Beneficial effect of soil-structure interaction to structural response derived from two building arrays in New Zealand

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1 Zha, J. (008) Beneficial effect f il-tructure interactin t tructural repne derived frm tw building array in New Zealand Prc. 18 th NZGS Getechnical Sympium n Sil-Structure Interactin. Ed. CY Chin, Auckland Beneficial effect f il-tructure interactin t tructural repne derived frm tw building array in New Zealand Jhn X. Zha GNS Science, Lwer Hutt, New Zealand Keywrd: kinematic interactin, inertial interactin, mdal parameter fr il-tructure ytem ABSTRACT The il ite pectra fr ite clae D and E in the current NZ deign cde impe a ignificant increae in the diplacement demand, between 50 and 300% fr a tructure with a perid f 1.0 r lnger, cmpared with a rck ite (cla A/B) at the ame lcatin. Hwever, fr many tructure n deep r ft il ite, effect f il-tructure interactin may partly ffet the ite amplificatin by mean f a filtering effect, and the rcking / tranlatin f the building fundatin relative t the free-field grund mtin. In thi tudy, reult derived frm building array in New Zealand are preented t prvide quantified reductin in the diplacement demand fr the tructure. 1 INTRODUCTION In a cnventinal apprach fr eimic analyi, the bae f a tructure i aumed t experience the free-field grund mtin, i.e., the bae ha n relative mtin t the free field. Thi aumptin i valid fr a tructure lcated n a rck r very tiff il ite but nt fr a heavy r mderately heavy tructure n a ft il ite. The mtin f the fundatin fr a tructure relative t the free-field are the effect f il-tructure interactin. There are tw kind f iltructure interactin, namely the kinematic and the inertial interactin. Kinematic interactin refer t the averaging effect f a male rigid bdy reting n r embedded in a il ite under a particular wave field. The kinematic interactin can be decribed by, Re[ T k in( γ ω) ( ω)] = γ ω where T k i the Furier pectral rati between the mtin f the rigid fundatin and that f the free-field and ω i the circular frequency. Re[ ] indicate the real part, and Im[ ] indicate the imaginary part f the Furier pectral rati. Parameter γ can be interpreted a the rati f the fundatin length and the apparent velcity fr eimic wave prpagating in the hrizntal directin alng the fundatin lab, and γ 1 i the amplitude cale factr fr the imaginary part. ( γ ω / 4) b in in( γ ω) γ = Im [Tk ( ω)] = γ 1 - c( γ ω) (1a,b,c) Va γ ω γ ω The inertial il-tructure interactin can be etablihed by a implified mdel (with a lumped ma fr each trey) a hwn in Figure 1, where the tructure i munted n tranlatin and rcking il pring and damper with cefficient K uu, K rr, C uu and C rr. The ubcript u dente the tranlatinal directin and r dente the rcking directin. The diplacement f the tructure at the equivalent Figure 1: A il-tructure ytem f a multi-trey tructure munted n il tranlatin and rcking pring and damper. 1

