Fuzzy Logic Model of Fiber Concrete

Transcription

1 Fratur Mhani Conrt Conrt Strutur - High Prforman, Fibr Rinford Conrt, Spial Loading Strutural Appliation- B. H. Oh, t al. (d) 2 Kora Conrt Intitut, ISBN Fuzzy Logi Modl Fibr Conrt A. Kohoutková, P. Štmbrk & N.Pokorná Czh Thnial Univrity in Pragu, Pragu, Czh Rpubli Fuzzy Logi Modl Fibr Conrt A. Kohoutková, P. Štmbrk & N.Pokorná Czh Thnial Univrity in Pragu, Pragu, Czh Rpubli ABSTRACT: Th hap tr-train urv fibr onrt in uniaxial tnion trongly dpnd on amount typ ud fibr. Sin vn a mall hang in doag au riou variation trtrain urv, numrial intrprtation tr-train urv hould b robut nough to ovr ubtl diffrn hih in turn afft ignifiantly prforman ntir trutur. Thi papr drib an altrnativ approah to dfinition tr-train urv uing fuzzy logi. Th propod tool allo dfinition mooth urv, ho hap an b aily orrtd xprt intrvntion if nary. Thi approah an alo hlp to ovrom lak xprimntal data. Th mthod i xplaind in xampl. INTRODUCTION Th mhanial proprti fibr rinford onrt, imilarly to plain onrt, ar afftd mix proportion bai ontitunt alo addd fibr hih ar uppod to nhan pot-pak bhavior rar brittl onrt. A varity fibr ranging from tl fibr tard hap to ynti fibr ith vry pifi hap finih ar availabl in y afft mhanial bhavior onrt in variou ay, laboratory tt nd to b ondutd in ordr to prdit fibr onrt bhavior. In ordr to av tim mony on xprimntal ork, numrial analy an b prformd intad. Epially hn fft ag hould b alo takn into aount, u numrial, or virtual, tting hould b onidrd. Th uniaxial tr-train urv i on fundamntal rlation ud in matrial modling numrial trutural analy. Thrfor, onidring havy dpndn fibr onrt on variou paramtr, thi tudy fou on dvlopmnt a mthod for impl dfinition trtrain urv. Sin rliabl xprimntal data ar quit xpniv to obtain, but on or h r ar xprt ho an radily drib fibr onrt bhavior, fuzzy t ory ha bn mployd. Th fuzzy t (Zadh 96) pifially fuzzy ontrolling (Ro 99) ha bn utilizd in dfinition dird tr-train urv bau y provd uful in modling mhanial rpon hih a diffiult to drib analytially. A a hon author arlir (Štmbrk 28), thi approah i appliabl for dfinition hardning onrt. Variou xprimntal data rportd in litratur r ud for alibration tr-train diagram fibr rinford onrt inluding aging fft. Th mthod i xplaind in xampl it appliability in numrial analy i diud. 2 STRESS-STRAIN DIAGRAM OF FIBER REINFORCED CONCRETE Th xprimntal invtigation fibr rinford onrt i motly run on ylindrial, ubi or bam pimn. Suh pimn ar ubjtd to ir uniaxial tnil or ompriv loading or to flxur. Th rult xprimnt ar rordd uing for-diplamnt or tr-train diagram, hih allo dtaild undrting rpon onrt to loading, pially in a fibr rinford onrt in pot-pak rgion hn tl fibr ar ativatd hlp to bridg idning rak. Th rult variou xprimntal ork publihd in (Alhozaiamy t al. 99, Ding & Kutrl 2, Camp t al. 28) ar ud in thi tudy to prov appliability prntd approah. 3 FUZZY LOGIC IN DEFINITION OF STRESS- STRAIN CURVES Sin xprimntal data ar rar xpniv to obtain, xprimntal invtigation i arfully

