On bond failure by splitting of concrete cover surrounding anchored bars

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1 O bo failue by spliig of oee ove suouig ahoe bas M. Talaa & K.M. Mosala Depae of Civil a Evioeal Egieeig, Uivesiy of Califoia, Beeley, USA ABSTRACT: This suy evelops aalyial expessios fo he bo sess level suouig a logiuial seel ba ha auses he ove oee o fail i a spliig oe, wih ba-o-sufae as foig i he logiuial ieio paallel o he ba. The popose oels use as a fouaio he faue ehaisbase ohesive-elasi ig oel, evelope by Reiha&Va e Vee (99) base o oigial wo by Tepfes (979). They popose foulaios ha bee aess he assupios a siplifiaios ae i he oigial oel, aely he biaxial behavio of oee i esio, he a-opeig isplaee pofile, a he aeial law goveig pos-aig esio sofeig. The elaive sigifiae of he popose oel ehaees is esablishe hough hei peiio of bo sess a he assoiae opuaioal os fo a opuaioal beha poble ivolvig a seel ba pullou fo a oee ylie. Fially, he obusess of he efeee a popose oels, easue by hei sesiiviy o he ueaiy i hei espeive paaees is evaluae a opae usig a eeiisi sesiiviy aalysis. Base o suh aalysis, eoeaios ae give o he os suiable a paial ehaees of he oigial oel. INTRODUCTIUON. Moivaio The use of Faue Mehais (FM) i esiaig oee behavio a eeiig he segh of oee elees has eeive osieable aeio ove he pas yeas, piaily beause i a esibe a iepe size effes i he expeieally-obseve behavio of oee suues. I he fiel of applyig FM o oee, wo appoahes ae o be wiely aepe wihi he egieeig ouiy, boh of whih aop he assupios of Liea Elasi Faue Mehais (LEFM). The fis is he Fiiious Ca Moel (FCM) ue o Hillebog e al (97). The seo appoah is he Ca Ba Theoy oel, ioue by Baza a Oh (98). Of he wo, he foe has a avaage of o elyig o a epiial paaee suh as he a ba wih, whih aes i oe eaily aapable fo ipleeaio i Fiie Elee (FE) oes. The FCM appoah has bee use o evelop he ohesive-elasi bo-spliig oel fo esiaig he ove-spliig segh alog a eifoig seel ba base o bo sess (Tepfes 979). I his suy, his oigial oel is esigae A a is biefly eviewe fo opleeess a is siplifyig assupios ieifie. Fou aleaive oels ae evelope a ioue o aheaially aess hese assupios a esigae A hough A. The popose oels ae opae hough hei esiaio of bo segh i a ypial ba pull-ou exaple of a seel ba ebee i a oee ylie. Afe ieifyig he oe sigifia oels aog he popose aleaives, he sabiliy of hei peiios wih espe o he ueaiy i hei iiviual paaee values is ivesigae usig a eeiisi sesiiviy aalysis, aely he Toao iaga aalysis (Lee & Mosala 5) a opae o ha of he efeee oel wihi he oex of he beha poble. Besies esablishig he sesiiviy o oelig assupios, he isussio of he beha poble esuls aesses he ifluee a ehos of seleio fo he ube of aial as i he oel ue boh eeiisi a pobabilisi oexs.. Bagou Moel A The efeee bo-spliig oel assues he isibuio of sesses a efoaios show i Figue fo a sigle ba ebee i oee. As he ba is beig pulle fo he oee, ibs o is peiee esul i a ilie esisig foe, whih a be esolve io aial pessue a logiuial bo opoes, elae hough a agle of ieal fiio α, whih efles he sufae oiios. The sess sae is assue axi-syei a