2 Zha, J. (008) Beneficial effect f il-tructure interactin t tructural repne derived frm tw building array in New Zealand height (/3 f the ttal height fr a unifrm hear beam) can be derived a Kuu Krr ω Cuu ω Crr ω h = ω r = ξ h = + ξ g ξ r = + ξ g Me Me he Kuu Krr (a,b,c,d) ω ω ω = + + = + ξ ξ N ξ N ξ N N = + h + r ω N ω ω h ω r ω h ω ω r ω ω h ω r where ω i natural frequency f the fixed-bae tructure, ξ i the material damping rati f the tructure, the ξ g i the material damping rati f the urrunding il, ξ h and ξ r are the radiatin damping rati aciated with the fundatin tranlatin in the hrizntal directin and rcking f the fundatin, repectively. The natural frequency f the il-tructure ytem, ω N, i alway le than ω h and ω r and the damping rati f the il-tructure ytem, ξ N, i uually f imilar rder fr the damping rati f the tructure. The natural frequency f a il-tructure ytem withut fundatin tranlatinal mtin i dented by ω h. The diplacement f the tructure relative t the bae (the defrmatin f the tructure that lead t inter-try-drift) can be lved apprximately frm the fllwing equatin (Wlf 1985, ectin 3.4), ω N i u t ξ ω u t ω u t u t u t T ω U ω e ω t & ( ) + N & N ( ) + N ( ) = & gk ( ) & gk ( ) = k ( ) g ( ) dω & (3a,b) ω 0 where U g i the Furier amplitude f the free-field acceleratin and T k (ω) i alway equal t r le than 1.0. Nte that ξ N i taken a an equivalent vicu damping rati in Equatin (3a). The dt and the duble dt fr diplacement u tand fr differentiatin f u with repect t time, i.e., the velcity and acceleratin in the time dmain. Equatin (3a) ugget that equivalent input grund mtin i that f the filtered grund mtin in Equatin (3b) (alway leading t a reductin in high frequencie) caled dwn further by the quared rati f natural frequency f the il-tructure ytem ver that f the fixed-bae tructure. The benefit f the il-tructure interactin are evident in Equatin (3). BUILDING ARRAYS One f the building array invetigated here i the Gibrne Pt Office building, a 6-trey reinfrced cncrete mment-reiting frame building with a 0.38m thick reinfrced cncrete raft fundatin in the baement. The building ha tw bay in the N44E directin (16.5m) and 10 bay in the S46E directin (50.m) and the building height abve the mat fundatin i 5.5m. The embedment depth f the fundatin i abut.4m. The building i lcated n a ft il ite with abut 40m f recent marine and fluvial ediment abve a ilttne bae. The hear wave velcity f the ite ha been meaured a 98 m/ near the urface, gradually increaing t 40 m/ at a depth f 4m. Three intrument are lcated inide the building almt in the centre f different level f the building. A carpark (free-field) ite i abut 0m away frm the building. Tw cmplete et f earthquake recrd were btained in 198 and The 198 earthquake had a lcal magnitude f 5.1 and an aigned depth f 33 km. The epicentral ditance t the Gibrne Pt Office wa 5 km and the epicentral directin at the building ite wa in N56W. A maximum hrizntal acceleratin f 0.09g wa recrded at the tp flr, 0.04g at the grund flr and 0.06g at the carpark ite. The 1993 (Ormnd) earthquake wa centred at an epicentral ditance f 3 km frm Gibrne Pt Office, and had a mment magnitude f 6. a fcal depth f 37 km. A maximum hrizntal acceleratin f 0.5g wa recrded at the tp flr, 0.14g at the grund flr and 0.6g at the carpark. The building and the il repnded eentially elatically in the 198 earthquake but nnlinear repne pibly ccurred in the 1993 earthquake becaue f apparent reductin in natural perid and tiffne (Zha 1998b). The Vgel building i a 17-trey reinfrced cncrete tructure in central Wellingtn, with tw trey embedded in il. The baement i fully embedded and the lwer grund flr i partially embedded. The average embedment depth i abut 5-6m. The fundatin length i

3 Zha, J. (008) Beneficial effect f il-tructure interactin t tructural repne derived frm tw building array in New Zealand 5.6m in the N0E directin and 3.9m in the N88W directin. The building height frm the tp f the fundatin lab t the rf lab i 59.75m. It ha hear wall, the thickne f which reduce lightly with height and there i an additinal reinfrced cncrete tiffener at bth the baement and the lwer grund flr. The il cmprie cmpletely weathered terrace gravel with a ite cla D in the current New Zealand lading cde. The tpgraphy arund the building ite i quite cmplex and the grund urface ha a gentle lpe in the nrth-uth directin. Sn after cntructin the Vgel building wa intrumented with fur trng mtin accelergraph. In the 1973 Central Nrth Iland earthquake, recrd were btained frm three f the intrument, the lcated in the baement, the 14th flr f the building and a carpark (the free field) abut 50 m away frm the baement intrument. In the 1977 Ck Strait earthquake a cmplete et f fur recrd wa btained. The 1973 earthquake ccurred at a ditance f 40km frm Wellingtn with a depth f 173km and mment magnitude f 6.6. A maximum acceleratin f 0.10g wa recrded at the 14th flr, 0.03g at the baement and 0.04g at the carpark. The 1977 M w =6.0 earthquake wa centred 64km away frm Wellingtn at a depth f 33km. A maximum acceleratin f 0.17g wa recrded at the 14th flr, 0.07g at the baement and 0.08g at the carpark. The effect f high-frequency attenuatin f the fundatin mtin wa reprted by McVerry (1984). 3 KINEMATIC INTERACTION Figure hw tranfer functin, which are the Furier pectral rati between the tranlatin mtin f the fundatin and the free-field mtin btained frm the carpark fr the Gibrne Pt Office building and the Vgel building, fr tw et f earthquake. The pectral rati at frequencie ver 6 Hz are maller than 0.5, i.e., the grund mtin amplitude in the Frequency dmain at the fundatin lab are le than 50% the in the free field. At lw Figure : Tranfer functin derived frm recrded accelergram by uing ytem identificatin methd (Zha 1998), fr the Gibrne Pt Office building, (a) N44E, (b) S46E, fr the Vgel building, (c) N0E and (d) N88W frequencie, uch a 1.0 Hz, the Furier pectra f the fundatin mtin are imilar t the f the free-field. The tranfer functin i a functin f fundatin dimenin and the prpagatin velcity f eimic wave in the directin alng the fundatin lab (Equatin 1). The tranfer functin differ mderately fr grund mtin frm different earthquake, but their general trend in the variatin with increaing frequency are very imilar. The attenuatin f highfrequency mtin hwn in Figure reduce the high-frequency flr acceleratin f the 3

