THE SOIL STRUCTURE INTERACTION ANALYSIS BASED ON SUBSTRUCTURE METHOD IN TIME DOMAIN

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1 THE SOIL STRUCTURE INTERACTION ANALYSIS BASED ON SUBSTRUCTURE METHOD IN TIME DOMAIN Musafa KUTANIS Ad Muzaffe ELMAS 2 SUMMARY I is pape, a vaiaio of e FEM wic is so-called geeal subsucue meod is caied ou fo aalysis of espose of sucues o eaquake goud moio. Te ieacio focedisplaceme elaiosip is calculaed by usig e cosise ifiiesimal fiie eleme cell meod. Assemblig e ieacio foce-displaceme elaiosip of e ubouded soil medium wi e equaio of moio of e sucue leads o e basic equaios of e oal dyamic sysem. To solve ese equaios i ime domai, a foa code is developed. As a esul, iegula bouded medium maeial iomogeeiies ca be pocessed ad olieaiy of soil ca be cosisely ake io accou. To veify e sudies, a wo dimesioal, plai sai, soil sucue ieacio sysem is solved i ime domai. A e ed, se of umeical esuls ae peseed ad discussed. INTRODUCTION Dyamic soil-sucue ieacio aalysis ave sigifica effec o e espose of e sucue o eaquake exciaio. Due o e complexiy of is peomeo ad is pacical impoace, cosideable amou of wok as bee doe ove e las quae of e 2 ceuy. Te modelig ad aalysis of SSI ivolves a good kowledge of sucual dyamics, wave mecaics ad soil dyamics. Teefoe i as a callegig aue amog eseaces ad egiees. Is complexiy icludes uceaiies suc as wave composiio, spaial vaiaio of goud moio, geomeical ad maeial olieaiies of soil medium ad maemaical modelig of SSI. Amog vaious meods, e developme of modelig ad aalysis of SSI as followed wo diffee meods, amely Diec Meod ad Subsucue Meod. Tese meods ae evideced ad well documeed i wo exbooks publised [Wolf 985], [Wolf 988]. I ece yeas, bo meods ae sill beig developed o acieve e desied esuls. Amog em, a commo fomulaio equally applicable o bo meods is peseed by Aydıoğlu [Aydıoğlu 993a],[Aydıoğlu 993b]. Tis is acieved by cagig e size of iegula soil zoe ad defiiio of dyamic bouday codiios alog e ieacio oizo. I deemiaio of e ieacio foce-displaceme elaiosips of e degees of feedom i e odes o e soil-sucue ieface fo use i e cosise fomulaio of diec ad subsucue meod, e igoous fomulaio based o similaiy ad fiie eleme meod, wic is oigially developed by Wolf ad Sog [Wolf ad Sog 996], as bee pove o be vey effecive. Te aim of is pape is pefom a umeical dyamic soil-sucue ieacio aalysis i ime domai by usig e compue pogam ENLAS, wic is oigially developed by Kuais. I ode o compue uiimpulse espose maix fo ime domai aalysis of ubouded medium, aoe compue pogam called SIMILAR, povided by Wolf ad Sog, is icopoaed io ENLAS. FUNDAMENTAL EQUATIONS A sysemaic fomulaio ad discussio of oliea soil sucue ieacio is peseed i e aicle by Aydıoğlu [Aydıoğlu 993a]. 2 Saü, Mu. Fak. Isaa Bol. Eseepe Kampus-Adapazai, Tukey kuais@eseepe.sau.edu. Saü, Mu. Fak. Isaa Bol. Eseepe Kampus-Adapazai, Tukeye

