13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 2004 Paper No. 3480

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1 3 th World Confrnc on arthquak nginring Vancouvr, B.C., Canada August -6, 24 Papr No. 348 SISIC WAV NRY VALUATION IN SURFAC LAYRS FOR PRFORANC-BASD DSIN Takaji KOKUSHO, Ryu-ichi OTOYAA 2, Shogo ANTANI 2 and Hiroshi OTOYAA 2 SUARY nrgy flow of sismic wavs obsrvd during th 995 Hyogo-kn Nambu arthquak in vrtical array sits is calculatd by assuming vrtical propagation of SH wavs in surfac layrs. Wav nrgy flow in a 2-layrs systm is also invstigatd basically. Th major findings ar; () Upward wav nrgy gnrally tnds to dcras as it gos up from th bas layr to th ground surfac, (2) A gnral prcption that soft soil sits ar pron to havir damag may not b xplaind in trms of upward nrgy, bcaus larg damping ratio tnds to cancl nrgy storag ffcts by rsonanc if it vr occurs. (3) Th wav nrgy, which is dirctly rlatd with inducd strain in suprstructurs, can play a ky rol for th prformanc-basd dsign. For that purpos, dsign sismic motion should also b dfind in trms of wav nrgy. Ky Words: Sismic wav nrgy, SH wav, Impdanc ratio, Damping, Prformanc-basd dsign INTRODUCTION Convntional sismic dsign has bn basd on inrtia forc givn by acclration or sismic cofficints. Historically this forc-basd dsign mthod has long bn usd to dat. In prformanc-basd dsign mthods incrasingly mployd rcntly, th dgr of structural dformation is a targt to valuat rathr than th safty factor against ultimat failur. It has bn rcognizd incrasingly that acclration may not b an appropriat paramtr not only for dformation valuation but also for sismic damag valuation in gnral. or and mor strong. Profssor, Chuo Univrsity, Tokyo, Japan, mail: kokusho@civil.chuo-u.ac.jp 2. x-graduat studnt, diito

2 acclrograms xcding hav bn obtaind in rcnt yars without any significant damag at all such as in Tarzana during 994 Northridg arthquak, in Hokkaido during 23 Tokachi-oki arthquak, tc. Vlocity is incrasingly usd in plac of acclration bcaus it is blivd to closly connctd with nrgy. Thn why don t w dirctly us wav nrgy in sismic dsign? In th first part of this papr, nrgy flow of sismic wavs obsrvd during th 995 Hyogo-kn Nambu arthquak (somtims calld as th Kob arthquak) in vrtical array sits is calculatd. Accumulatd wav nrgy, nrgy flow rat and its dissipation in surfac layrs ar calculatd from vrtical array rcords by assuming vrtical propagation of SH wavs in surfac layrs. Thn, 2-layrs systms with variabl impdanc ratios and damping ratios ar studid for bttr undrstanding on nrgy flow and dissipation mchanism. Prformanc-basd dsign using th wav nrgy is finally proposd basd on th analytical rsults. WAV NRY VALUATION BY VRTICAL ARRAY RCORDS It is wll rcognizd sinc th pionring work by Kanai [] that th major portion of a sismic rspons of a ground can b valuatd with a simpl on-dimnsional modl in which SH wav is postulatd to travl only vrtically. Basd on th postulat, th nrgy can also b assumd to propagat vrtically. A wav nrgy incrmnt transmittd vrtically by th SH-wav through a unit ara in a tim incrmnt t is xprssd as; 2 du = k + = ρ s V t dt whr ρ = soil dnsity, V s = wav vlocity and du dt = particl vlocity of th soil. Not that th wav nrgy is shard 5% by kintic nrgy k and 5% by strain nrgy dfin th tim drivativ of th nrgy 2 (). Lt us du = t = d dt = ρv s (2) dt and nam it nrgy flow rat. If a tim intrval for a sismic motion to go through a point is t = t t2, th accumulatd nrgy is xprssd as 2 t2 du = 2 = ρ s t t ( t t) V dt dt (3) Not that du dt in qs.() and (2) is th particl vlocity not dirctly of a rcordd motion but of travling wav in on dirction. Thrfor it is ssntial to sparat a masurd motion at a point into upward and downward wavs in ordr to valuat th individual nrgis. If a sit consists of a st of horizontal soil layrs and th soil bhavs as a linar matrial, upward and downward propagating wavs at any point can b calculatd basd on th multipl rflction thory [2] from which th flow of th nrgy thr is radily valuatd. Howvr, if th soil xprincs

