INVESTIGATION OF STRESS REDUCTION EFFECT ON STRUCTURES DUE TO BASEMAT UPLIFT USING ENERGY CONCEPT

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1 In. J. of GEOAE, arh, 14, Vol. 6, No. 1 (Sl. No. 11), pp Geoeh., ons. a. and En., ISSN:186-98(P), (O), Japan INVESIGAION OF SRESS REDUION EFFE ON SRUURES DUE O BASEA UPLIF USING ENERGY ONEP akafumi Inoue 1 and Asushi ikami 1 Graduae Shool of Adaned ehnoloy and Siene, he Uniersiy of okushima, Japan; Insiue of ehnoloy and Siene, he Uniersiy of okushima, Japan ABSRA: his paper sudies sress reduion effes indued on sruures (suh as bride piers) due o basema uplif and soil yieldin by he use of a maro-elemen model for foundaions plaed on sand. A foundaion-soil sysem is modeled as four ases; (1) fixed base, () elasi soil, (3) elasi soil wih basema uplif and (4) elaso-plasi soil wih basema uplif. ime hisories wih differen frequeny haraerisis are onsidered as inpu moions o he models. omparisons of responses of he models show a remarkable reduion of seion fore due o basema uplif and soil yieldin, dependin on haraerisis of inpu moions. Reardin he ase where deree of sress reduion effe is lares, enery balane for he sysem is esimaed. In his ase, he inpu enery impared o he sruure by an earhquake ends o be redued due o he effe of basema uplif. Keywords: Bride Pier, Sress Reduion Effe, Basema Uplif, aro-elemen, Enery 1. INRODUION As desin mehods shif o performane-based desin, i beomes more imporan o auraely esimae he response of supersruures aompanied by foundaion roaion and basema uplif. Basema uplif is reporedly indued een by weak and/or medium round moions [1], hene, i is neessary o inorporae he effe of basema uplif ino a desin ode. Hayashi [] assessed slihly damaed buildins sandin on he mos seerely damaed area durin he 1995 Hyooken-Nanbu Earhquake. By usin numerial simulaion, he has sudied damae reduion effe due o basema uplif of buildins whih were subjeed o sron round moions, and showed ha he damae reduion effe someimes beomes remarkable dependin on sruural parameers and inpu moions. he finie elemen model was used in his analysis reain soil as a linear or equialen linear medium. Iwashia e al. [3] examined he effe of uplif a pile head on sruural response. hey disussed he inpu enery impared o sruures by an earhquake. hey hae reaed he round as a kind of sprin and assumed ha he sprin doesn resis ensile fore in order o ake he effe of uplif ino aoun. he auhors hae sudied he reduion effe of a seion fore indued on sruures due o basema uplif and soil yieldin by he use of a maroelemen model and showed ha he deree of base shear reduion depends on he frequeny haraerisis of inpu moions relaie o he sysem [4]. his paper sudies he reduion effe of a seion fore indued in he sruure due o basema uplif and soil yieldin from a iewpoin of enery by he use of a maro-elemen model for foundaions plaed on sands. A foundaion-soil sysem is modeled as four ases; (1) fixed base, () elasi soil, (3) elasi soil wih basema uplif and (4) elaso-plasi soil wih basema uplif. ime hisories wih differen frequeny haraerisis are onsidered as inpu moions in he model.. ARO-ELEEN ODEL In his sudy, a maro-elemen model deeloped by Nakaani e al. [5] is employed o sudy sress reduion effe of sruures due o basema uplif and soil yieldin. A brief oeriew is desribed in his seion. Deails an be referred o in Shirao e al. [6]..1 Relaionship beween Displaemens and Loads of a aro-elemen odel In he maro-elemen model, he foundaion is assumed o be riid, and foundaion-soil model whih is subjeed o ombined loads is modeled as one elemen. Displaemens and loads a he ener of he fooin are defined as shown in Fi. 1 and he followin equaions. 749

