NOVEL DEVELOPMENTS AND FINDINGS FOR THE SAFETY ASSESSMENT OF EARTHQUAKE-EXCITED DAM-RESERVOIR SYSTEMS

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1 Th 4 th Wold Cofc o Eathua Egiig Octob -7, 8, Biig, Chia NOVEL DEVELOPMENTS AND FINDINGS FOR TE SAFET ASSESSMENT OF EARTQUAKE-EXCITED DAM-RESERVOIR SSTEMS N. Bouaaai, F. Lu, C. Pault 3, M.A. Chago, ad I. Gogoi 4 Associat Pofsso ail: aib.bouaaai@oltl.ca, Rsach Gaduat Assistat, 3 Rsach Assistat Datt. of Civil, Gological ad Miig Egiig, Écol Poltchiu d Motéal, Caada 4 Lctu, Datt of Civil Egiig, Assa Egiig Istitut, Guwahati, Idia ABSTRACT : Ma das woldwid hav b i svic ov 5 as ad a locatd i high sisicit aas. Th iitial sisic dsig of ths citical stuctus was gall coductd usig silifid thods that do ot full ta ito accout of th daic atu of athua citatio ad th col fluid-stuctu itactio. Although sigificat wo has b do to valuat th sisic sos of das, th is still a d to iov cool usd silifid thods ad to accuatl assss th fficic of o sohisticatd os. Th fist at of this a ooss w actical foulas to valuat athua-iducd hdodaic loadig o coct das. This oigial tchiu galizs th classical addd-ass foulatio b icludig th ffcts of da flibilit ad svoi botto absotio. Fuc sos fuctios of hdodaic ssus withi th svoi a coad to aaltical solutios. It is show that th thod accuatl dicts hdodaic loads ad that it ca b asil iltd i a cout oga o a sadsht. Th scod at of th a ivstigats fiit lt odlig ascts to assss th sisic foac of coct das. Sval fiit lt odls of da-svoi ssts with vaious disios a usd to coduct fuc ad ti doai aalss. Pottial-basd fluid lts ad viscous bouda coditios a validatd agaist aaltical solutios ad th a show to fo aduatl fo actical sisic aalsis of da-svoi ssts. KEWORDS: Da saft, dodaic loadig, Sisic ffcts, Nuical odlig.. INTRODUCTION Da failus a sult i catastohic cosucs, causig cosidabl loss of lif ad ot. Rsach dalig with da saft has b tsivl activ duig th last 5 as to iov udstadig of th col bhavio of da-svoi ssts ad ilt o liabl aoachs ito th cods of actic. Rigoous tchius to ivstigat daic da-svoi itactios a lativl w coad to o stablishd static da aalsis tools. Th ilsto of such igoous tatt dats bac to th ioig wo of Wstgaad 933, who oosd to odl wat actio o a da subctd to hoizotal goud acclatios as a uivalt addd ass hight-wis distibutio alid o th da fac. Although Wstgaad s aaltical solutio glctd da flibilit ad wat cossibilit, it has b widl usd fo a dcads to dsig athua sistat coct das. Daic itactios i da-svoi ssts a col hoa uiig advacd athatical ad uical odlig. Although availabl sohisticatd tchius ca hadl a ascts of ths hoa, silifid ocdus a usful ad still dd to globall valuat th ffcts of da-svoi itactio. This sctio of th a ooss a oigial ad actical ocdu to valuat athua iducd da-svoi itactios, icludig th ffcts of da flibilit, wat cossibilit ad svoi botto wav absotio. I a vious wo, th fist autho of th st a oosd a silifid closd-fo foulatio to valuat athua-iducd hdodaic ssus o coct das Bouaaai t al. 3. Th thod icluds th ffcts of wat cossibilit ad svoi botto wav absotio. Th ifluc of da dfoabilit was howv glctd ad thfo th total hdodaic ssu td o a da duig a athua could ot b dtid. Th fist at of this a ooss a wl iovd ad actical foulatio wh th igid da stictig assutio is waivd.