3 strong nonlinarity du to strain-dpndncy or liqufaction during dstructiv arthquaks, such a linar modl no longr holds. Th sismic motions ar vry much influncd by th soil nonlinarity xhibitd nar th surfac. Bcaus a lot of nrgy has alrady bn lost on th way whn th sismic wav arrivs at th surfac, it is hard to valuat th nrgy from th surfac rcord. In a vrtical array systm, sismic motions in a dpr ground ar availabl. It has alrady bn dmonstratd that th dpr th soil is, th mor soil bhavs as a linar matrial vn during strong arthquaks [3]. If th upward and downward wav componnts can b sparatd from sismic rcords at som dpr lvl whr th sismic wav is lss contaminatd by soil nonlinarity, th nrgy flow can b valuatd mor rliably [4]. A harmonic SH wav with an angular frquncy, ω, is xprssd as i( ωt+ kz) i( ωt kz u = A + B ) (4) whr, u is displacmnt in th horizontal dirction, t and z is tim and vrtical axis positiv in th downward dirction, rspctivly, and, A and B ar constants. Th first and scond trms corrspond to upward and downward componnts, rspctivly. Th constant k is th wav numbr givn by ρω ρω k = = * + i (5) Sismogragh Layr No. round whr + i is a complx shar stiffnss of soil. A surfac Hr th soil damping is assumd as non-viscous as in s s 2 Surfac gotchnical nginring practic. As shown in Fig., layr th on-dimnsional soil modl consists of a st of B A horizontal soil layrs numbrd from to n. Th m B m m u d m th layr has th thicknss, h m, th soil dnsity, r m, th complx stiffnss, m *, th wav numbr, k m, C th constants A m, B m and so on. Taking a local A n n B n d coordinats z downward from th uppr boundary for u z th m th layr, th following rcursion formula on A m, Bas layr B m can b obtaind basd on th agrmnt of dformation and strss at th boundary btwn m th Fig. nrgy flow in vrtical array systm and (m+) th layrs. é * * * * km m kmm ikmh k m m m km ù m - ikmhm * * ì ï Am+ ü ï 2km+ m+ 2km+ m+ ì ï Amï ü ì Am ét ù = = ï ü ï í ý í ý * * * * m+ Bm+ k B ë ûí ý ïî ïþ m m kmm ikmh k m m m km m ik m B m mh ïî ïþ m ïî ïþ * * 2km+ m+ 2km+ êë m+ úû (6) Th matrix in q.(6) is dnotd hr as ét m + ù ë û. Sismic rsponss ar givn at th top of th m th and n th layrs, at Point B and C in Fig. as

4 iwt iwt iwt iwt um = Um = ( Am + Bm), un = Un = ( An+ Bn) (7) Th sparation of upward and downward wavs bcoms possibl basd on th multipl rflction thory. Basd on q.(6), q.(8) can thn b drivd corrlating th constants A m, A n and B m, B n in th two layrs. An Am Am = [ Tn][ Tn ] [ Tm+ ] Tn, m+ B K = n B m B (8) m Th 2 by 2 matrix in q.(8) is xprssd hr as ét T ù é 2 T ù ë nm, + û = êt 2 T ú 22 ë û Thn, by using qs.(7) to (9), th following quation can b drivd. ì ï Unü ï ét + T2 T2 + T22 ùì ï Amü ï ì Am P ï ü ï í ý= í ý= é ù nm, + Um B ë ûí ý () ï ê ú î ïþ ë ûî ï m ïþ î ïbmþ ï Consquntly, A m and B m can b obtaind by th quation; ì ï Amü ï - ì Un P ï ü ï ì é ù í ý= nm, + B ë û í ý, ï Anü ï - ì Un Tnm, P ï ï ü í ý= é ùé ù + nm, + ïî m ïþ î ïumþ ï B ë ûë û í ý () ïî n ïþ ïîum ïþ q.() givs th amplituds for a harmonic motion with th angular frquncy, w. In ordr to obtain th rspons to irrgular sismic motions, a rcordd motion is xprssd as a suprposition of harmonic wavs with diffrnt angular frquncis by using th complx Fourir sris. Thn th Fourir sris ar incorporatd togthr with q.() to comput tim historis (Schnabl t al. 972) of th upward and downward componnts. Wav nrgis or nrgy flow rats can b calculatd from th vlocity tim historis by q.(2) or q.(3). On th othr hand, th upward nrgy at a ground surfac (Point A in Fig.) can b calculatd by substituting a half of th vlocity tim history into du dt in q.(2) or (3). (9) Vrtical array rcords usd in th analysis wr obtaind in Port Island in Kob city (PI), Rsarch Institut of Kansai lctric Powr Company [KPCO] in Amagasaki city (SK), KPCO powr plant in Takasago city (TKS) and KPCO transformr station at Kainan-ko in Wakayama city (KNK). PI is just nxt to th causativ fault, SK is about 2km and KNK is about 65km far from it. In Fig.2, th soil profils of th 4 sits ar shown togthr with th sismograph installation lvls. Thr to four sismographs ar installd btwn th ground surfac and th dpst lvl of 84 to m. In th sam charts, profils of S-wav vlocitis (Vs) masurd by S-wav logging tsts ar shown togthr with Vs and damping ratios (D) back-calculatd from th main shock rcords. Dtails on th back-calculation ar availabl in othr litraturs [3]. Acclration rcords in two horizontal dirctions at th dpst (Point C) and th scond dpst lvls (Point B) shown in Fig.2 ar utilizd to valuat th nrgy flow at th scond dpst lvl. In th analysis, soil proprtis btwn ths two lvls, whr soil nonlinarity is lss pronouncd than in th surfac layr, ar usd. Th dgr of soil nonlinarity xhibitd in th vrtical array sits during th main shock was alrady back-calculatd by th invrsion tchniqu [3]. Th