2 In. J. of GEOAE, arh, 14, Vol. 6, No. 1 (Sl. No. 11), pp V u lenh. Frequeny dependene of he oeffiiens is inored..3 Uplif ompliane H Uplif ompliane is deermined based on he up followin model for uplif. he relaionship is expressed by Fi. 1 Definiion of displaemens and loads for he maro-elemen model x (1) F V () u H where he supersrip sands for ransposiion. he relaionship beween inremenal displaemens and loads is expressed by df (3) D D D dx el up pl 1 el up pl where D, D and D are elasi ompliane, uplif ompliane and plasi ompliane, respeiely.. Elasi ompliane In order o deermine elasi ompliane, equialen elasi sprin oeffiiens orrespondin o he erial, ranslaional, and rokin omponen suesed by Gazeas [7] are used. he oeffiiens for a reanular foundaion are expressed by 4.54G B / K 1 (4) up (7) 4 up 3 (8) where and are momens ha are influened by soil plasiiy and roaion a whih he uplif iniiaes. hen he up relaionship is expressed by up (9) up (1) B Plasi ompliane Plasi ompliane is also need o be deermined by usin bearin apaiy surfae. A shemai diaram of his is shown in Fi.. Shirao e al. [6] assumed he followin expression for bearin apaiy surfae. f r h (11) where m V /Vm 1, h H /, m / V m BV m 9G B / K h (5) H / B 3.6G B / K r 1 (6) 3 where G and are shear modulus and Poisson s raio of he underlyin soil and B is he fooin Fi. Shemai diaram of bearin apaiy surfae V 75

3 In. J. of GEOAE, arh, 14, Vol. 6, No. 1 (Sl. No. 11), pp and V is bearin apaiy in erms of enered m erial loadin. Parameers and are anens a he oriin on he V H, V planes, respeiely. o desribe plasi deformaions, a yield funion is defined based on Noa and onrasio [8] as follows: f (1) h m / y 1 where is he hidden parameer ha speifies insananeous size of he yield surfae and ranslaes insananeous ombined loads ino he norm of an equialen erial fore. In order o relae size of he yield surfae and inremenal displaemens, he hardenin rule and flow rule are required. As for he hardenin rule, isoropi hardenin, whih defines similar bearin apaiy surfae and yield surfae, is assumed. he hardenin funion is expressed by R 1 exp Vm (13) pl where R is iniial radien of he V ure. Here, is expressed by (14) pl pl pl u B. 5 where and are non-dimensional parameers ha inorporae he onribuion of horizonal displaemen and roaion ino hardenin. As for he flow rule, a non-assoiaed flow rule is adoped. Reardin suh a nonassoiaed flow rule, a plasi poenial funion is defined as follows: h (15) m 1 / where,, and are parameers ha speify he shape of he plasi poenial surfae. 3. SRESS REDUION AGAINS AN AUAL EARHQUAKE Here, sress reduion effes of a sruurefoundaion-soil sysem aains real earhquakes are reiewed. he sysem was subjeed o differen ypes of aeleraion-ime hisories. A foundaionsoil sysem is modeled as four ases, and i s sress reduion of piers is disussed. 3.1 Sruure-Foundaion-Soil Sysem A shemai and parameers of he sruurefoundaion-soil sysem are shown in Fi. 3 and able 1. A supersruure was modeled by a lumped mass and Bernoulli-Euler beam. he oal derees of freedom of he sysem were six; onsisin of hree derees of lumped mass and hree derees of he maro-elemen. A foundaionsoil sysem is modeled as four ases; (1) fixed base, () elasi soil, (3) elasi soil wih basema uplif and (4) elaso-plasi soil wih basema uplif. he dampin oeffiien of he beam elemen was assumed o be proporional o he elemen siffness marix and 5% of he dampin oeffiien was aken ino aoun. Frequeny dependene of elasi omplianes of he maro-elemen was inored. Dampin oeffiiens of he maroelemen orrespondin o he erial, ranslaional, and rokin omponen were se based on Gazeas [7]. Parameers of yield funion, plasi poenial and hardenin funion were se based on Noa and onrasio [8] and Nakaani e al. [5]. 