2 ay aius. The ylie elose wihi he ove suouig he ba is assue o have ieial a sable as ha exe aially o a legh e. A pola ooiae syse is use whee he aial a ageial ieios ae iiae by subsips a, espeively. The hoop (ageial) sess a e is equal o he aig sess f, a is assue o vay elasially i he uae egio, > e. The oel assues ha eighboig logiuial bas ae fa eough a ha hei bo sess fiels o o ovelap. I he ae egio, e, he ageial sess eeases owas he ee wih he wieig of he a wih w uil i vaishes a a a wih w, followig a powe law as follows, σ ( w) f ( w w ) () whee aeial paaee eeie fo he esile faue eegy G F. The hoop sai a e, egleig Poisso s effe, is obaie fo ε ( e) f E ε () whee E oee oulus of elasiiy. This value of he aial sai is assue osa ove he ae pa e. Thus, π eε ( e) πε ( ) + w( ), ε ) ε ( e) ε ( (a, b) This yiels a liea isibuio of a wih, i.e. w( ) πε ( e ) fo e () whih gives a explii foula fo he hoop sess i he ae egio, aely, σ ( ) σ ( w() ) fo e (5) whee ax { s /, e w / πε } efies he e of he ohesive zoe whee sofeig ous. Give he elasi soluio (Tiosheo & Gooie 95) of sesses a aius, i a hi-walle ylie of i a o ie a oue aii, espeively, subjee o ieal pessue p i, i.e. σ ( ) pi σ ( ) pi i o i o i i o + o fo e (a, b) The pessue p a he ba sufae oibue by boh egios, elasi a ae, a he be alulae by supeposiio of he equilibiu soluio fo he elasi egio a he iegal of σ () ove e... Elasi Coibuio, p e Fo Equaio b we a eue he pessue aig a he ba sufae give he pessue applie a he ie wall of he elasi ig. Hee, e e ( + s ) e pe pi f (7) s s ( + ) + e s whee σ (e) f a he ose of aig, s ba iaee i e, a o + s / i Equaio... Cohesive Coibuio, p A ay aius e, fo he igi boy ehais assuig Equaio hols, usig Equaios,, a 5 a fially iegaig he hoop sesses ove he ae egio leas o ( w() ) f w() f σ p s f e s e f πε s + w ( e ) ( e ) w (8) Supeposig Equaios 7 a 8 leas o he oal pessue, aely p p e + p (9) Subsequely, fo equilibiu, he shea sess is τ p aα () whih epeses he bo segh a a legh e. Eligehause e al. (98) alulae he aveage value of he agle of ieal fiio α, usig ueial esuls of sess isibuio aou a ba wih laeal ibs fo a age of ove hiess a ba iaee values. The esuls wee iepee of he oee qualiy, wih values vayig bewee.9 a.. Pesely, α is lef ou by esiig he opuaio o he aial pessue p ue o he ibs o he ba a he pull-ou aio of he logiuial sess. Thus, he pessue apaiy is give by p axe{ p} () whee p he axiu pessue value he ig a susai as he a popagaes aially, afe whih he a beoes usable a us all he way o he sufae ausig a logiuial spliig a. oee seel ba α α (a) Sess fiel aou ba + s / elasi sofeig s e σ f sofeig elasi (b) Cohesive-elasi ig iealizaio of ove egio Figue. Cohesive-elasi a oel (Tepfes 979, Reiha & Va e Vee 99).