2 J D h T h (, () plannd only f rprntativ amount fibr Th ar proportionality ltd. Thn, offiint matrial nginr i alld try to moitur timat prmability fft intrmdiat it i a nonlinar amount funtion fibr, hr in om a tatitially upportd intrpolation i attmptd, or mor prfrably xprt rlativ humidity h tmpratur T (Bažant & Najjar 972). Th moitur ma balan rquir dra ir on onluion try to add ir ida that variation in tim atr ma pr unit in matrial modl. Th fuzzy logi an n bom a vry uful tool a it allo xprt in volum onrt (atr ontnt ) b qual to divrgn fild matrial modling moitur flux J to add hi opinion in matrial modl, hil matrial modl an b radily = applid J in numrial analy, motly bad (2) on t finit lmnt mthod. Th atr ontnt an b xprd a um 3. Fuzzy vaporabl Logi atr (apillary atr, atr vapor, Th fuzzy adorbd t ory atr) i attributd to Lotfi non-vaporabl A. Zadh, (hmially ho publihd bound) hi famou atr papr (Zadh n (Mill 96) hr 966, Pantazopoulo h formulatd & Mill foundation 99). It thi raonabl ory. Th to aum fuzzy t that ory vaporabl provd vry atr uful i for a funtion tho problm ho humidity, input h, paramtr dgr ar hydration, impri α rlativ or, illdfind, ilia tn rprntd fum ration, αlinguiti, i.. = xprion. (h,α,α ) dgr = Thi ag-dpndnt i alo tru in orption/dorption a dfining iorm dpndni Mjonll tr-train 997). Undr diagram thi on aumption variou para- (Norling mtr, ubtituting mot Equation hih ar dribd into Equation in linguiti 2 on obtain trm xprind matrial intit, uing fuzzy logi. Sin it introdution fuzzy logi provd a flxibl robut intrumnt for ontrolling a hvarity pro ranging from tiny ( D h) = α& α& & n (3) ltroni h quipmnt h to α maiv αindutrial prodution thnology, (Klir 997), (Qurhi 26a), (Ro 99). Alo, in matrial modling, fuzzy logi ha bn / h i lop orption/dorption hr ud hn not nough xprimntal data iorm r availabl, (alo alld.g. in moitur (Akkurt 24), apaity). (Qurhi Th govrning 26b), (Štmbrk quation 26), (Equation (Tanyildizi 3) mut 27), b ompltd or (Unal appropriat 27). boundary initial ondition. Th Th rlation bai btn fuzzy logi, ho amount or i vaporabl diion-making, rlativ onit humidity thr i bai alld tp. adorption Firtly, atr iorm fuzzifiation maurd i prformd, ith inraing hn input rlativity variabl ar aignd dorption a dgr iorm mmbrhip in oppoit to a humidity a. fuzzy Nglting t. Sondly, ir diffrn diion-making (Xi t al. 994), itlf in i run, folloing, hn orption output variabl iorm ar givn ill b a ud dgr ith rfrn mmbrhip to both to it orption fuzzy t aording dorption to ondition. xprt By rul. Thirdly, ay, if through hytri dfuzzifiaton, a ingl moitur ral iorm valu ould obtaind. b For takn into fuzzy aount, logi, it to i ruial diffrnt to rlation, did a vaporabl propr numbr atr v fuzzy rlativ t humidity, for both mut input ud aording output variabl to ign hap variation ir mm- b rlativity brhip funtion humidity. o Th that hap prforman orption iorm fuzzy logi for HPC ytm i inflund i both aptably many pri paramtr, pially omputationally tho that inxpniv. influn xtnt rat hmial To fuzzy-logi ration, approah in turn, to dfinition dtrmin por trutur tr-train urv por iz fibr ditribution onrt (atr-to-mnt ar dribd in ratio, folloing. mnt hmial ompoition, SF ontnt, uring tim mthod, tmpratur, mix additiv, t.). 