5 (a) PI Damping ratio D (%) L-m A WL S L-4.m L-6.4m 2 B S L-32.4m 4 S ) (m 6 D pth 8 C L-83.4m Sismograph S-wav vlocity Vs (m/s) (c) TKS A B Damping ratio D (%) L-m 5 5 WL SF L-2.5m L-25m 2 ) (m 4 S D pth 6 8 C L-m Sismogragh S-wav vlocity Vs (m/s) (b) SK Damping ratio D (%) A L-m SF WL L-2.m B SF L-25m 2 ) (m 4 S D pth 6 8 C L-97m Simograph S-wav vlocity Vs (m/s) (d) KNK Damping ratio D (%) L-m A S WL L-2.m S Vs-initial 2 B Vs-inv.NS S L-25m Vs-inv.W C ) 4 D-inv.NS SF (m D-inv.W 6 F D pth 8 Rock C L-m 2 Simograph S-wav vlocity Vs (m/s) Fig.2 Borhol log and profils of masurd or back-calculatd Vs and damping ratio at 4 vrtical array sits for 995 Hyogokn Nambu arthquak. back-calculatd S-wav vlocity dcrasd by 5 to 8% of th initial valus in PI, whil Vs blow Point B changd by lss than 2% vn in PI. In othr sits th nonlinarity was lss pronouncd than in PI in dpr part in particular. In th nrgy valuations, th back-calculatd S-wav vlocity and damping ratio indicatd in Fig.2 ar assignd to th soil proprtis btwn Points B and C, and also at Point A. Th soil dnsity is stimatd from th soil typ and th ground watr lvl shown in th soil profil. Th vrtical array rcords usd in th analysis wr alrady corrctd for sismograph installation rrors dtctd by th maximum cohrnc analysis [5]. In PI, th horizontal acclration rcords convrtd to th major principal axis (in which th largst acclration occurs) and th minor principal axis ar usd, whil, in othr thr sits, rcords in NS and W dirctions ar usd. Acclration rcords at th ground surfac and th two dpr lvls ar transformd into frquncy spctra by th FFT tchniqu. Th low frquncy portion of th spctra (f<.hz) is thn cut off to rmov a long priod drift basd on th assumption that th nrgy contribution for th frquncy lowr than.hz may b ngligibl.