3 This value is epee o he assue ube of aial as whose iease esuls i a eease i he a opeig w pe a a ay give a legh e, whih leas o a iease i he aveage ageial sess wihi he ae egio a a oespoig iease i he ohesive pessue e p. The seoay effe of iseely-spae asvese eifoee is o expliily oele i his oel ye a be ilue i he paaee α. MODEL ENHANCEMENTS A lose ivesigaio of Equaio 9 eveals ha he esulig pessue is iely popoioal o he esile segh f, faue eegy G F, ove hiess, ube of as, a liiig a wih w, while i is ivesely popoioal o he eifoig ba iaee s. Howeve, his oel ivolves he followig assupios a siplifiaios: The oee aeial is assue o behave uiaxially. This is eflee i egleig he effe of aial ilaio i alulaig ε i Equaio, as well as assuig ha aig i esio aes plae upo violaig a uiaxial sess ieio i he hoop ieio whih egles he effe of he aial sess. This aial sess is opessive fo he give efoaio oe, whih shoul eue he uiaxial esile segh a lea o uosevaive esiaes usig oel A. The a opeig is assue o vay liealy wih he aius i Equaio. This equies ha he ageial sai alog he a legh is equal o he aig sai, whih is oly vali a e (Equaio ). Sofeig i he egio < e will esul i he bul aeial bewee as elasially uloaig o lowe sais a, subsequely, a o-liea a wih isibuio alog he aius. This is eglee, wih he ague beig ae ha a opesaig effe is expee fo egleig aial ilaio. The oel assues ha he exa shape of he esio sofeig elaioship oes o sigifialy affe he esulig segh, as log as he faue eegy elose by he sofeig uve eais he sae. Thus, he oel aops a siple powe sofeig law (Equaio ), whose oeffiie is eeie by equaig o G F he iegal of σw ove he age < w < w. Fuheoe, while f is eihe iely easue o esiae fo he opessive segh, G F is iffiul o easue a is ooly esiae as a fuio of f, a w is ypially esiae as a uliple of he aveage aggegae size (Raaale & Wehaaaa 989), leaig o opoue ueaiy i he oel esiaio. The followig subseios will pese he aheaial foulaios evelope o aess eah of he iiviual assupios ieifie above.. Moel A Biaxial behavio of oee The iouio of a oee biaxial failue ieio expliily aous fo he effe of aial ilaio i he ae egio. The oifie aig sess f is aope fo Gabaova e al. (99), σ + ( e) f f.8 f () whee f opessive segh a σ aial (asvese) sess (esio posiive). Diviig Equaio a by Equaio b a seig σ (e) f, ( + ).8 s + e f σ ( e) f + () ( + s ) e f Subsiuig Equaio i Equaio a solvig fo p e as i Equaio 7 leas o he fis e i Equaio. The seo e is aalogous o ha i Equaio 9 afe eplaig f by f. Aoigly, he oal pessue susaie i he ig suouig he ba is give by f p f + s s () ( + ) s e ( + ) ( e ) + e.8 f + s e f w + w () whee he a wih w he salle of w a he a wih a he seel-oee iefae, a a be expesse as w ( πε ( e )) (5) Equaio expliily iopoaes he effe of he biaxial sess sae i he plae of he ba ossseio o he esile aig i oee. The oel beoes fuhe opliae upo osieig -D sess sae effes. Howeve, i is ague ha spliig failue is ivesigae i bewee wo exisig flexual as a ha oee sesses i he logiuial ieio ae heefoe isigifia. I is also assue ha sess fiels suouig eighboig logiuial bas ae fa eough elaive o he ove hiess. The effe of aial ilaio is aoue fo by upaig ε i Equaio fo eah ial a legh e aoig o ( e) ( f vσ ( e) ) E ε () whee v Poisso s aio fo oee.. Moel A Noliea a wih isibuio Aouig fo he oliea a wih isibuio equies he soluio of a ieaive oliea poble. The goveig opaibiliy equaio is πε ( ) + w( ) πε ( e) π eε (7)