3.2 Claial In litratur Fuzzy-logi variou Approah formulation to Dfinition an b found Str-train to drib Diagram orption iorm normal onrt (Xi t al. 994). Hovr, in prnt papr Th firt propod mi-mpirial modl xprion u laial propod fuzzy logi thniqu, hn ah ombination Norling Mjornll (997) i adoptd bau it fuzzy t dribing input variabl i aignd xpliitly aount for volution hydration a ration fuzzy t SF output ontnt. variabl. Thi orption Spifially, iorm laial rad produr ud for dfining tr-train urv fibr rinford onrt run a follo. µ ( h, α, α ) Input = G ( α- train, α ) ( ) g α α h ( g Strain α α ) h K ( α, α ) hr µ firt trm Input (gl- ag iorm) rprnt phyially bound 8 (adorbd) 27 6 atr 8. ond trm (apillary iorm) rprnt apillary atr. Thi xprion i valid only for Hour lo ontnt SF. Th offiint... G rprnt amount atr pr unit volum hld in gl por at % rlativ humidity, it an b xprd (Norling Mjornll 997) a µ Input amount fibr G ( α, α ) = k α k α () vg vg Fibr hr k vg k vg ar matrial paramtr. From maximum amount atr pr unit volum that an fill all por (both apillary por gl por), on an alulat K a on obtain Matrix Fuzzy Rul α α K (, ) g α α Strain α α G = g α α STRESS Fibr Not that, at arly ag, in hmial ration µ Output - tr aoiatd ith mnt hydration SF ration ar xormi, tmpratur fild i not. uniform for non-adiabati ytm vn if nvironmntal tmpratur i ontant. Hat ondution Str an b dribd in onrt,... at lat for tmpratur. 4 not xding C (Bažant & Kaplan 996), Fourir la, hih rad STRESS (4) (6) Th matrial paramtr k vg k vg g an b alibratd Ag fitting xprimntal data rlvant to fr (vaporabl) atr ontnt in onrt at variou ag (Di Luzio & Cuati 29b). 2.2 Tmpratur volution q = λ T (7) hr q i hat flux, T i abolut Figur tmpratur,. Flohart λ dfinition i hat uing ondutivity; laial fuzzy in logi thi produr. Proding FraMCoS-7, May 23-28, 2

3 Firtly, input train, input ag input amount fibr ar fuzzifid. Sondly, fuzzy t rprnting tr orrponding to fuzzy t xpring train, ag amount fibr ar ltd, thirdly, tr i dfuzzifid obtaind in form a ingl valu. Th flo laial fuzzy logi produr i hon in Figur. Th ntri in matrix fuzzy rul r ltd to giv minimum rror at a ltd numbr point. Thi a don manually a numbr tr-train urv a lo. Similarly, fuzzy rul r dfind in (Štmbrk 28), (Tanyildizi 27) (Unal 27). Mamatially, thi modl rprnt linar intrpolation btn point ith dgr mmbrhip qual to unity. Th drabak laial fuzzy logi mthod hn linar mmbrhip funtion ar ud i a rar rough hap tr-train urv diontinuou firt drivativ. Of our, hap rulting tr-train urv an b moor if a largr numbr fuzzy t i ud. Thi hovr man a muh largr numbr fuzzy rul, hih nd to b didd hih ould mak thi mthod vry diffiult for u matrial nginr ho hav poor bakground in fuzzy logi. Or, nginr ould not b abl to dfin ubtl diffrn in bhavior tr-train diagram, hih ould unnaturally mrg ith finly rfind train tr. Thrfor, it m mor raonabl to modify fuzzy logi modl o that gnration optimization numbr hap fuzzy t i don automatially only diion-making dfind jut a f rprntativ ombination train, ag, amount fibr tr rmain to b didd matrial nginr. 