4 Zha, J. (008) Beneficial effect f il-tructure interactin t tructural repne derived frm tw building array in New Zealand building and reduce ptential damage t nn-tructural element and cntent hued by the building. Fr frequencie up t Hz, the effect f kinematic interactin ha little effect n the fundatin mtin and therefre will have little effect n the building bae hear and verturning mment fr bth building (Zha 1998). Figure 3 cmpare the repne pectra f the grund mtin at the free-field and at the building baement lcatin. The high-frequency attenuatin f the fundatin mtin due t kinematic interactin i evident, with the hrt perid peak pectra f the fundatin mtin being reduced t nearly 50% the f the free-field grund mtin. At perid ver 0.6, the repne pectra f the fundatin and free-field mtin are very imilar. Figure 3: Cmparin f repne pectra at free field and building baement 4 INERTIAL INTERACTION (ROCKING AND FOUNDATION TRANSLATION) When a building at a deep/ft il ite experience a eimic excitatin, the fundatin f the building will tranlate and rck relative t the free field grund mtin. The tructural diplacement due t fundatin tranlatin and rcking d nt induce inter-trey drift and therefre d nt need t be accunted fr in the deign f a tructure. Hwever, the diplacement due t the fundatin mtin relative t the free field i part f the diplacement demand f the free-field mtin. In anther wrd, the fundatin mtin (including rcking) relative t the free-field mtin effectively reduce the damaging diplacement demand n the tructure a hwn in Equatin (3a) where the effective excitatin i the free-field grund mtin caled by ω ω. N / Table 1 hw the natural frequencie, damping rati and the frequency rati. Nte that the natural frequency f the il tructure ytem wa reduced frm 1.8Hz in bth directin fr the fur recrd dicued abve in the 198 event t 0.93Hz in the N44E directin and t 1.0Hz in the in the S46E directin in the 1993 event, uggeting pible nnlinear repne in the tructure and the urrunding il becaue f trng haking. The fundatin tranlatin frequencie derived frm the 1993 event are le than 0.5 time the in the 198 event, a pible reult f il nnlinear repne. The value derived fr the Vgel building pibly have a cniderable errr band a the ignal/nie rati in the baement recrd may be lwer than.0 (Zha 1998a). 4

5 Zha, J. (008) Beneficial effect f il-tructure interactin t tructural repne derived frm tw building array in New Zealand The ditributin f the accelergraph in bth building de nt allw etimatin f the fundatin rcking frequencie and it i nt pible t derive the fixed-bae natural frequency f the building. Zha (1998b) etimated the rati between K rr and K uu fr the Gibrne Pt Office Building and the fixed-bae natural frequency in a range f Hz in the N44E directin fr the 198 event, Hz in the ame directin fr the 1993 event. The reductin f the natural frequencie fr the fixed bae building i intuitively cnitent with the expected tructural nnlinear repne. Anther methd fr etimating the upper bund f the fixed bae natural frequency i t ue the deep trugh in the tranfer functin between the recrded fundatin and the free-field mtin, a illutrated in Figure 4 where the frequency f the firt trugh (after the natural frequency ω N ) i 1.4Hz. Fr an ideal mdel that ha a male rigid fundatin, the frequency f thi trugh i ω h. Hwever, fr a mdel with a bae ma, the trugh tend t ccur between the fixed bae frequency ω and ω h, thu 1.Hz wuld be an adequate etimate fr the fixed-bae building in the N44E directin in the 1993 event. The cale factr t cmpute the diplacement demand ω ω in Equatin (3a) i N / Figure 4: Tranfer functin between mtin f fundatin and free field Table 1: Mdal parameter derived frm earthquake recrd Gibrne Pt Office building 198 Earthquake 1993 Earthquake N44E S46E N44E S46E ω N /π (Hz) ξ N (%) ω h /π (Hz) Vgel building 1973 earthquake 1977 earthquake N88W N0E N88W N0E ω N /π (Hz) ξ N (%) ω h /π (Hz) Nte: ω h i derived frm the effective mdal participatin factr frm Zha (1998b) 0.6, i.e., the actual damaging diplacement demand fr the Gibrne Pt Office building during the 1993 earthquake i nly 60% that f the diplacement demand f the carpark recrd in the N44E directin. In the S46E directin, fundatin rcking i negligible becaue f the large fundatin length in thi directin. The natural frequency f the fixed-bae tructure i very cle t the natural frequency f the il-tructure ytem. In the 198 event, ω wa reprted t be Hz / (Zha 1998b) leading t ω N ω = , uggeting that the inertial interactin i negligible, pibly becaue the extent f il nnlinear repne i mall in the 198 event. Becaue f the pible lw ignal/nie rati f the baement recrd frm the Vgel building, the fixed-bae frequencie will nt be etimated here. A final nte i that the diplacement demand that caue inter-trey drift cannt be cmputed by uing the grund mtin recrded at the fundatin f a tructure and a cnventinal tructural mdel that de nt allw rcking mtin f the rundatin. In thi cae, the 5

6 Zha, J. (008) Beneficial effect f il-tructure interactin t tructural repne derived frm tw building array in New Zealand hrizntal tructural diplacement that caue tructural inter-trey diplacement can be cmputed frm ω h t ω h ω h u& ( t) + ξ ω h u& ( t) + ω h u ( t) = u& ( t) ξ = ξ + ξ h h r (4) ω ω ω r t where u& i the recrded acceleratin in the hrizntal directin. Nte that ω h i alway le than r equal t ω. Zha (1998b) reprted ω h /π=0.97 Hz fr the Gibrne Pt Office building fr the N44E cmpnent during the 1993 earthquake and the cale factr / ω h ω =0.65 can be derived. The cale factr ω h / ω i nly marginally larger than ω ω, uggeting that the majr fundatin mtin i the rcking in the N44E directin. N / 5 CONCLUSIONS The mdal parameter f the Gibrne Pt Office building and the Vgel building in Wellingtn are preented. Effect f kinematic il-tructure interactin (filtering f free-field grund mtin by the fundatin lab) and inertial interactin (tranlatin and rcking f the fundatin relative t the free field) are ignificant. At hrt perid, the kinematic interactin reduce the hrt perid mtin f the fundatin ignificantly and the hrt-perid flr acceleratin fr the building, with a ptential benefit t reduce the hrt perid repne f nn-tructural element and the cntent hued by the building during very trng grund haking. During the 1993 earthquake, the inertial interactin fr the Gibrne Pt Office building in the N44E directin reduce the diplacement demand (that caue inter-trey drift) by a much a 40% f the free-field recrd. The rcking mtin f the fundatin in the N44E directin i identified a the majr cmpnent f the inertial interactin. The il nnlinear repne i al a pible factr fr the trnger inertial interactin in the 1993 earthquake fr thi building. The extent f the inertial interactin i prprtinal t the quared frequency rati between the natural frequencie f the il-tructure ytem and that f the fixed-bae building and the il nnlinear repne may lead t the decreae f the il-tructure ytem. Therefre the effect f inertial interactin may increae with increaing haking level even when ignificant nnlinear repne develped in the tructure. ACKNOWELEGEMENT The reearch preented here wa upprted by the New Zealand Fundatin fr Reearch Science and Technlgy. The authr wuld like t thank Dr. Jim Cuin and Dick Beetham fr their review f the manucript. REFERENCES McVerry, G.H. (1984) Cmparin f remte ite and baement recrd a excitatin f the Vgel building, Bulletin f New Zealand Natinal Sciety. fr Earthquake Engineering. 17, 3-14 (1984). Wlf, J.P. (1985) Dynamic il-tructure interactin, Prentice-hall, Englewd Cliff, New Jerey Zha, J.X. (1998a) Etimating kinematic interactin f raft fundatin frm earthquake recrd and it effect n tructural repne, Sil dynamic and earthquake engineering, 17(): Zha, J.X. (1998b) The etimatin f tructural mdal parameter frm the repne f the Gibrne Pt Office building in recent earthquake. Bulletin f the New Zealand Natinal Sciety fr Earthquake Engineering, 31(1):

7 Zha, J.X. (1998b) The etimatin f tructural mdal parameter frm the repne f the Gibrne Pt Office building in recent earthquake. Bulletin f the New Zealand Natinal Sciety fr Earthquake Engineering, 31(1):

Name Student ID. A student uses a voltmeter to measure the electric potential difference across the three boxes.

Name Student ID. A student uses a voltmeter to measure the electric potential difference across the three boxes. Name Student ID II. [25 pt] Thi quetin cnit f tw unrelated part. Part 1. In the circuit belw, bulb 1-5 are identical, and the batterie are identical and ideal. Bxe,, and cntain unknwn arrangement f linear