2 Th 4 th Wold Cofc o Eathua Egiig Octob -7, 8, Biig, Chia O th oth had, tsiv wo has b ddicatd to th dvlot of solid ad fluid fiit lt foulatios, ad thi iltatio i fluid-stuctu itactio obls. Aog ths tchius, Eulia-basd foulatios st sval advatags ad w succssfull alid to tasit wav oagatio obls Nilso t al. 98; Evsti t al. 983, Olso ad Bath 985. I th scod at of this a, a ottial-basd foulatio is adatd to ivstigat da-svoi ssts. Th foulatio is validatd agaist aaltical solutios obtaid ov a wid fuc ag.. SIMPLIFIED FORMULATION.. Thotical bacgoud Th silifid got of a da-svoi sst is show i Figu. Th da has a total hight s ad it iouds a si-ifiit svoi of costat dth. Sdits that a b dositd at svoi botto a also cosidd. A Catsia coodiat sst with as ad with oigi at th hl of th stuctu is adotd ad th followig ai assutios a ad: i th da ad th wat a assud to hav a lia bhavio; ii th wat i th svoi is cossibl ad iviscid, with its otio iotatioal ad liitd to sall alituds; ad iii gavit sufac wavs a glctd. Ud ths assutios, th hdodaic ssu,,t i th svoi i css of th hdostatic ssu obs th wav uatio C t.. wh is th Lalac difftial oato, t th ti vaiabl; ρ th ass dsit of wat ad C th cossio wav vlocit giv b C μ ρ.. i which μ dots th bul odulus of wat. Figu. Da-svoi sst with a silifid got. Cosidig haoic goud otios, hdodaic ssu i th svoi ca th b ssd i fuc doai as t,, t,, i wh th suscit dots th o athua dictio, th citig fuc, ad,, a col-valud fuc sos fuctio. Itoducig this tasfoatio ito E... ilds th classical lholtz uatio

3 Th 4 th Wold Cofc o Eathua Egiig Octob -7, 8, Biig, Chia, C + ;..3 Th col valud ssu fuc sos fuctios alog dictios, ca b ssd as Fvs ad Choa 984,,, Z,,,, ; s..4 wh is th fuc sos fuctio fo th hdodaic ssu at igid da fac du to goud acclatio alog, dictio, is th fuc sos fo hdodaic ssu du to hoizotal acclatio, ψ ψ of th da usta fac, Z is th galizd coodiat alog athua citatio dictio, ad s th total ub of od shas icludd i th aalsis. Thoughout this a, hdodaic ssus ad will b fd to as th igid ad th flibl ats of th total hdodaic ssu, sctivl. Th bouda coditios to b satisfid b hdodaic fuc sos fuctios taslat coatibilit of ssus ad dislacts at da-svoi itfac ad wav absotio at svoi botto Fvs ad Choa 984. Bouda coditios to odl f sufac, gavit wavs o th sc of a ic cov at svoi sufac w also oosd Bouaaai t al. 3. Th col fuc sos fuctios of hdodaic ssus ad ca th b ssd as th suatio of sos fuctios ad cosodig ach to a svoi od g, I a,,,, β ρ..5, I,,,, β ρ..6 wh ad a col-valud fuc ddt igvalus ad othogoal igfuctios satisfig, fo ach svoi od + i..7 [ ] [ ], i i ad wh th ts β,, I ad I a giv b [ ] ; i β + C..9 ; d, I d, I ψ.... Silifid ssios Th coot of th stuctual od sha ψ ca b aoiatd as a oloial fuctio a s ψ.. wh is th coodiat vaig ov th hight of th stuctu asud fo th botto. W show th that

4 Th 4 th Wold Cofc o Eathua Egiig Octob -7, 8, Biig, Chia th igid ad flibl hdodaic ssus at acoustical od a latd b,, G,, F +.. ag I i which l Λ l l Λ l+ F a + a+..3 l Λ s l Λ + s i i G F + a a +..4 Λ s Λ + s ad wh th col-valud fuctio Λ is dfid b z Λ z..5! fo col ad itg ubs, z ad, sctivl. This iotat ad oigial latio lats th flibl ad igid ats of hdodaic ssu fo a giv svoi acoustical od to th vibatio of th stuctu alog a giv od sha. Th igid ssu ca th b dtid usig closd-fo ssios siila to thos dvlod b th fist autho of this a Bouaaai t al. 3. Ths ssios ta accout of wat cossibilit ad wav absotio at svoi botto ad th w show valid fo a wid fuc ag..3. Nuical alicatio Th silifid thod std i th vious sctio is alid to a silifid tiagula da coss-sctio with got isid fo th tallst o-ovflow oolith of Pi Flat da Fvs ad Choa 984. Th da has a hight s.9, a dowsta slo of.8 ad a vtical usta da fac. Th followig da atial otis a slctd: a Poisso s atio ν s. ad a ass dsit ρ s 4 g/ 3. Two valus of odulus of lasticit E s 5 MPa ad E s 35 MPa a cosidd. Th wat is assud cossibl, with a vlocit of ssu wavs C 44 /s, a ass dsit ρ g/ 3 ad a bul odulus ν. 3 MPa. A cubic ofil is chos to aoiat th fist stuctual od sha ψ. Es...3,..4 ad.. a usd to dti th sos fuctios F, G ad. E...4 is th usd to cout th hdodaic ssu fuc sos fuctios illustatd i Figu. Fuc soss a lottd agaist th fuc atio / wh is th fudatal vibatio fuc of th da o igid foudatio with a t svoi. A sufficit ub of svoi ods N 5 is icludd i th aalsis. Th figu shows a cllt agt btw th silifid foulatio ad th aaltical solutio. W also obsv that th ualit of th aoiatio dos ot dca as wav flctio cofficit dcass. 3. FINITE ELEMENT MODELING 3.. Pottial-basd foulatio Th aaltical foulatio std abov icluds th cobid ffcts of wat cossibilit, da flibilit ad wav absotio at svoi botto. It is howv staid b th silifid ctagula got of th ioudd svoi. I this sctio a φ U ottial-basd foulatio is usd to ivstigat da-svoi-foudatio ssts with igula gotis. Assuig a iotatioal wat otio ad ifiitsial vlocit ad dsit chags, ilis th istc of a vlocit ottial φ,, t satisfig th uatios of cotiuit ad g cosvatio Ladau ad Lifshitz 959 φ φ 3.. C t