3.3 Modifid Fuzzy-logi Approah to Dfinition Str-train Diagram Th main diffrn modifid modl from laial fuzzy logi on i rprntd paration diion-making from dfinition knon tr-train urv, hn in laial approah all knon tr-train urv ar dfind am numbr fuzzy t rprnting train. Obviouly, minimum numbr fuzzy t nary for dription tr-train urv at givn auray dpnd on omplxity it hap our it may diffr for diffrnt tr-train urv. In modifid approah, optimization i prformd automatially indpndntly ur, hih man ur do not hav to dfin mot rprntativ point in tr-train urv aording to xprimntally obtaind tr-train urv ur xprti, hih i nary in laial fuzzy logi modling. Th rprntativ point ar rprntd J D ( h, T h ntri in diion-making matrix, hih orrpond to n-tupl Th proportionality fuzzy t xpring offiint input variabl. moitur prmability it i a nonlina rlativ humidity h tmpratur & Najjar 972). Th moitur ma balan µ Input - train that variation in tim atr ma volum onrt (atr ontnt ) b q divrgn moitur flux J Strain = J t µ Input - ag Th atr ontnt an b xprd a vaporabl atr (apillary a vapor, adorbd atr) non- (hmially bound) Hour atr n (Mil... 8 Pantazopoulo &. Mill 99). It i ra aum that vaporabl atr i a fu rlativ humidity, h, dgr hydration µ Input amount fibr dgr ilia fum ration, α, i.. = = ag-dpndnt 2 4 orption/dorption 6 (Norling Mjonll 997). Undr thi aum ubtituting Equation Fibr into Equati obtain h ( D h) = α& α& h h α α Fuzzy Diion-making on Group Optimizd Fuzzy St Group hr 4 / h i lop orption/ iorm (alo alld moitur apa govrning quation (Equation 3) mut b Group 3 appropriat boundary initial onditi Th rlation btn amount Group 2 atr rlativ humidity i alld iorm if maurd ith inraing Group humidity dorption iorm in th a. Nglting ir diffrn (Xi t al. folloing, orption iorm ill b rfrn to both orption dorption By ay, if hytri iorm ould b takn into aount, to rlation, vaporabl atr v rlativ humi b ud aording to ign varia rlativity humidity. Th hap iorm for HPC i inflund many p pially tho that influn xtnt hmial ration, in turn, dtrm trutur por iz ditribution (atrratio, mnt hmial ompoition, SF uring tim mthod, tmpratur, mix t.). In litratur variou formulatio found STRESS to drib orption iorm onrt (Xi t al. 994). Hovr, in th Figur 2. Flohart papr dfinition uing mi-mpirial modifid fuzzy xprion logi pro produr. Norling Mjornll (997) i adoptd b Modl - kg fibr Modl - 2 kg fibr Modl - 4 kg fibr Modl - 6 kg fibr Proding FraMCoS-7, May 23-28, 2

4 J D h T h (, () In modifid approah, ur tak i to did Th proportionality numbr offiint rprntativ intrval i alld moitur train prmability ag, on ah it intrval i a nonlinar to did funtion aording to hi/hr xprti ho tr-train urv rlativ humidity h tmpratur T (Bažant for a givn amount fibr i lo to any & Najjar 972). Th moitur ma balan rquir knon tr-train urv. For xampl, at firt that variation in tim atr ma pr unit quartr tr-train urv, ontrutd volum onrt (atr ontnt ) b qual to tr-train urv hould follo a rtain knon divrgn urv. In ond moitur quartr, flux J it hould b lightly abov am knon urv, in rmaining part = J tr-train diagram it hould b idntial (2) to t am urv. Thi approah dfinition fuzzy logi modl i natural for xprind matrial nginr. Th atr Th ontnt flo an b modifid xprd approah a um i hon vaporabl in Figur 2. atr Alo, it hlp (apillary to utiliz atr, atr xat vapor, hap adorbd knon atr) tr-train non-vaporabl urv, hih (hmially ould b lot bound) hn uing atr laial n (Mill approah 966, ith Pantazopoulo a limitd numbr & Mill fuzzy 99). t. It An i xampl raonabl rult obtaind that vaporabl thi approah atr i i doumntd a funtion to aum rlativ any humidity, gray urv h, dgr in Figur 3 hydration, to 9 ( xplanation