6 ANALYTICAL RSULTS AT 4 SITS Figs.3 to 6 show analytical rsults in th major principal dirction in PI and in NS dirction in othr 3 sits. In ach figur, th top chart indicats tim-historis of nrgis and th scond to fourth charts rprsnt vlocity tim historis of upward and downward wavs at Points A, B and C, rspctivly. Th nrgy tim historis ar drawn for upward nrgis at Points A, B and C, downward nrgis and thir diffrncs at Points B and C. All nrgis ar in KJ/m 2 corrsponding to th amount of sismic wav nrgy passing through a unit ara of m 2. As shown in Fig.3 for th major principal axis of PI, th upward nrgis within th first two cycls of strong acclration until t=6.3 s. Th final valu of u rmarkably incras u at th dpst lvl (Point C; L-83.4m) amounts to 35 kj/m 2 as a scalar sum of th nrgis in th major and minor principal axs. This is quivalnt to th nrgy givn by th drop of a mass of on ton from th hight of 3 m onc in vry squar mtr. At L-32.4 m (Point B), u, which shows an almost idntical tim-dpndnt chang, is about 8% of Point C. At th ground surfac (Point A), th upward nrgy u is about 2% of Point C, indicating a clar dcrasing trnd of upward nrgy with dcrasing dpth. It is notd that u and d show monotonic incras bcaus thy ar th cumulativ nrgy transportd by on-dirctionally propagating wavs. In contrast, th diffrnc ( u - d ) indicats th nrgy balanc in th soil layrs abov a givn lvl and hnc shows both incras and dcras. Th dcras in ( u - d ) implis that th nrgy tmporarily stord in th surfac layrs rturns back to dpr ground. With som small fluctuations, - ) tnds to climb up to a final valu, ( u d indicating that th nrgy dissipation in th surfac layrs is dominantly larg compard to th nrgy storag ffct at PI sit. Th tim history of ( u - d ) riss to 75% of th final valu in lss than two cycls in th major sismic motion. It has bn dmonstratd that during this intrval th surfac soil actually nrgy (kj/m 2 ) u ( s ), d, u - d L -m L-32.4m,, L-83.4m,,.9.6 L-m U p,d ow n L-32.4m U p, D ow n L-83.4m Up, D ow n Tim (s) Fig.3 Tim-historis of nrgy (top) and particl vlocitis (bottom) at PI sit.

7 liqufid by mans of an idntification analysis in tim domain using th sam vrtical array rcords [6]. Thrfor, this rapid ris in ( u - d ) at L-32.4 m sms to rflct th nrgy loss by th liqufaction in th surfac soil as wll as that by th soil nonlinarity of clay and alluvial sand abov that lvl. Th valu ( u - d ) rachs to a final valu at t=7 s, which is idntical with th dissipatd nrgy in th surfac layrs, w. This amounts to 55 kj/m 2 at L-32.4 m in th two dirctions and about 65% of th corrsponding upward wav nrgy, u at th sam lvl. Similar rsults for SK sit in th NS dirction ar shown in Fig.4. Th total upward nrgy at L-97m adding th NS and W dirction is 83kJ/m 2 at t=5s, only 27% of that at L-83.4m in PI sit. Th upward nrgy u at L-25m (Point B) and at th surfac (Point A) valuat about 9% and lss than 2%, rspctivly, of u at L-97m (Point C), indicating again th clar dcrasing trnd of upward nrgy with dcrasing dpth. Th valu u obviously incrass until t=25 s, whil ( - ) shows rapid incras until t=5 s and stays almost constant with small fluctuations aftr that. Considring a low possibility of liqufaction in this sit judging from th soil condition, this incras sms to rflct th hystrtic nrgy dissipation du to a nonlinar strss vrsus strain rlationship in non-liqufid soils during strong shaking. Aftr t=5s, th incrasing rat of ( u - d ) bcoms minimal, whil u and d individually still kp rising with almost th sam rat. u d nrgy (kj/m 2 ) u ( s ), d, u - d L-m L-24.9m,, L-97m,,.2. L-m. -. Up,Down L-24.9m. -. Up, Down L-97m. -. Up, Down Tim (s) Fig.4 Tim-historis of nrgy (top) and particl vlocitis (bottom) at SK sit. nrgy (kj/m 2 ) u ( s ), d, u - d L -m L-25m,, L-m,, L-m Up, D ow n Tim (s) L-m Up,Dow n L-25m Up, D ow n Fig.5 Tim-historis of nrgy (top) and particl vlocitis (bottom) at TKS sit.