5 Th 4 th Wold Cofc o Eathua Egiig Octob -7, 8, Biig, Chia Figu. Absolut valu of fuc sos fuctios of oalizd hdodaic ssu at da hl: a α.95 ad E s 5 MPa; b α.95 ad E s 35 MPa; c α.65 ad E s 5 MPa; d α.65 ad E s 35 MPa; Aaltical solutio; -- Silifid foulatio. E. 3.. is associatd to th sstial bouda coditio φ 3.. o th f sufac ad igid boudais, ad to th atual bouda coditio φ u& 3..3 o ovig fluid-stuctu itfacs with ositiv oal vlocit u&, cosodig to uit sufac oal vcto oitig ito th fluid ad out of th stuctu. Usig stadad tchius, th wa vaiatioal fo of E. 3.. ca b obtaid ρ & d + d + d φ δφ V ρ u& δφ S ρ φ δφ V 3..4 C V S V i which V idicats th svoi doai, ad S a svoi bouda wh oal vlocit is scibd. Ud athua citatio, th daic sos of th da ad th svoi a could though coatibilit of vlocit ottial s. hdodaic ssu ad scibd oal vlocit s. oal acclatio at da-svoi itfac. Da-svoi itactio is cotaid i th scod t of E Figu 3 shows a fiit lt sh of a da oolith ioudig a svoi with a igula sha. Usig classical Gali disctizatio, th coulig btw th da ad svoi sub-stuctus ilds th sst of uatios M ss U&& Css Cs U& K ss U - Mss u&& g t M Φ && Cs C & Φ - K Φ - Cs u& g t wh vctos U ad Φ cotai th odal dislacts lativ to th goud ad th odal vlocit ottials, sctivl.

6 Th 4 th Wold Cofc o Eathua Egiig Octob -7, 8, Biig, Chia Figu 3. Fiit lt odl a da-svoi sst ad cosodig bouda coditios. Sub-atics M ss ad K ss st th ass ad stiffss atics fo th da substuctu, ad M ad K thos fo th svoi. A Raligh daig ati C ss is cosidd fo th da substuctu ad sub-atics C s ad C s accout fo da-svoi itactio though focd uilibiu ad coatibilit at fluid-stuctu itfac as illustatd i Figu 3. Sub-ati C accouts fo daig du to g dissiatio at th botto ad/o at th fa usta bouda of th svoi ad is giv b T C ρ N NdS 3..6 S i which N is a stadad isoaatic sha fuctio ati fo fluid lts ad S s dots sufac of th svoi botto bouda. Usig th tchiu oosd b Ls ad Kuhl 969, th absotiv coditio at svoi botto ca b aoiatd b a sis of viscous das lacd at th svoi-foudatio itfac. To su coatibilit btw fluid ad da lts ad abl fluid-stuctu itactio, isoaatic ba lts a istd alog svoi-foudatio itfac. Da lts a th built b coctig ba lt ods to th goud. Da ad ba lt ods a costaid to ov ol diculal to th svoi botto bouda. I th t sctio, th ottial-basd foulatio ad bouda coditios dscibd viousl a cofotd agaist aaltical solutios wh availabl o bouda lt solutios othwis. 3.. Nuical sults Gavit da ooliths ioudig svois with difft shas w aalsd usig th ottial-basd foulatio std abov. Rsults a show fo th sa tiagula da coss-sctio dscibd i sctio.3. Th fiit lt odls a built usig th softwa ADINA 6. Th da ad svoi a odld usig 9-od isoaatic la stss fiit lts icludig icoatibl ods ad 9-od ottial-basd fiit lts, sctivl. Aaltical ad fiit lt solutios a std i Figu 4 fo a ctagula svoi lgth L s ad hight s. W cosid fuc sw atios / vaig fo to 4 wh πc / dots th atual fuc of th full svoi. Th figu illustats a cllt agt btw th sults of ottial-basd fluid lts ad th aaltical solutio is cllt fo th igid cas. It is s that da flibilit ad stuctual daig affcts th accuac of th sults with so slight discacis aaig at high fucis lag tha 3. Figu 5 illustats th ffcts of svoi sha ad wav absotio at svoi botto. Th viscous bouda coditio dscibd i th vious sctio is alid alog th svoi botto usig cosistt luig.