i givn ilia in fum ration, folloing α α, dgr tion)., i.. =If (h,α ur,α ) = do ag-dpndnt not pify fft orption/dorption amount fibr iorm on (Norling hap Mjonll 997). tr-train Undr urv thi aumption uing nonlinar ubtituting mmbrhip Equation funtion, into hih Equation drib 2 on obtain tranition btn knon tr-train urv, only to fuzzy t ar ud for ntir rang train, rult i a linar intrpolation btn to h knon nighboring tr-train urv. ( D h) = α& α& & n (3) Hovr, h a a h pointd α out abov, α ur an alo rfin fft amount tl fibr on tr-train urv dividing rang train hr into a numbr / h i lop orption/dorption rprntativ intrval. Thn iorm ur an aily (alo dfin alld hr moitur an amount apaity). tl Th fibr mak quation onrt (Equation bhav 3) mut imilarly b ompltd (or ho govrning muh appropriat imilarly) boundary to a knon initial tr-train ondition. urv or urv Th rlation ah intrval. btn amount vaporabl atr rlativ humidity i alld adorption iorm if maurd ith inraing rlativity humidity 4 RESULTS dorption AND DISCUSSION iorm in oppoit a. Nglting ir diffrn (Xi t al. 994), in Th folloing, rult prntd orption iorm diud in ill thi b tion ud ith ha rfrn bn obtaind to both uing orption modifid dorption approah ondition. dfinition tr-train ay, if urv. hytri moitur By iorm Th xprimntal ould b takn data into hon aount, in Fig. to 3 to diffrnt r rlation, takn from vaporabl (Ding & atr Kutrl v rlativ 2), humidity, hr only mut b ompriv ud aording tr-train to ign urv for variation ag 9 rlativity 8 hour humidity. for plain Th onrt hap tl fibr orption onrt r for prntd. HPC i inflund Th only aompanying many paramtr, infor- iorm pially mation on tho volution that influn xtnt matrial ovr rat tim i hmial givn ration a tabl ompriing, in turn, volution dtrmin por trutur ompriv por trngth iz ditribution ag 8, (atr-to-mnt, 8, 3, 48 ratio, 72 mnt hour hmial for ompoition, tl fibr onrt SF ontnt, mix uring ith, tim 2, 4 mthod, 6 kg tmpratur, tl fibr. mix Th additiv, tak in t.). thi a In a litratur to dfin variou intrmdiat formulation tr-train an b found urv to bad drib on orption providd iorm xprimntal normal data, onrt hih r (Xi rar t al. ar. 994). Fig. Hovr, 3 ho in dfinition prnt papr tr-train mi-mpirial urv for xprion onrt at propod ag 9 hour ith amount tl fibr, 2, 4 Norling Mjornll (997) i adoptd bau it 6 kg. Th tr-train urv for amount xpliitly aount for volution hydration ration 6 kg r SF alibratd ontnt. uing Thi orption availabl iorm xprimntal rad data hil tr-train urv for intrmdiat amount tl fibr r dfind modifid fuzzy-logi algorithm. ( h, α, α ) = G ( α, α ).8 ( g α α ) h xprimnt (4) modl.6 ( g α α ) h K ( α, α ).4 6, 6 hr 4.2 firt trm (gl iorm) rprnt 2 phyially bound (adorbd) atr ond, trm (apillary iorm) rprnt apillary atr.. Thi xprion i valid only for lo ontnt SF. Th offiint 2 G4 rprnt 6 8amount atr pr unit volum Strain hld [mm/m] in gl por at % rlativ humidity, it an b xprd (Norling Figur Mjornll 3. Str-train 997) a urv ontrutd modifid approah from xprimntal data at 9 hour ag. Str [MPa] G ( 3 α, α ) = k α k α () vg vg xprimnt 3 modl hr 2 k vg k vg ar matrial paramtr. From maximum amount atr 6, 6 pr unit volum that an fill 2 all por (both apillary 4 por gl por), on an 2 alulat K a on obtain Str [MPa] K g α α,.88α.22α G ( α, α ) = g α α Strain [mm/m] Figur Th 4. Str-train matrial paramtr urv ontrutd k vg modifid k vg approah g an from b alibratd xprimntal data fitting at 8 hour xprimntal ag. data rlvant to fr (vaporabl) atr ontnt in onrt at variou 3 ag (Di Luzio & Cuati 29b). 