4 Thus, alog he a fae, aoig o Equaio he ageial sess isibuio follows Equaio 8; while i he bul oee bewee wo as, assuig uifo liea-elasi uloaig, he ageial sess isibuio follows Equaio 9. Fially, ivoig equilibiu equies equaliy bewee Equaios 8 a 9. ( ) () f ( w() w ) σ (8) () E ε () σ (9) Subsiuig Equaio 9 i Equaio 7 leas o w () π ( eε σ () E ) () Subsiuig Equaio i Equaio 8 yiels π w σ ( ) f [ eε σ () E ] () Equaio is oliea of he fo x G(x) fo x σ. Covegee equies ha G(x) / x <. This is iee saisfie, as illusae by Equaio G ( σ () ) σ () π w f E [ () ] ( eε σ E ) () Nueial ivesigaio of ypial paaee ages sugges ha he soluio will ovege, albei slowly. Afe evaluaig he hoop sess a suffiie pois alog he aius, he pessue i he ig is alulae by ueial iegaio of Equaio 8.. Moels A a A Aleae sofeig laws Seveal esile sess a wih sofeig laws have bee popose i he lieaue. A ee eview is available i va Mie (997). A all-ilusive suvey woul be pohibiive a beyo he sope of his suy. Isea, wo aleaive laws ae osiee a show o have a sigifia effe o he esuls. Moel A uses he esile sofeig law give i Gabaova e al. (99) by he foula w w σ ( w) f () + w a whee a aveage aggegae size a oel paaee. The elasi oibuio o he oal pessue p e i Equaio 9 is o affee by Equaio. Howeve, usig Equaio fo alulaig he eivaive / w a oig ha w eeases as ieases, he ohesive oibuio p beoes ( w() ) f w() f + w() f σ p s e s e a f + + w w πwε s a a w a + w l a () Moel A uses a aleae fo of he powe law i Equaio, aoig o σ ( w) f ( w w ) (5) whee oel paaee. This leas o he ohesive pessue e i Equaio 9 beoig ( ) + f () w w f πε p ( e ) () s w ( + ) e π εs w Fo he pupose of opaig oels A, A a A a isolaig he shape effe of he esile sofeig uve, paaees a ae selee so ha he esile faue eegy G F ue he sofeig uve i Equaios a 5 is aiaie equal o ha ue he sofeig uve i Equaio fo a oespoig value of. Figue peses gaphi opaiso of he aleae sofeig laws. σ/f.5 G f w / f....8 w/w Figue. Tesio-sofeig pofiles fo equal faue eegy. BENCHMARK PROBLEM The elaive sigifiae of he ehaees esibe i Seio is evaluae usig a hypoheial beha poble of ypial paaee values. This beha poble osies he ba-pullou esisae of a sigle eifoig seel ba ebee i a oee ylie a evaluaes he axiu aial pessue evelope befoe bo-spliig failue ous. The aial pessue is opue a axiize alog he a legh fo a vaiable ube of aial as. The esiae espose usig oel A is opae o esiaes usig oels A hough A o ivesigae he sesiiviy o he iiviual siplifyig assupios. The opuaioal ie eee by eah oel is also opae o assess is paialiy. I aiio, he sesiiviy of he oel esiae o he assue ube of as is ivesigae a obie wih expeieal obsevaios o esiae a value fo he paaee i he absee of expeieal aa peie o he poble of iees. I he pesee of suh aa, a pobabilisi appoah is oulie o aou fo aoess i.. Poble saee The beha poble geoey is siila o Figue. Sie he goveig equaios ae highly oliea, he use of oalize quaiies fo foe A A A