3. Sress Reduion aains an Aual Earhquake In his seion, deree of sress reduion effes of a sruure is sudied. he aforemenioned sruure-foundaion-soil sysem is subjeed o inpu moions in he ime domain. wo kinds of round moions are onsidered as he inpu moions here; subduion-ype earhquake (aeleraion ime hisory whih was reorded a a por in Hahinohe durin he 1968 okahi-oki Earhquake) and inland-ype earhquake (aeleraion ime hisory obsered a JR akaori saion durin he 1995 Hyooken-Nanbu Earhquake). hese ime hisories are shown in Fi. 4 and 5. For onduin nonlinear analysis wih he maro-elemen model, ime sep for seismi response analysis was se a.1 seonds by inerpolain he inpu ime hisories whih were oriinally reorded a. seond inerals. Linear Vs V p ρ K Kh K r h r V μ ψ ζ λ χ α γ Fi. 3 Shemai diaram of sruure-foundaionsoil sysem B ms m f m J s h E AIη J f R 751

4 In. J. of GEOAE, arh, 14, Vol. 6, No. 1 (Sl. No. 11), pp able 1 Parameers of sruure-foundaion-soil sysem Parameer Value Lumped mass m () 5 s omen of ineria of he sruure J s ( m ) 4167 Heih h (m) 1 Youn modulus E (kn/m ) 45 Seion area A (m ) 4.43 Seond momen of area I (m 4 ) Dampin oeffiien of he sruure.5 Fooin lenh B (m) 1 ass of he foundaion m f () 1 omen of ineria of he foundaion J ( m ) f 833 Shear wae eloiyv s (m/s) 3 Lysmer s analo wae eloiy V La (m/s) 356 Ground densiy (/m 3 ) 1.63 Verial elasi sprin oeffiien K (kn/m) 75 ranslaional elasi sprin oeffiien K h (kn/m) 4 Rokin elasi sprin oeffiien K r (kn m/rad) 545 Verial dampin oeffiien (kn s/m) 55 ranslaional dampin oeffiien h (kn s/m) 369 Rokin dampin oeffiien r (kn s m) 998 Bearin apaiy of enered erial loadinv m (kn) 961 Parameer of yield funion.9 Parameer of yield funion.48 Parameer of yield funion.95 Parameer of plasi poenial.45 Parameer of plasi poenial.45 Parameer of hardenin funion R Parameer of hardenin funion.8 Parameer of hardenin funion 1.7 aeleraion mehod was used for he numerial ineraion. he ime hisory of base shear ha Aeleraion (al) Fi. 4 Aeleraion ime hisory Aeleraion (al) Fi. 5 Aeleraion ime hisory ourred in he sruure for subduion zone ype earhquake is shown in Fi. 6. he hin blak doed-line, he hin ray line, he hik blak doline and he hik ray line orrespond o responses for fixed base ase, elasi soil ase, elasi soil wih basema uplif ase and elaso-plasi soil wih basema uplif ase, respeiely. ase (1) shows ime response differen from oher ases; and his differene implies he wae radiaion effe. Howeer, linear ases and nonlinear ases show similar ime responses. his means ha sress reduion effe due o basema uplif is sinifian, and soil yieldin are no apparen in hese ases. Seondly, an inland-ype earhquake is onsidered as inpu moion ino he sysem. alulaed responses are shown in Fi. 7. eanins of ures are he same as in Fi. 6. Responses show sinifianly differen waeforms. he fixed base ase and elasi soil ase show similar ime responses (his differene implies he wae radiaion effe). Howeer, when basema uplif is onsidered, base shear beomes sinifianly differen from linear ases. Nonlinear ases show drasi reduion of base shear, hus loner period moions are implied. When soil yieldin is onsidered, he period of he moion beomes een loner. We an reonize from hese resuls ha sress reduion of sruures due o basema uplif and soil yieldin an our in some ases dependin on inpu round moions. In order o examine faors ha mih brin abou differenes in he leel of sress reduion, some arifiial inpu moions ha hae differen frequeny haraerisis are onsidered in he nex seion. 75