8h-6 xprimnt 3 8h- modl 2.22Tmpratur volution 48h-6 48h- Not 2 that, at arly 24h-6 ag, in hmial ration aoiatd ith mnt 24h- hydration SF ration ar xormi, tmpratur fild i not uniform for non-adiabati ytm vn if nvironmntal tmpratur 9h-6 i ontant. Hat ondution an b dribd in 9h- onrt, at lat for tmpratur not xding C (Bažant & Kaplan 996), Fourir la, hih 2 rad Str [MPa] (6) q = λ T (7) Figur. Str-train urv ontrutd modifid approah for ag hour. hr q i hat flux, T i abolut tmpratur, Sin no additional λ i information hat ondutivity; for volution in thi tr-train urv a availabl, a impl li- Proding FraMCoS-7, May 23-28, 2

5 nar intrpolation btn knon tr-train urv a aumd. Th rulting tr-train urv obtaind fuzzy modl (gray urv) in Fig. 4 r obtaind imilarly. Of our, if mor dtaild information i availabl, tranition btn kno urv an radily rflt that information, hih ould rult mot probably in nonlinar tranition. Str [MPa] %. %.2 %. %.2 %. %.3 % markr = xprimnt lin = modl Figur 6. Str-train urv ontrutd modifid approah for intrmdiat fibr amount. %.2 %. In Fig. 6, miing tr-train urv amount. %.2 % in (Alhozaiamy 99) r addd uing modifid fuzzy modl. Th raoning in diion-making produr onidrd inonitny in xprimntal data hn avrag train-train urv for oupl % 3 % % 2 % r not idntial. Thrfor, non-linar tranition btn knon tr-train urv a didd ith additional knoldg on imilarity tr-train urv for variou amount fibr at diffrnt part tr-train urv, hih alo ommonly ud in fratur modl onrt,.g. (Stahli & van Mir 27). Str [MPa] d 7d 2d markr = xprimnt lin = modl Figur 7. Evolution tnil tr-train urv plain onrt. Fig. 7 to 9 ontain xprimntal data on volution tnil trngth fibr onrt, pifiall tr-train urv for plain fibr onrt at ag 2, 7 28 Th day proportionality publihd in (Camp offiint t al. 28). Fig. 7 moitur to 9 try to prmability doumnt apability it i a nonlina modifid fuzzy approah to opy prily rlativ humidity h tmpratur xprimntally obtaind mhanial bhavior fibr onrt in tnion. & Najjar 972). Th moitur ma balan that variation in tim atr ma volum onrt (atr ontnt ) b q divrgn moitur flux J Str [MPa] 4 3 markr = xprimnt lin = modl 2 Th atr ontnt an 7d b xprd a vaporabl atr (apillary a vapor, adorbd atr) 2d non- (hmially bound) atr n (Mil Pantazopoulo & Mill 99). It i ra aum that vaporabl atr i a fu rlativ humidity, h, dgr hydration dgr ilia fum ration, α, i.. = Figur 8. Evolution = tnil ag-dpndnt tr-train urv orption/dorption tl-fibrrinford onrt (ntir train rang). (Norling Mjonll 997). Undr thi aum ubtituting Equation into Equati obtain 24d 4 markr = xprimnt h 3 ( lin D = hmodl ) = α& α& h h α α Str [MPa] D ( h, T h 2 7d hr / h i lop orption/ 2d iorm (alo alld moitur apa govrning quation (Equation 3) mut b appropriat boundary initial onditi Th rlation btn amount atr rlativ humidity i alld iorm if maurd ith inraing Figur 9. Evolution humidity tnil tr-train dorption urv tl-fibrrinford onrt (lo-up). iorm in th a. Nglting ir diffrn (Xi t al. folloing, orption iorm