2 Sucue Nea-field/Fa-field ieface base Bouded-iegula soil zoe (ea-field) Seismic ipu moio Hypoeical disa bouday Ubouded-egula soil zoe (fa-field) Fig.. Commo model fo diec ad geealized subsucue meods. (i) c (a) s (b) (i) f b e b d d Fig. 2. Ideificaio of (a) soil sucue sysem, (b) uexcavaed fee field Refeig o e soil sucue model give i Fig. ogee wi coespodig idices sow i Fig. 2, e basic equaios of e soil-sucue sysem ca be expessed i ime domai as [Aydıoğlu 993a]: () c Mii M i M M i i i () Q i() + + = i i () Q () R () P () () wee M, Q, R, P ae mass maix, oliea ieal foces, effecive foce veco ad ieacio foces, especively. Te espose veco, of eq. () is epeseed by oal displaceme wic ae idicaed by supescip. Te fis em o e lef-ad side epeses e ieial foces i especive pas of e sysem wi e las compoe, Q i (), beig e oliea ieal foces acig o e ie face of ieacio oizo. Fo e geealized subsucue meod, e ieacio foce-displaceme elaiosips i e ime domai ca be expessed i ems of e elaive ieacio displacemes calculaed alog e ieacio oizo, amely, e diffeece bewee e oal ad e fee-field displacemes, wic is fomulaed as: R () = S ( τ) ( τ)dτ P () wi S () epeseig e fa-field dyamic siffess maix i ime domai. Te secod em o e igad side is e ime effecive foces, ca be expessed as: (2) 2

3 P () = S ( τ)v f ( τ) dτ wee v f ( τ ) is obaied fom oliea aalysis of e uexcavaed fee-field. Te elaive ieacio displacemes wic ae defied as: (3) f () = () v () (4) Tus fom eqs (2)-(4): R () = S ( τ) ( τ) dτ Fially, e o-zeo effecive foce veco compoe of eq () ca be expessed as: (5) f i vi i P () = [ Mi Mi ] + P () f (6) v wee e secod em epeses e ieal foces acig o e ie face of e ieacio oizo as obaied fom oe- o wo-dimesioal oliea aalysis of uexcavaed fee-field sysem icide seismic waves. To ovecome e umeical difficulies ad o simplify e fomulaio ad e deivaio, e ieacio foces is expessed as a covoluio iegal of e acceleaios [Sog ad Wolf 996]: R () = M ( τ) ( τ) dτ wee () is e acceleaio ui impulse espose maix i e ime domai. I ca be deemied diecly wi e cosise ifiiesimal fiie eleme cell meod wic is addessed i Wolf & Sog 995. M Te ieacio foces of e soil medium a e soil-sucue ieface eq (7) ae disceized a ime saio fo a piecewise cosa acceleaio ui impulse espose maix [Wolf ad Sog 995] as: (7) f { R } = γ [ M ]{} γ [ M ]{ v } + ( γ) [ M ]{ } + [ M ] ({ } { } ) j= j+ j j (8) NUMERICAL IMPLEMENTATION Te pocedues peseed i e pevious secios ae ow used o solve e ieacio poblems i ime domai. As a example, usig e daa give i Fig. 3 ad Table, fis, seismic fee-field ipu moio alog e ieacio oizo is deemied. Tis is acieved by e aalysis of uexcavaed vigi soil i e absece of e sucue. Fo is pupose, a well-kow compue pogam, SHAKE, is used. Te, assumig e fafield o be liea, dyamic bouday codiios alog e ieacio oizo is defied by calculaig e uiimpulse espose maix of e fa-field i ime domai (Fig 4). I e id sep, e aalysis of e soil sucue sysem ude e acio of fee-field ipu moio deemied i e fis sep, subjec o e dyamic bouday codiios deemied i e secod sep, is caied ou. A e fis sage of e aalysis, oce, e ime isoy acceleaio of fee-field ipu moio a e suface is also obaied (Fig. 5), usig e Fouie asfom eciques specal acceleaio (g) vesus peiod (sec) is ploed (Fig.6). I ode o illusae e effecs of seismic soil sucue ieacio, a simple saegy as bee followed: Fis, by modifyig e siffess of e sucue e fixed base peiod of e sucue is vaied fom T=.8 sec o T=2.5 sec. Te, a e same peiods, e sucue is e-aalyzed by akig io cosideaio of e SSI effecs. Te esuls ae obaied i ems of oal base sea (N) vesus ime isoy (sec). To cay ou e SSI aalysis, a simple wo dimesioal sucue wi igid foudaio is cosideed. Te sucue ad ea-field soil medium is modeled by usig e plai sai fiie eleme meses. As a ipu moio Ezica (992) E-W compoe is used o be a veically icide sea wave. 3