7 Th 4 th Wold Cofc o Eathua Egiig Octob -7, 8, Biig, Chia Figu 4. Absolut valu of fuc sos cuvs of oalizd hdodaic ssus at th hl of th da ioudig a ctagula svoi with α.: a ad b Rigid da; c ad d Flibl da with 5% stuctual daig. Aaltical solutio; -- Pottial-basd fiit lt solutio. Figu 5. Absolut valu of fuc sos cuvs of oalizd hdodaic ssus at th hl of th da: a ad b Rctagula svoi with α.6; c ad d Tiagula svoi with α.6. Aaltical solutio; -- Pottial-basd fiit lt solutio.

8 Th 4 th Wold Cofc o Eathua Egiig Octob -7, 8, Biig, Chia Fo th tiagula svoi Figs. 5 c ad d, fiit lt sults a coad to a bouda lt solutio obtaid usig a oga dvlod b th fist autho Bouaaai ad Pault 5. Figu 5 clal shows that th ottial-basd fiit lt foulatio cobid with th viscous bouda coditio giv cllt sults fo wid fuc ad wav absotio ags. This ottial-basd foulatio ca also b fficitl usd with oth bouda coditios to accout fo g dissiatio at th svoi fa usta o fo daic itactio with a ic sht covig th svoi Bouaaai ad Chago CONCLUSIONS This a std silifid ssios ad o advacd fiit lt tchius to assss th ffct of fluid-stuctu itactio i sisicall citd da-svoi ssts. Sval da-svoi ssts with vaious shas w usd. Th hdodaic fuc sos cuvs obtaid usig th oosd thods w validatd agaist aaltical solutios wh availabl ad bouda lt solutios othwis. Ecllt agt is obtaid ov actical fuc ad wav absotio ags. Th oosd tchius a show to fo aduatl fo actical sisic aalsis of da-svoi ssts i fuc ad ti doais. ACKNOWLEDGEMENTS Fiacial suot fo th Natual Scics ad Egiig Rsach Coucil of Caada ad th Qubc Fud fo Rsach o Natu ad Tcholog is gatfull acowldgd. REFERENCES ADINA Tho ad Modlig Guid. Rot ARD ADINA R & D, Ic. Bouaaai, N. Pault, P., ad Poul, J. 3. A closd-fo foulatio fo athua-iducd hdodaic ssu o gavit das. Joual of Soud ad Vibatio, 33, Bouaaai, N. ad Pault, P. 5. A w bouda coditio fo g adiatio i covd svois usig BEM. Egiig aalsis with bouda lts, 9: 9, Bouaaai, N. ad Chago, M-A. 6. Sisic aalsis of Ic-Da-Rsvoi ssts. st Itatioal Stuctual Scialt Cofc - Caadia Socit of Civil Egiig, Calga, Ma 3-6, Pa ST-. Fvs, G. ad Choa, A.K EAGD-84, a cout oga fo athua aalsis of coct gavit das. Rot No. UCB/EERC-84/, Uivsit of Califoia, Bl, Califoia. Ls, J. ad Kuhl, R.L Fiit daic odl fo ifiit dia. Joual of th Egiig Mchaics Divisio, ASCE, 95, Nilso,.C., Evsti, G.C., ad Wag,.F. 98. Tasit sos of a subgd fluid-could doubl-walld shll stuctu to a ssu uls. Joual of th Acoustical Socit of Aica, 7, Evsti, G.C., Macus, M.S., ad Quzo, A.J Fiit lt aalsis of fluid-filld lastic iig ssts. Elvth Nasta Us's Collouiu, Ma, 4-6. Ladau, L.D. ad Lifshitz, E.M Fluid chaics. Pgao Pss. Olso, L.G. ad Bath, K.J Aalsis of fluid-stuctu itactios: a dict stic could foulatio basd o th fluid vlocit ottial. Couts ad Stuctus, :/, -3.