5 In. J. of GEOAE, arh, 14, Vol. 6, No. 1 (Sl. No. 11), pp ase (1) ase () ase (3) ase (4) Fi. 6 Base shear ime hisory ase (1) ase () ase (3) ase (4) Fi. 7 Base shear ime hisory 4. SRESS REDUION OF SRUURE FOR INPU OIONS OF DIFFEREN FREQUENY HARAERISIS he same sruure-foundaion-soil sysem is onsidered. As he inpu moion, harmoni waes ha hae differen frequeny haraerisis are ien. An example of he harmoni seismi wae whih has a naural frequeny of 1.989Hz is shown in Fi. 8. he ampliude radually inreases unil i reahes an ampliude of 5al. As he former seion, foundaion-soil sysem is modeled as four ases; (1) fixed base, () elasi soil, (3) elasi soil wih basema uplif and (4) elaso-plasi soil wih basema uplif. hree ases wih differen exiaion frequenies are onsidered: (a) exiaion frequeny fe is lower han he naural frequeny of he elasi soil sysem fn (fe/fn=.9) (b) exiaion frequeny is he same as he naural frequeny of he elasi soil sysem (fe/fn=1.) () exiaion frequeny is hiher han he naural frequeny of he elasi soil sysem (fe/fn=1.1). he naural frequeny of he elasi soil sysem is 1.989(Hz). 4.1 Sress Reduion for ase (a) he ime hisory of base shear indued in he Aeleraion (al) Fi. 8 Aeleraion ime hisory sruure is shown in Fi. 9. he meanins of he ures are he same as before. Base shear responses of fixed base and elasi soil model are larer han nonlinear ases. When basema uplif effe is inorporaed in he model, base shear redued sinifianly. No lear differene an be seen by he soil yieldin effe. 4. Sress Reduion for ase (b) alulaed responses are shown in Fi. 1. In his ase, base shear of he elasi soil model beomes muh larer han ohers. his is beause he elasi soil sysem reahed resonane wih exiaion frequeny beomin sysem frequeny. ompared o he elasi soil ase, base shear of he models ha inorporaed basema uplif effe showed sinifian reduion. 4.3 Sress Reduion for ase () 753

6 In. J. of GEOAE, arh, 14, Vol. 6, No. 1 (Sl. No. 11), pp ase (1) ase () ase (3) ase (4) Fi. 9 Base shear ime hisory 5 ase (1) ase () ase (3) ase (4) Fi. 1 Base shear ime hisory 5 ase (1) ase () ase (3) ase (4) Fi. 11 Base shear ime hisory he resuls are shown in Fi. 11. In his ase, exiaion frequeny is hiher han he elasi soil sysem and loser o he fixed base model. For his reason, base shear of he fixed base model is lares. Owin o radiaion dampin effe, base shear of he elasi soil model was sinifianly redued. Furhermore, basema uplif effe works o drasially redue he base shear of he sruure in his ase. 5. INVESIGAION OF SRESS REDUION EFFE USING ENERGY ONEP Reardin ase () where deree of sress reduion effe was he lares in he preedin haper, enery balane for he sysem is esimaed. Various enery erms an be defined by inerain he equaion of moion ino he sysem. If he maro-elemen model deeloped by Nakaani e al. [5] is employed, he equaion of moion of he sysem is expressed by u u K u F P (16) where is he mass marix, is he dampin marix, K is he siffness marix for a pier, F is he soil reaion fore marix from maroelemen, and P is he exernal fore marix. 754