ill b rfrn to both orption dorption CONCLUSION By ay, if hytri To approah iorm to dfinition ould b takn tr-train into aount, to urv fibr rinford rlation, onrt vaporabl r atr propod. v rlativ In humi firt approah, b hih ud aording i bad on to ign laial varia fuzzy-logi ontrol, rlativity matrial humidity. nginr Th i xptd hap to dfin numbr iorm for fuzzy HPC t i for inflund dription many p train, ag onrt, pially tho amount that influn fibr xtnt tr, to dfin hmial fuzzy ration rul, hih, ar in olltd in diion-making trutur matrix. por iz Sin ditribution thi ap- (atr- turn, dtrm proah, pially ratio, hn mnt only fuzzy hmial t ith ompoition, linar SF mmbrhip funtion uring ar tim ud, mthod, rquir tmpratur, a larg mix numbr fuzzy t, t.). hih In ubquntly litratur variou rquir formulatio a larg numbr fuzzy found diion to drib to b t, orption it i blivd that matrial onrt nginr (Xi t may al. find 994). uh Hovr, dfi- in th iorm nition matrial papr modl rar mi-mpirial tdiou, vn though xprion pro thi approah giv Norling him onidrabl Mjornll frdom (997) in i d- adoptd b finition matrial bhavior. J t = J 24d Proding FraMCoS-7, May 23-28, 2

6 J D h T h (, () Thrfor, a modifid approah a propod hih Th proportionality prform optimization offiint numbr i alld moitur fuzzy t prmability hap it i a fuzzy nonlinar t automatially. Thi man that thi part modl dfini- funtion rlativ humidity h tmpratur T (Bažant tion i prformd indpndntly matrial nginr hih rdu ur orkload & Najjar 972). Th moitur ma balan rquir that variation in tim atr ma pr unit nur objtivity. Thn, only tak lft for volum onrt (atr ontnt ) b qual to matrial nginr i vry natural duty diding divrgn rang train moitur flux J ag hr hap tr-train urv hould b rfind to hih = matrial J bhavior invtigatd pimn t i mor imilar. (2) Sin fuzzy-logi matrial modl on outid Th i atr idntial ontnt to tard an b funtion xprd dfining a um matrial vaporabl modl, hih atr man (apillary input atr, paramtr atr vapor, funtion adorbd atr) output ar non-vaporabl idntial, (hmially fuzzy-logi matrial bound) modl atr an b n radily (Mill ud in 966, xiting finit lmnt & Mill od. 99). It i raonabl to Pantazopoulo aum that vaporabl atr i a funtion rlativ humidity, h, dgr hydration, α, dgr 6 ACKNOWLEDGEMENT ilia fum ration, α, i.. = (h,α,α ) = ag-dpndnt orption/dorption iorm (Norling Th finanial Mjonll upport 997). Undr Minitry thi aumption Eduation, Youth ubtituting Sport Equation Czh into Rpubli, Equation projt 2 on obtain MSM684773, i gratfully aknoldgd. 7 REFERENCES h ( D h) = α& α& & n (3) h h α α Akkurt, S., Tayfur, G. & Can, S. 24., Fuzzy logi modl for prdition mnt ompriv hr trngth. / h i lop orption/dorption Cmnt onrt rarh 34: 429- iorm 433. (alo alld moitur apaity). Th govrning Alhozaimy, quation A.M., Sorouhian, (Equation 3) P. mut & Mirza, b ompltd F. 99. appropriat Mhanial boundary proprti initial polypropyln ondition. fibr Th rinford rlation onrt btn amount fft vaporabl pozzolani atr matrial. rlativ Cmnt humidity & Conrt i alld Compoit adorption 8: iorm if maurd ith inraing rlativity humidity Camp, G., Turtinz, dorption A., Sllir, iorm A., in Eadilla, oppoit G. a. & Nglting Bourbon, ir X. 28. diffrn Stl-fibr-rinformnt (Xi t al. 994), in folloing, hydration orption oupld iorm fft on ill onrt b ud tnil ith rfrn bhaviour. to both Enginring orption Fratur dorption Mhani ondition. 