8 Th rsults of TKS sit in NS dirctions ar shown in Fig.5. At this sit, u at th surfac (Point A) is again much smallr than th dpr lvls at L-25 m (Point B) and L- m (Point C) dspit that th amplitud of th vlocity tim history is vidntly largr at th surfac. ( u - d ) at L- m approachs to an almost constant valu at t=2.5 s whil u and d rapidly incras thraftr. Th valu - ) at L-25 m shows a ngativ valu in ( u d th lattr part of th tim history probably du to rrors involvd in soil modling. Th rsults for KNK sit in th NS dirction ar shown in Fig.6. A rmarkabl diffrnc xists U p, D ow n in this sit in th vlocity amplitud btwn L-25 m and L- m in both dirctions on Tim (s) account of th big diffrnc in th impdanc btwn th bas rock of Vs=63 m/s and th Fig.6 Tim-historis of nrgy (top) and particl vlocitis (bottom) at KNK sit. ovrlying soil layr as shown in Fig.2. Th upward or downward nrgy incrass with a highr rat until t=7s or t=23s and thn kps constant or slowly incrass aftr that. In a good contrast with th prvious 3 sits, th upward nrgis at L- m (Point C), L-25 m (Point B) and L- m (Point A) ar not so diffrnt to ach othr dspit th aformntiond diffrnc in wav amplitud. In this sit, too, ( u - d ) stops rising at t=4 s dspit th sustaind incrass in u and small compard to u, and th ratio d thraftr. Th dissipatd nrgy u w is vry w / u is much lowr than that in th prvious thr sits. This indicats that th sismic motion causd minimal nonlinarity vn in th uppr layr in this sit, as was also dmonstratd by th invrsion analysis [3], rsulting in a small nrgy loss in th surfac layr and a larg nrgy rturn into th dpr ground. In most of th nrgy valuations dscribd abov, th incrasing trnd in ( u - d ) almost stops in th middl of th rcords dspit that u and d ar still incrasing. Th momnt whn ( u - d ) sms to stop its incras is pointd out by th arrow mark in Figs. 4 to 6. It may b notd that, aftr th arrow marks, th vlocity tim historis in th upward and downward dirctions bcom almost idntical in trms of th amplitud and sm to includ longr priod motion than bfor. Ths obsrvations sm to imply that surfac wavs bcom dominant in th lattr part of th rcords, in which th wav nrgy propagats horizontally. Up to that tim, th wav nrgy may b assumd to propagat ssntially in th vrtical dirction as th SH wav. Consquntly, th accumulatd nrgis ar all calculatd up to ths points to b usd in th latr nrgy analyss. nrgy (kj/m 2 ) u ( s ), d, u - d L-m L-25m,, L-m,, L-m Up,D own L-25m Up, Dow n L-m

9 NRY FLOW AT 4 SITS Fig.7 shows th nrgy flow rat pr scond at thr dpths in th principal axis of PI sit calculatd from th accumulatd nrgy tim historis indicatd in Fig.3. Th upward nrgy flow rats = d dt ar vry variabl with tim comprising multipl paks which corrspond to th stpr gradints of th tim history of cumulativ nrgis and hnc rflct wav form charactristics. Th gratr th dpths, th highr th flow rat paks and th arlir thy appar. Fig.8 indicats th rlationships btwn th cumulativ valu or maximum flow rat of upward nrgis vrsus th dpth obtaind by similar calculations at th 4 sits. Th nrgis in th horizontal axis ar xprssd in th logarithmic scal indicating that thr xists grat diffrnc in upward nrgis among th 4 sits. It should b notd that both th cumulativ nrgy and th nrgy flow rat rduc drastically as thy approach to th ground surfac xcpt in KNK sit whr th sismic shaking was mildr without significant soil nonlinar ffct. Lt us thn compar th surfac nrgis s or dissipatd nrgis w valuatd at Point B with th damping ratios in th corrsponding sits. Hr, th damping ratios in individual sublayrs, which wr back-calculatd in a sparat invstigation by Kokusho t al. [3], ar avragd by multiplying th wight of thicknss of ach sublayr shallowr than Point B of Fig.2. In Fig.9, th nrgy ratios s u ar plottd vrsus damping ratios D with opn symbols in th two dirctions at th 4 sits. It may wll b assumd dspit som data /s) 2 J / m ( k o w f l y g r n u82.4 u Tim (s) Fig.7 Tim-historis of nrgy flow rat at PI sit. ) ( m h pt D nrgy flow d/dt (kj/m 2 /s) or Accumulatd nrgy (kj/m 2 ).2 a t r PI s/u w PI ds/du l o f u SK s/u..8 SK ds/du x m a n d a TKS s/u.6 TKS ds/du o r s KNK s/w g y n KNK ds/du r.4 w n b t.2 o f o i R a t Damping ratio D (%) Fig.9 Accumulatd nrgy and nrgy flow rat vrsus optimizd damping ratio at 4 sits. s PI d/dt PI SK d/dt SK TKS d/dt TKS KNK d/dt Fig.8 Distributions of accumulatd nrgy and nrgy flow rat along dpth at 4 sits. KNK