7 In. J. of GEOAE, arh, 14, Vol. 6, No. 1 (Sl. No. 11), pp Hene, he arious enery erms an be expressed by u u d u u d u K u d u Fd u Pd (17) he rih side of his equaion is enery inpu o he sysem. he firs erm on he lef side is kinei enery of he sysem assoiaed wih is moion relaie o he round. he seond erm on he lef side is enery dissipaed by isous dampin. he hird erm on he lef side is he poenial enery of he sruure. he fourh erm on he lef side of his equaion is he poenial enery of he soil. he ime hisories of enery for he sysems are shown in Fi. 1. In his ase, he inpu enery impared o he sruure by an earhquake ends o be smaller due o he effe of basema uplif. 6. ONLUSIONS his sudy examined he reduion effe of a seion fore indued in sruures due o basema uplif and soil yieldin from a iewpoin of enery onep. A maro-elemen model deeloped by PWRI whih an deal wih basema uplif is used. he foundaion-soil sysem was modeled as four ases; (1) fixed base, () elasi soil, (3) elasi soil wih basema uplif and (4) elaso-plasi soil wih basema uplif. ime hisories wih differen frequeny haraerisis were onsidered as inpu moions in he models. omparisons of responses Enery (m / s ) inpu enery kinei enery poenial enery of he sruure poenial enery of he soil dampin enery of he sruure radiaion dampin enery fixed base ase elasi soil ase elasi soil wih basema uplif ase elaso-plasi soil wih basema uplif ase Fi. 1 Enery ime hisory (ase ()) 755

8 In. J. of GEOAE, arh, 14, Vol. 6, No. 1 (Sl. No. 11), pp for he models showed remarkable reduion of seion fore due o basema uplif and soil yieldin. herefore, i may be onluded ha he deree of base shear reduion depends on frequeny haraerisis of inpu moions relaie o he sysem. Reardin he ase where deree of sress reduion effe was he lares, enery flow for he sysem was esimaed. In his ase, he inpu enery impared o he sruure by an earhquake ended o be redued due o he effe of basema uplif. 7. AKNOWLEDGEENS he auhors express heir raiude o he Publi Works Researh Insiue, sukuba, Japan, for proidin he analysis proram. 8. REFERENES [1] Fukui J, Kimura Y, Ishida and Kishi Y, An inesiaion on he response of shallow foundaions o lare earhquakes, ehnial emorandum of PWRI, Publi Works Researh Insiue, (367), 1999, (in Japanese). [] Hayashi Y, Damae reduion effe due o basema uplif of buildins, Journal of Sruural and onsruion Enineerin (ransaions of AIJ), 485, 1996, pp. 53-6, (in Japanese). [3] Iwashia K, aniuhi H, Ishihara, Enery Approah o he Earhquake Response of Buildin Allowin Uplif a Pile Head Journal of Sruural and onsruion Enineerin (ransaions of AIJ), 564, 3, pp. 3-3, (in Japanese). [4] Inoue, and ikami A, Sress Reduion Effe of Sruure due o Basema Uplif and Soil Yieldin, In: Proeedins of he 1h Inernaional onferene on Urban Earhquake Enineerin, okyo, JAPAN, 13. [5] Nakaani S, Shirao, and Kouno, Deelopmen of a numerial model for he seismi nonlinear behaior and irreersible displaemen of a shallow foundaions PWRI Repor, Publi Works Researh Insiue, (411), 8, (in Japanese). [6] Shirao, Paolui R, Kouno R, Nakaani S, Fukui J, Noa R, di Priso, Numerial simulaion of model ess of pier-shallow foundaion sysems subjeed o earhquake loads usin an elaso-uplif-plasi maro elemen Soils and Foundaions, 48(5), 8, pp [7] Gazeas G, Foundaion ibraions Foundaion Enineerin Handbook, Fan HY (ed.), an Nosrand Reinhold: NY, [8] Noa R, and onrasio L, Selemen of shallow foundaions on sand, Géoehnique, 41(), 1991, pp In. J. of GEOAE, arh, 14, Vol. 6, No. 1 (Sl. No. 11), pp S No. 367 reeied on June 16, 13 and reiewed under GEOAE publiaion poliies. opyrih 14, Inernaional Journal of GEOAE. All rihs resered, inludin he makin of opies unless permission is obained from he opyrih proprieors. Perinen disussion inludin auhors losure, if any, will be published in he arh. 15 if he disussion is reeied by Sep, 14. orrespondin Auhor: akafumi Inoue 756