55% o the isolto displcement o the FPS, without signiicntly mpliying the cceletion esponse o the supestuctue. 6. CONCLUSIONS In ode to llevite the polem o excessive isolto displcement encounteed in ne-ult ethqukes, vile isoltion system composed o vile-equency ocking eings (VFRB) ws expeimentlly studied in this wok. By popely selecting the geomety o the ocking suce o the eings, the isoltion equency o the VFRB eings ecomes unction o the eing displcement, nd is exclusively detemined y the eing geometic pmetes nd independent o the stuctul mss. To impove the isoltion peomnce unde ne-ult ethqukes, this study poposed sixth-ode polynomil unction to deine the ocking suce o the pototype eings used in the test. Two types o shking tle tests wee conducted o the pototype VFRB system. The conclusions o the tests e summized elow. (1) In the ist shking tle test, igid mss lock isolted y the pototype eings ws tested, in ode to otin the hysteetic digm o the VFRB system itsel without the dynmic eect o the supestuctue. The test esults show tht the expeimentl hysteesis loop mtches ily well with the theoeticl one. This conims tht the deived VFRB theoy is le to cptue the vile hysteetic popety o the eing, nd the VFRB is esile wy to chieve the techniques o pssive vile isoltion. () By popely selecting the coeicient vlues o the six-ode polynomil unction tht deines the eing ocking suce, the pototype eings hve eltively highe initil stiness ollowed y sotening ehvio. Becuse o this mechnicl etue, the test esults show tht s comped to the esponse o FPS system, the VFRB isoltion system is le to eectively suppess the lge isolto displcement induced y stong ne-ult ethquke (PGA=.1 ), while etining equl eduction te on the supe-stuctul cceletion. This indictes tht the VFRB cn e pomising technology o ne-ult seismic isoltion. AKCNOWLEDGEMENT This esech ws inncilly suppoted y the Ntionl Science Council o R.O.C. (Tiwn) though Gnt NSC1-65-M-37-1, nd techniclly suppoted y the Ntionl Cente o Resech on Ethquke Engineeing (NCREE, Tipei). The ist utho is lso gteul to his ome gdute students M. I-Ling Yeh nd M. Shih-Wei Yeh o pocessing the test dt. REFERENCES Jngid, R.S. nd Kelly, J.M. (1). Bse isoltion o ne-ult motions. Ethquke Engineeing nd Stuctul Dynmics. 3:5, Lu, L.Y., Shih, M.H., Chng Chien, C.S. nd Chng, W.N. (). Seismic peomnce o sliding isolted stuctues in ne-ult es. Poceedings o the 7th US Ntionl Coneence on Ethquke Engineeing, July 1-5, Boston, MA, USA. Session AT-. Lu, L.Y., Lee, T.Z., Yeh, I.L. nd Chng, H. (9). Rocking Beings with Vile Fequency o Ne-ult Seismic Isoltion (in Chinese). Jounl o the Chinese Institute o Civil nd Hydulic Engineeing. unde eview, sumitted in Feuy. Lu, L.Y., Lee, T.Y. nd Yeh, S.W. (11). Theoy nd expeimentl study o sliding isoltos with vile cuvtue. Ethquke Engineeing nd Stuctul Dynmics. :1, Povidkis, C.P. (8). Eect o LRB isoltos nd supplementl viscous dmpes on seismic isolted uildings unde ne-ult excittions. Engineeing Stuctues. 3:5, Ngjih, S. nd Nsimhn, S. (6). Smt se isolted enchmk uilding Pt II: Phse I Smple contolles o line isoltion system. Jounl o Stuctul Contol nd Helth Monitoing. 13:-3, Neim, F. nd Kelly, J.M. (1999). Design o Seismic Isolted Stuctues: om theoy to pctice, John Wiley & Sons.