10 scattrs that th ratio of surfac nrgy s to th upward nrgy u at Point B dcrass with incrasing avragd damping ratio as approximatd by th thin curv. Almost th sam trnd can b rcognizd for th ratios of th nrgy flow rats plottd with th closd symbols in th sam figur. In Fig., th nrgy ratios w u ar compard with th avragd damping ratios, whr w and u ar th dissipatd nrgy in th surfac layr shallowr than Point B and th upward nrgy at Point B, rspctivly. / u w o i t a r y g r n Damping ratio D (%) Th incrasing trnd of w u with incrasing damping ratio may b approximatd by th thin lin. Th dissipatd nrgy in th surfac layr amounts to 7-5% of th upward nrgy at th bas in th nar-fault sit PI, whil it is around 2% or lss in th rmot sit KNK, indicating that th rst of th upward nrgy rturns to th dpr arth again PIw/u SKw/u TKSw/u KNKTw/u Fig. Dissipatd nrgy vrsus optimizd damping ratio at 4 sits. Th combination of Figs.9 and indicats that, in a sit with smallr shaking, dissipatd nrgy is small and a larg prcntag of surfac nrgy coms up to th ground surfac. In a nar-fault sit with strong shaking, mor than a half of th upward nrgy is lost by soil damping insid th surfac layr and only a small portion arrivs at th surfac. Not that th nrgy ratio s u or s u is much lowr than. xcpt in KNK, indicating that th surfac nrgy tnds to b lowr than th upward nrgy at th bas in thos sits with strongr shaking and hnc with largr soil damping. NRY FLOW ANIS IN 2-LAYRS SYST In ordr to undrstand what mchanism controls th nrgy flow in layrd ground undr th assumption of on-dimnsional propagation of th SH wav, a simpl study on a 2-layrs systm has bn carrid out as dpictd in Fig.. Th thicknss of th surfac layr is H=3m and th soil dnsity in th surfac and bas layrs ar ρ = ρ 2 =2. t/m 3. Ths valus ar chosn so that th two-layrs modl can roughly rprsnt th surfac layr rspons in th vrtical array sits. S-wav vlocity in th bas layr is kpt constant as Vs 2 =33 m/s whil that in th surfac layr Vs is z, r,vs r, As 2,Vs2 A 2 s Surfac layr A p u As B B 2 d Bas layr s Fig. Two-layrs modl for D propagation of SH wav. H

11 paramtrically varid from 33m/s to 3m/s. Th impdanc ratio α = ρvs ρ2vs2 corrspondingly varis from unity to.99. Th damping ratio in th bas layr is assumd D 2 = whil that in th surfac layr is varid, D =-4%. Th input motion shown in Figs.2(a) which is th sam as th upward componnt in th principal axis in PI sit is givn at th bas layr. Th Fourir spctrum of th input motion shown in Fig.2(b) is compard with th transfr functions of th two-layrs systm shown in Fig.2(c),calculatd for diffrnt Vs with th damping ratio D =5%. Not that th dominant frquncy of th input motion is about.8 Hz although th spctrum has svral pak frquncis around thr. A cc.(m /s 2 ) Fourir spc.(gal sc) Spc.ratio (a) 9 (c) 6 3 P I L-83.4m (Incidnt w av) Tim (sc ) (b) Input w av Impdanc ratio α Frquncy (H z) Fig.3 shows th ratio of surfac nrgy s to th upward nrgy u at th bas in th vrtical axis vrsus th impdanc ratio α in th horizontal axis calculatd from th paramtric study dscribd abov. For D =, s taks a maximum valu whn α =.82 du to th rsonant ffct as indicatd from Figs.2(b) and (c). Howvr, th rsonant ffct diminishs as D bcoms largr, and s monotonically dcrass as α dcrass for D >%. In Fig.4, th flow rat of th upward nrgy ds dt is takn in plac of th accumulatd nrgy in th vrtical axis. In this cas, too, th flow rat shows a monotonic dcras with dcrasing impdanc ratio for D %. This indicats that th softr th surfac soil, th smallr th nrgy or its flow rat bcoms undr high soil damping in th surfac layr. Fig.5 dpicts th ratio of dissipatd nrgy w to th upward nrgy Fig.2 Acclration(a), Fourir spctrum(b) and spctrum ratio(c) usd in th analysis... Im pdanc ratio α=ρ Vs /ρ 2 Vs 2 u at th bas vrsus α obtaind from th sam paramtric study. Whil w = quit naturally for D =, w taks th maximum valu whn α =.82 undr highr damping ratios bcaus th mor wav nrgy is trappd and dissipatd in th surfac soil du to th rsonanc ffct. nrgy ratio s/u D =% 2.5% 5.% % 2 % 4 % Fig.3 Surfac nrgy vrsus impdanc