5 a geoei paaees beoes a ae of fo a oveiee, beause he esuls eai speifi o he eighbohoo of he se of geoei a aeial popeies osiee. As suh, he sigifiae of he iffee oel ehaees, isusse above, is ivesigae o a poble ha epeses a ooly eouee se of paaees. The poble aa is as give below: f. MPa, w., f. MPa,., E. GPa, s., G F. MPa., a., a v.. This aa yiel he oel paaees. i Equaio, 77. i Equaio, a 5. i Equaio 5.. Copaiso Resuls Figue shows he opuaioal soluios alulae fo he beha poble usig oels A, A, A a A. Resuls fo oel A ae o oieably iffee fo hose of oel A a ae o show. The plos eosae he vaiaio of he oalize aial pessue apaiy p / f, vesus he oalize aial a legh e /, fo a age of assue aial as. The ube of as age fo o. The ase oespos o a assupio of p a o ohesio i he ae oee, i.e. bile esile aig. The ase oespos o a ase of a ifiiely-igi ofiig eiu ousie he ove egio. Togehe, boh ases efie he heoeial bous o he soluio. I a be obseve ha he aial pessue apaiy is posiively oelae o he ube of aial as, a ha i ieases as a esul of ieasig a legh up o a axiu value a he eeases as he a beoes usable a spliig failue ous. I a also be obseve ha he oalize aial pessue values opue usig oel A ae geeally highe ha hose of oel A a lowe ha hose of oel A. Give Equaio, he aial pessue apaiy peie o he bo-spliig failue is he axiu espose i Figue a eah value a a be eeie ueially. These values have bee opue fo,, a fo oels A hough A a abulae i Table. The opuaioal ie equie fo opleig he soluio is also iiae fo eah oel. Fo ease of opaiso, all values i he able have bee oalize by he oespoig value (o he sae ow) fo Moel A. Table. Copaiso bewee aial pessue apaiy of efeee a aleaive oels. Moel A Moel A Moel A Moel A Moel A Tie p/f e/ (a) Ca legh-aial pessue apaiy fo oel A e/ (b) Ca legh-aial pessue apaiy fo oel A e/ () Ca legh-aial pessue apaiy fo oel A e/ () Ca legh-aial pessue apaiy fo oel A Figue. Paial esuls fo beha poble. p/f p/f p/f. Disussio This seio isusses he behavio of he opue espose usig oel A a is epeey o he assue ube of aial as, a opaes is peiios wih hose of oels A hough A o esablish he effe of hei uelyig assupios. I isussig he oel sesiiviy o he ube of aial as i seio.., he opaiso is liie o oels A, A, a A. This is beause he peie espose of oels A a A is o sigifialy iffee fo ha of oel A... Effe of ube of aial as I is lea i Figue ha he ifluee of affes piaily he pea pessue apaiy, while is effe o he opue espose a lowe e / values is less sigifia. The opue espose expeiees a ajo iease upo osieig he ohesio oibuio (fo o ), a ha he sesiiviy eeases quily as ieases fuhe. A oseva-

6 ive esiae of is ypially assue i esig siuaios fo hoosig appopiae ove hiess a ba ahoage leghs. Howeve, expeieal obsevaios by Reiha e al. (98) epo a osise obsevaio of hee as o oe. I a also be ague ha he assupio of a axisyei sess sae, upo whih he oel foulaio is base, is gossly violae by he assupio of oe aial a. Figue shows ha he sesiiviy of he oel peiio o he ueaiy i he ube of aial as fo values of > is highes i he efeee oel A. This sesiiviy eeases sigifialy i oel A a is iial fo oel A (% iease i p fo o, vesus % a 5% ieases fo A a A, espeively). I he age of ooly-obseve values of bewee a 5, he sesiiviy i peiio fo he hee oels is opaable a is equal o 7%, % a % fo A, A, a A, espeively. I us be oe ha he ube of aial as is a fuio of he geoey a bouay oiios suouig he ebee logiuial ba, whih ay iffe fo he iealize beha poble. Theefoe, oe olues ha a assupio of o saisfies he oel assupios, esuls i a sable esiae, a osevaively agees wih expeieal obsevaios i ases whee expeieal aa peie o he appliaio of iees is o available. I he pesee of appliaio-speifi expeieal aa, a pobabilisi appoah a be followe ha iis he aoess of he poess; wheeby a be assige a isee pobabiliy isibuio (e.g. Poisso) whose paaees a be esiae fo he aa. By siulaig a suffiie ube of ies fo his assige isibuio a subsiuig i he bo-spliig oel, he isibuio of he esulig bo segh a be geeae a is ea a ispesio esiae... Effe of biaxial behavio of oee I a be obseve i Table a Figue b ha iopoaig he biaxial behavio of oee has o sigifia effes o he esiae espose. The obseve effe esuls i a eease of he esiae axiu aial pessue apaiy a a iease of he e / value whee he axiu apaiy is obaie. O aveage, aial pessue apaiy values opue usig oel A fo he beha poble ae osisely less ha hose opue usig oel A by appoxiaely %. This esuls i uosevaive esiaes bu is opesae fo by he assupio of liea a wih isibuio... Effe of oliea a wih isibuio I a be obseve i Table ha aouig fo oliea a wih isibuio i oel A esuls i a iease i he esiae aial pessue apaiy by appoxiaely 5% a equies appoxiaely ies oe CPU ie fo he beha poble. The iease i auay is eee ifeasible a ujusifie fo oelig suh a loal pheoeo i he oex of a FE oel, espeially beause he iease auay oes o ee he oigial oel uosevaive. Thus, he iiial siplifyig assupio of egleig his effe is osiee aequae a jusifie... Effe of sofeig law I a be obseve i Table a Figue a ha, oue o ooly assue, he shape of he sofeig uve oes esul i a sigifia effe boh o he aial pessue apaiy a he oespoig e / value. Fo oel A, he iffeee i esiae axiu pessue apaiies is appoxiaely 8%, while fo oel A, he iffeee is appoxiaely 7%; fo agig bewee a 5 as. This is eviee ha he esigaio of he faue eegy as a sole paaee i aiio o is beig usually epiially assue ahe ha iely easue a hus highly ueai isea of a oe auae epeseaio of he aual posaig behavio is a ajo soue of ueaiy fo his oel. DETERMINISTIC SENSITIVTY ANALYSIS I has bee esablishe i he pevious seio ha he assupio of aleaive aeial sofeig laws a he use of ohesive-elasi bo spliig oels foulae aoigly leas o a sigifia vaiaio i he peie espose aoss hese oels, aely A, A, a A. Theefoe, he aopio of esile faue eegy as a sole oel paaee o haaeize he sofeig behavio is a ajo soue of ueaiy i he oel. This ueaiy is fuhe opoue by he ueaiy i he esile faue eegy value, whih is ofe esiae fo iie easuees. This seio iiviually exaies he obusess of he hee oels A, A, a A by ivesigaig he sesiiviy of he espose peie wihi eah oel o he oel ipu paaees. The opaaive suy is pefoe usig a eeiisi sesiiviy aalysis appoah, ooly efee o i he lieaue as he Toao iaga aalysis eho. A suay of his eho is esibe ex. A exesive eview a be fou i (Lee & Mosala 5) a a siila appliaio of his appoah o he pese suy a be fou i (Biii & Mosala 7). The Toao iaga aalysis is a eeiisi eho evelope o ueially eeie he sesiiviy of a oupu quaiy of iees o ueaiy i ipu paaee values, a hus esablish he elaive ipoae of he ipu paaees wih espe o hei ao aue. I his eho, a ef-

7 eee poi is iiially se by opuig he peie oel espose usig he expee ea values of he ipu paaees. Nex, he paaees ae iiviually vaie wihi a give age of ueaiy, ypially paaeeize by hei oeffiie of vaiaio (COV). The esulig hages (swigs) i he peie espose quaiy is opue, opae a soe aoss he iffee paaees. A gaphi opaiso of he opue sesiiviy easues (swigs) is use o esablish he elaive ipoae of he paaees. A lage sesiiviy easue is a iiaio of a highe elaive ipoae of he assoiae paaee a, osequely, a lage ole fo he ueaiy assoiae wih sai paaee i eeiig he ouoe a auay of he oel. I iepeig he esuls fo he opaaive suy, he followig ieia ae osiee o iiae a highe egee of oel obusess: (a) Relaively lowe sesiiviy o ueaiy i ipu paaees, (b) sigifia sesiiviy o oly a salle ube of paaees, a () espeially low sesiiviy o paaees i whih a highe egee of ueaiy is aiipae.. Poble saee The beha poble efie i seio is use i he pese Toao iaga aalysis. The peie axiu pessue p is efie as he oupu quaiy of iees. The lis of ipu paaees beig osiee a hei ea values is opose of he quaiies efie a he e of subseio.. The eeiisi sesiiviy of he oel espose o paaee ueaiy is alulae usig he elaive hage (swig) i he peie axiu pessue oespoig o oe saa eviaio sep o eihe sie of he ea value fo eah ipu paaee, wih a assue COV of %. Sie he oel sesiiviy o paaee ueaiy is geeally oliea, a igh sep size (i es of COV) is eoee i oe o bee epese he sesiiviy i he eighbohoo of he ea espose.. Resuls Figue shows he Toao iaga esuls fo oels A, A, a A, whee he paaee epeses sofeig law paaees,, a, espeively. The show esuls oespo o he ase of. The os ipoa oel paaee is he ba iaee, a i has he sae sesiiviy easue fo all oels. This is followe by he ove hiess he esile segh (oe evese fo A ) a appoxiaely equal ipoae. The fouh paaee o he lis is esile faue eegy, whee hee is a sigifia iffeee i he sesiiviy easue aoss oels. Hee sas a sigifia eease i ipoae fo he eaiig paaee i oels A a A, bu o i oel A. The elaive ipoae of he subseque vaiables oiues o eease. The iiu sesiiviy easue value is zeo fo he aveage aggegae size i oels A a A, whee i is o ilue i he sofeig law foulaio. Regaig ueaiy i he powe law paaees, oel A is os sesiive wih paaee havig a ipoae a of ou of 8. Paaee has a a of i oel A, while has a a of i oel A. Howeve he value of he sesiiviy easue iiaes ha oel A is slighly oe sesiive o paaee ha oel A is o paaee. I is woh oig ha he sesiiviy of oels owas he assue % COV is oeasuable wih hei sesiiviy o he ube of aial as ove hei age of expee values (subseio..). Thus, fo paaees whose expee COV is ypially lowe (e.g. ba iaee), o ypially highe (e.g. faue eegy), he elaive ipoae of he ube of as a be eue. Paaee Paaee Paaee Paaee Ras 8 s 7 f 5 G F w E a Relaive hage i espose (a) Toao iaga esuls fo oel A 8 s 7 f 5 G F E a w Relaive hage i espose Paaee Ras (b) Toao iaga esuls fo oel A 8 s 7 f 5 G F E w a Relaive hage i espose () Toao iaga esuls fo oel A Figue. Resuls of Toao iaga fo aial as. Paaee Ras

8 . Disussio Refeig o he ieia of oel obusess oulie ealie i seio, all oels isplay appoxiaely he sae sesiiviy owas he hee highes-aig paaees. These hee paaees ae ypially easie o esiae o easue iely wih liie ueaiy. Howeve, oels A a A o o isplay sigifia sesiiviy owas he eaiig paaees, wheeas oel A oes. Moeove, oel A is sigifialy sesiive o he faue eegy, whose esiaio ypially ivolves high ueaiy, a o he powe law paaees a w, whih ae highly ueai owig o peeive aoess i esio-sofeig espose. Theefoe, he popose oels A a A ae oe obus ha he efeee oel A. This is fuhe eifoe by he elaive sesiiviy of he hee oels o he ube of aial as peviously obseve i subseio... Moeove, sie oel A isplays less sesiiviy owas ueaiy i he eaiig paaees ha oel A, is o affee by he ueaiy i esiaig he aveage aggegae size, a shows eeasig sesiiviy owas faue eegy a he lowe-aig paaees wih iease ube of aial as (o show), i is osiee he os obus oel. 5 CONCLUDING REMARKS Fo he pevious isussios, he followig oluig eas a be ifee:. The ohesive-elasi oel fo bo failue bewee oee a logiuial seel bas by spliig has bee eviewe, a is assupios a siplifiaios have bee ieifie fo ivesigaio. Fou aleae oels have bee foulae o expliily aess eah assupio.. A beha poble has bee ioue o assess he elaive sigifiae of ipovig he iiviual oelig assupios.. I has bee eosae ha igoig he biaxial behavio of oee i esio esuls i a isigifia oveesiaio of bo segh. This effe is oue-balae by he equally isigifia effe of assuig liea a wih isibuio alog he a legh.. I has bee eosae ha he shape of he esio-sofeig aeial law is a sigifia fao of ueaiy i he aalyial oel, a ha i is ipoa o sele a sofeig law ha eliably epeses he osiee appliaio. 5. The oel sesiiviy o he ube of aial as has bee ivesigae. Reoeaios fo seleig a vali esiae i boh eeiisi a pobabilisi oexs wee pesee.. The elaive obusess agais paaee ueaiy i he efeee oel as well as wo oels foulae usig aleaive esio-sofeig aeial laws was assesse usig a Toao iaga aalysis fo he beha poble. 7. The efeee oel was fou o be elaively os sesiive o ueaiy i paaees whih ypially have a highly ao aue a hus is he leas obus. The wo aleae oels wee fou o be sigifialy less sesiive o highlyao paaees a shoul heefoe esul i a oe eliable peiio of bo segh. ACKNOWLEGMENT This suy is suppoe by he Eahquae Egieeig Reseah Cees Poga of he NSF ue Awa No. EEC-9758 o PEER a UC Beeley. Opiios a fiigs pesee ae hose of he auhos a o o efle views of he sposos. REFERENCES Baza, Z & Oh, B. 98. Ca ba heoy fo faue of oee. Maeials a Suues. (9): Biii, B. & Mosala, K. 7. Aalysis of eifoe oee olus eofie wih fibe eifoe polye laia. Coposies B: Egieeig. 8(): 5-7. Eligehause, R., Popov, E. & Beeo, V. 98. Loal bo sess-slip elaioships of efoe bas ue geealize exiaios. UCB/EERC-8/. Eahquae Eg. Reseah Cee, Uiv. of Califoia, Beeley, USA. Gabaova, P., Rosai, G & Shu, C. 99. A elasoohesive oel fo seel-oee bo. I Baza, Bia, Jiase, & Mazas (es) Faue a Daage i Quasibile Suues: Expeie, Moelig, a Copue Aalysis. Chapa a Hall: Hillebog, A, Moee, M. & Peesso, P. 97. Aalysis of a foaio a a gowh i oee by eas of faue ehais a fiie elees. Cee a Coee Reseah. : Lee, T.-H. & Mosala, K. 5. Seisi ea sesiiviy of eifoe oee shea-wall builig usig FOSM eho. Eahquae Egieeig a Suual Dyais. (): Raaale, S, & Wehaaaa, M Evaluaio of exisig faue oels i oee. I Li & Baza (es) Faue Mehais: Appliaio o Coee. ACI SP-8: -. Reiha, H & Va e Vei, C. 99. Spliig failue of a sai-sofeig aeial ue o bo sesses. I Capeiei (e.), Appliaio of Faue Mehais o Reifoe Coee. Elsevie Applie Siee: -. Reiha, H, Coeilsse, H. & Hoij, D. 98. Tesile ess a failue aalysis of oee. Joual of Suual Egieeig. ASCE. (): -77. Tepfes, R Caig of eifoe oee ove alog ahoe efoe eifoig bas. Magazie of Coee Reseah. (): -. Tiosheo, S. & Gooie, J. ( E.) 95. Theoy of Elasiiy. MGaw-Hill. Va Mie, J Faue Poesses of Coee. CRC Pess.