7: By ay, if hytri moitur iorm ould b takn into aount, to diffrnt rlation, vaporabl atr v rlativ humidity, mut b ud aording to ign variation rlativity humidity. Th hap orption iorm for HPC i inflund many paramtr, pially tho that influn xtnt rat hmial ration, in turn, dtrmin por trutur por iz ditribution (atr-to-mnt ratio, mnt hmial ompoition, SF ontnt, uring tim mthod, tmpratur, mix additiv, t.). In litratur variou formulation an b found to drib orption iorm normal onrt (Xi t al. 994). Hovr, in prnt papr mi-mpirial xprion propod Norling Mjornll (997) i adoptd bau it xpliitly aount for volution hydration Ding. ration Y. & Kutrl, SF ontnt. W. 2. Thi Compriv orption iorm trtrain rlationhip tl fibr-rinford on- rad rt at arly ag. Cmnt Conrt Rarh 3: Klir, G., St.Clair, U. & Yuan, B Fuzzy t ory: ( h, α, αfoundation ) = G ( α, α ) appliation. Uppr Saddl Rivr: Prnti-Hall. ( g α α ) h Qurhi, M.F. & Bharti, I.C. 26a. Fuzzy bad (4) tudy imulation loal hat ( g α tranfr α ) h offi- int at irumfrn K ( α, α ) horizontal tub in fr board rgion fluidizd bd. Modlling, Maurmnt & Control B. Solid & Fluid Mhani hr & Thrmi, firt Roboti trm (gl Mhanial iorm) Sytm, rprnt Civil Enginring, AMSE 7(): -2. phyially bound (adorbd) atr ond Qurhi, M.F., Gabl, R.K. & Hota, H.S. 26b. trm (apillary iorm) rprnt apillary Fuzzy raoning bad imi har dign atr. Thi xprion i valid only for lo ontnt rinford onrt trutural all. Modlling, SF. Th offiint G Maurmnt & Control rprnt amount B. Solid & Fluid Mhani atr pr unit & Thrmi, volum hld Roboti in Mhanial gl por at Sytm, Civil % rlativ humidity, Enginring, it an AMSE b 7(6): xprd (Norling Ro, Mjornll J.T. 997) 99. a Fuzzy logi ith nginring appliation. N York: MGra-Hill, In. Stahli, P. & van Mir, G ( α, α ) = k α k J.G.M. α 27. Manufaturing, () fibr aniotropy vg vgfratur hybrid fibr onrt. Enginring Fratur Mhani 74: 223- hr 242. k vg k vg ar matrial paramtr. From Štmbrk, maximum P., amount Pokorná, atr N. & pr Kohoutková, unit volum A. that 28. an fill Matrial all por modl (both apillary hardning por onrt gl por), bad on on an fuzzy alulat logi. Kin a Mult on (d.), obtain Pro. Int l Conf. on Modling Simulation 28, Palma d Mallora, 8-2 Jun 28. Palma d Mallora: Univritat d Ill Balar. g α α.88α.22α G Tanyildizi, H. 27. Fuzzy logi modl for prdition α, α ) = bond trngth high-trngth lightight (6) K ( onrt. Advan in genginring α α Star 4: Unal, O., Dmir, U. & Uygunoglu, T. 27. Fuzzy logi Th matrial approah paramtr to prdit ktr-train vg k vg urv g an b tl alibratd fibr-rinford fitting xprimntal onrt in data omprion. rlvant to fr Building (vaporabl) nvironmnt atr ontnt 42: in onrt at Zadh, variou L. ag A. 96. (Di Luzio Fuzzy & t. Cuati Information 29b). Control 8(3): Tmpratur volution Not that, at arly ag, in hmial ration aoiatd ith mnt hydration SF ration ar xormi, tmpratur fild i not uniform for non-adiabati ytm vn if nvironmntal tmpratur i ontant. Hat ondution an b dribd in onrt, at lat for tmpratur not xding C (Bažant & Kaplan 996), Fourir la, hih rad q = λ T (7) hr q i hat flux, T i abolut tmpratur, λ i hat ondutivity; in thi Proding FraMCoS-7, May 23-28, 2