4 CONCLUSIONS I is sudy, aloug e fomulaio [Aydıoğlu 993a] is deived fo oliea aalysis of SSI, fo e sake of simpliciy ad bee udesadig, e aalysis is caied ou i liea pocedue. Te coclusio ca be summaized as follows: Ude e elaively sof soil codiios (a is, sea wave velociy is less a 3 m/s). If e fis mode peiod of e fixed base sucue is cosideed o be e lef of poi a (Fig. 6), a is e sucue is exemely siff, i is obseved a e SSI effecs plays a impoa ole ae a fixed base sysem (Fig.7). 2. As e peiod of e sucue iceases fom e lef of poi a o e ig of poi b (Fig.6), e SSI effecs is dimiisig. Ta is, e fixed base sysem becomes domia. 3. Te, i is demosaed a e effecs of SSI is paiculaly impoa, if e sucue is exemely siff ad e soil medium is elaively sof. Te elp of D. M.N. Aydıoğlu is ackowledged. ACKNOWLEDGEMENTS REFERENCES Aydıoğlu, M.N., Cosise Fomulaio of Diec ad Subsucue Meods i Noliea Soil-Sucue Ieacio, Soil Dyamics ad Eaquake Egieeig, Vol. 2, pp.43-4, 993a Aydıoğlu, M.N., Developme of Aalyical Teciques i Soil-Sucue Ieacio, i Developme i Dyamic Soil-Sucue Ieacio, ed. P.Gülka & R.W.Cloug, NATO Advaced Sudy Isiue, Keme- Aalya, Tukey, 992, Kluwe Academic Publises, pp.25-42, Dodec, 993b Vuceic, M., ad Doby, R., 99, Effec of Soil Plasiciy o Cyclic Respose, Joual of Geoecical Egieeig, Vol. 7, pp Wolf, J.P., 985, Dyamic Soil Sucue Ieacio. New Jesey: Peice-Hall, Ic., Eglewood Cliffs. Wolf, J.P. 988, Soil Sucue Ieacio Aalysis i Time Domai. New Jesey: Peice-Hall, Ic., Eglewood Cliffs Wolf, J.P., ad Sog, C., 995, Ui-Impulse Respose Maix of Ubouded Medium by Ifiiesimal Fiie- Eleme Cell Meod, Compue Meods i Applied Mecaics ad Egieeig, Vol. 22, pp Wolf, J.P. ad Sog, C., 996, Fiie Eleme Modelig of Ubouded Media. Wes Sussex: Jo Wiley & Sos. 4

5 DAMPING RATIO PERCENT OCR=-5 So il w i P I= 5 So il w i PI=2 Rock. E-5 E-4 E G/Gmax E-5 E-4 E-3.. CYCLIC SHEAR STRAIN, PERCENT Fig. 3. Modulus educio cuves ad dampig aio wi cyclic sea sai (Afe Vuceic & Doby, 99) Table. Soil pofile daa Laye No Soil Type Tickess Dampig Ui Weig Sea Wave (f) (%) (kcf) (fps) PI= PI= PI= PI= PI= PI= Rock H B iegula soil medium R Regula, ubouded soil medium Fig 4. Geomey ad disceizaio of e SSI sysem 5

6 Fig. 5. Time isoy acceleaio of fee-field ipu moio a e suface. (Ezica, E-W 992) Specal acceleaio (g) a b PERIOD (sec) Fig. 6. Fee-field specal acceleaio a e fee suface. 4E+6 Toal base sea (N) 2E+6-2E+6-4E+6 T=.8 Fixed base SSI Toal base sea (N) -6E+6.5 E+6 E+6 5E+5-5E+5 -E+6 -.5E Time (sec) Fig. 7. Te effecs of SSI a small-peiod age T=2.5 Fixed base SSI T im e (sec) 6