12 According to Figs.3, 4 and 5, it may b said that th sismic wav nrgy at th ground surfac is mostly smallr in soft soil sits than in stiff soil sits during dstructiv arthquaks, bcaus th soil damping in th surfac layr tnds to b gratr du to strong shaking particularly in soft soil sits. This viw sms to disagr with widly accptd prcption that arthquak damag is largr in soft soil sits. In discussing this problm, it is ssntial to distinguish gotchnical and structural aspcts in arthquak damag. Ndlss to say, gotchnical damag tnds to concntrat in soft soils. During th 923 Kanto arthquak, largr numbr of woodn houss ar said to hav collapsd in down-town soft soil ara than Plistocn stiff soil ara in Tokyo and triggrd grat firs killing many popl. Howvr, during 995 Kob arthquak on th contrary, woodn houss wr damagd mostly in stiff soil ara and littl shaking damag of suprstructurs including woodn houss occurrd in soft soil aras along th coast. In what follows, som considrations ar mad how th sismic wav nrgy is rlatd to structural failurs and on a possibility of th prformanc basd dsign using th sismic wav nrgy. Ratio of (d s/dt) max ;(surfac/bas) nrgy ratio w / u Im pdanc ratio α=ρ Vs /ρ 2 Vs 2..5 D =% 2.5% 5.% % 2 % 4 % Fig.4 nrgy flow rat at surfac vrsus impdanc ratio for diffrnt damping ratios. D =% 2.5% 5.% % 2 % 4 %.. Im pdanc ratio α=ρ Vs /ρ 2 Vs 2 Fig.5 Dissipatd nrgy vrsus impdanc ratio for diffrnt damping ratios. PRFORANC-BASD DSIN BY WAV NRY Obviously, structural damag is dirctly rlatd to inducd strain in mmbrs of suprstructur. Hr, a suprstructur is idalizd by a shar vibrating systm rsting on a foundation ground as dpictd in Fig.6. If th width of th structur is larg nough, th intraction btwn th foundation ground may b approximatd by th 2-layrs systm. Thn, shar strain in th supr structur is xprssd as

13 * * 4sinkst ( Hst z) αst s γ = * ik ( ) * * ( ) * 3 st Hst ik st H α st st αst ρstvs + + st (2) / 2 z whr, H st =hight of suprstructur, k * st =complx * Shar-vibrating H wav numbr in suprstructur, α st =complx st structur, impdanc ratio, ρ st =quivalnt dnsity of structur r st, Vsst, and Vs st =quivalnt S-wav vlocity of structur. r,vs s This quation indicats that th structural strain is proportional to th squar root of th nrgy flow rat at Foundation ground th foundation ground, s = ds dt, and proportional to Fig.6 Two-layrs shar-mod th squar root of th impdanc ratio btwn th systm approximating a structur structur and th foundation ground, αst = ρstvsst ρvs. rsting on soil q.(2) indicats th nrgy flow rat at th ground surfac s dirctly controls th inducd strain in th suprstructur. In rality, suprstructurs ar not so simpl as idalizd by uniform shar bams. Thy bhav mor lik lumpd mass-spring systms with limitd width and vibrat in bnding-shar mods. Howvr, it may b possibl to find quivalnt paramtrs for th idalization which basically satisfis q.(2). Th inducd strain thus valuatd from th nrgy flow rat can b compard with yild strain and corrlatd with diffrnt stps of structural intgrity to b usd for th prformanc-basd dsign. st st For structurs with high flxibility and low damping such as buildings and houss, shar strain inducd cycl by cycl sms dcisiv for th failur of th structur. Consquntly, th nrgy flow rat bcoms a ky paramtr as indicatd in q.(2) for th prformanc basd dsign. In contrast, for structurs with highr rigidity and highr damping ratio such as rtaining walls, soil structurs, slops, tc., total strain accumulatd by a numbr of loading cycls ar ssntial for th structural prformanc. Thrfor, th accumulatd nrgy should b usd in plac of th nrgy flow rat in dsigning such structurs. So far, in sismic dsign practic th sismic input has bn dfind by acclration, vlocity or thir spctral valus. In ordr to us sismic wav nrgy for th prformanc-basd dsign, dsign wav nrgy should b dfind in plac of th convntional paramtrs such as acclration or vlocity. Not only th nrgy but also tim historis or spctral data ar ncssary in ordr to comput nrgy flow or flow rat. Consquntly th nrgy approach is similar to dtaild dynamic analyss using sismic motions. Howvr, th ky of th nrgy approach is to dfin a dsign input motion in trms of nrgy, which nabls diffrnt analytical rsults using dsign motions with diffrnt dominant frquncy, diffrnt duration, tc. to compar on th sam scal through th nrgy concpt.

14 CONCLUSIONS nrgy analyss on rcordd motions at 4 vrtical array sits yild th following major findings; ) It is possibl to quantify nrgy flow in a surfac ground by using vrtical array rcords basd on th assumption of th vrtical propagation of th SH wav so long as th influnc of surfac wavs is ngligibl. 2) Th ratio of th upward nrgy at th ground surfac to th upward nrgy at th bas, s u, is much lowr than. in sits with strong shaking bcaus of soil modulus dgradation and incrasd soil damping, which almost cancls th nrgy storag ffct in th surfac layr by rsonanc vn if it vr occurs. 3) Th dissipatd nrgy w in th surfac layr amounts to 65% of th upward nrgy u at th bas in th nar-fault sit with strong input motion PI, whil it is around 2% or lss in a distant sit KNK in indicating that th rst of th upward nrgy rturns to th dp arth. 4) Th flow rat of upward nrgy is vry variabl with tim comprising multipl paks which corrspond to th stpr gradints of th accumulatd nrgis and hnc rflct wav form charactristics. 5) Th upward nrgy and th nrgy flow rat tnd to rduc drastically as thy approach to th ground surfac in thos sits xprincing strong motion attacks and hnc significantly rflct soil nonlinarity ffct. Simpl analyss on SH-wav propagation in 2-layrs systm with variabl impdanc ratio, in which a sismic motion is givn at th bas layr, indicat th following; 6) With incrasing damping ratio in th surfac layr, th surfac nrgy dcrass whil th dissipatd nrgy incrass, rspctivly. Th trnds ar vry similar to thos obsrvd in th analytical rsults for th nrgy flow in th vrtical array sits. 7) Th surfac nrgy or its flow rat which is xpctd to incras du to rsonanc in th surfac layr cannot bcom so larg bcaus of xrtd larg soil damping in soft soil sits. If larg damping ratio of mor than % is assumd, th surfac nrgy tnds to dcras with dcrasing impdanc ratio. 8) Basd on 5) and 7) abov, th gnral prcption that soft soil sits ar mor suscptibl to havir arthquak shaking damag than stiff soil sits may not b appropriat if th ground surfac nrgy is th ky paramtr for structural failurs by sismic shaking. If a structur rsting on a ground can b idalizd by a two-layrs systm of shar-mod vibration, th inducd strain in th structur is dirctly rlatd to th sismic wav nrgy. Consquntly, th prformanc-basd dsign in which inducd structural strain is compard with thrshold strains for various structural prformanc may b rcommndd by using th sismic wav nrgy. Th nrgy approach nabls diffrnt analytical rsults using dsign motions with diffrnt dominant frquncy, diffrnt duration, tc. to compar in th sam nrgy principl.

15 ACKNOWLDNTS Th Kansai lctric Powr Company and th Kob unicipal Offic who succssfully rcordd th vrtical array data and CORKA (Th Committ for arthquak Obsrvation Rsarch in Kansai Ara) who gnrously distributd thm ar gratfully acknowldgd. RFRNCS. Kanai, K., Tanaka, T., Yoshizawa, S. Comparativ studis of arthquak motions on th ground and undrground. Bulltin of th arthquak Rsarch Institut, Tokyo Univrsity, Vol.37, 959: Schnabl, P. B., Lysmr, J. & Sd, H. B. SHAK, A computr program for arthquak rspons analysis of horizontally layrd sits. Rport RC 72-2, Univrsity of California Brkly, Kokusho, T., atsumoto,. and Sato, K. Nonlinar sismic proprtis back-calculatd from strong motions during Hyogokn-Nambu Q. Proc. World Confrnc on arthquak nginring (Acapulco), 996, CD-publication. 4. Kokusho, T. and otoyama, R. nrgy dissipation in surfac layr du to vrtically propagating SH wav. Journal of otchnical and onvironmntal nginring, ASC, Vol.28, No.4, 22: Kokusho, T. and atsumoto, : Nonlinarity in sit amplification and soil proprtis during th 995 Hyogokn-Nambu arthquak. Spcial Issu of Soils and Foundations, 998: lgamal,a.w., Zghal,. and Parra,. Idntification and modling of arthquak ground rspons. Proc. st Intrnational Confrnc on arthquak otchnical nginring, Balkma, Rottrdam, Th Nthrlands, Vol.3, 995: