Fratur Mhani Conrt Conrt Strutur - Amnt, Durability, Monirg Rtrittg Conrt Strutur- B. H. Oh, t al. (d) 2 Kora Conrt Intitut, Soul, ISBN 978-89-578-8-5 Influn tmpratur ompoition upon dryg onrt F. Bru, Y. Liang, N. Burlion & F. Skozyla Laborair d Méaniqu d Lill (LML), illnuv d Aq, Fran X. Bourbon & G. Camp Andra, Châtnay-Malabry, Fran ABSTRACT: Th Frnh long-trm rpoiry for trmdiat lvl/long livd nular wat onit a ntwork undrground onrt tunnl dp gologial mdium. ariou loadg will our durg rpoiry rvi-lif. Among phyial ontrat, pially d-aturation/r-aturation pro, por prur variation tmpratur hang will afft onrt proprti. Th d-aturation pro i lkd rlativ humidity dra, rlation tmpratur variation. D-aturation lad hrkag tra that tn du miro-rakg. Miro-rak an ra onrt prmability dra mhanial proprti. Thi xprimntal tudy fou on dryg pro it onqun. Th tudid matrial ar onrt, bad on I or /A-typ mnt. Th flun tmpratur mnt ompoition upon dryg hrkag i hown b important. Du thi, tranport proprti dpnd on mnt ompoition. An ra tmpratur up 8 C alrat dryg mhanim by man rmal ativation. INTRODUCTION Th Frnh National Agny for Nular Wat Managmnt (Andra) ha dign tudy long-trm nular wat rpoiry faibility dp gologial mdium. Th urrnt onpt for trmdiat lvl/long livd nular wat onidr failiti at 5m dpth, a lay layr (Callovo- Oxfordian argillit), loatd Eat Fran. Th rpoiry i dignd a a tunnl ntwork, whih lad onrt vault whr nular wat will b plad. Whn vault ar filld with wat, a mixd lay onrt plug lo a gallry. Th dign ha tak aount phyial hmial phnomna du wat ativity, a wll a pro rlation gologial mdium bhavior (Andra 25). Among poibl phnomna, hot rok d-aturation/r-aturation pro, rlation rpoiry buildg xploitation, will afft onrt omponnt rpoiry. Part trmdiat lvl wat i xormi. Thu, a rmal loadg ha b takn aount. A a rquirmnt, maximal tmpratur trmdiat lvl wat vault ha b l than 7 C (Andra 25). Morovr, ordr drib long-trm (ovr thou yar) mhanial volution rpoiry, hrkag rp hav b ad a wll a poibl. Both mhanial loadg du -itu tr daturation/r-aturation pro ar volvd a ommon agg pro thi mut b takn aount. In rlation ritial dutrial iu, prnt tudy vtigat d-aturation pro undr ontrolld tmpratur rlativ humiditi, for two onrt matrial bad on I mnt typ. 2 EXPERIMENTAL APPROACH 2. Conrt formulation Th tudid matrial ar rfrn onrt Andra program for rpoiry dign. Two typ mnt ar ud: () a I typ, whih i mad Portl lkr, (2) a /A typ, whih i ontitutd 6% lkr ma, 22% blatfurna lag, 4% iliou fillr (i.. fly ah) 4% ttg rgular, aordg NF EN 96-4 Europan Stard (Andra & CEBTP 2, Andra & LERM 2). Blat furna lag fly ah at a pozzolani additiv /A mnt. Th diffrn btwn both formulation will b mirotrutur onrt ( tion 2.5). Conrt mad with a I mnt ha a --mnt ratio (W/C) qual.43 i alld I. Conrt prpard with a /A mnt, with a W/C ratio qual.39, i namd. Tabl giv both onrt formulation.
Tabl J = D. ( Conrt h, T ) h formulation. Natur Quantity [kg/m 3 () ] Matrial I Cmnt Th proportionality I 52.5 R offit 4 D(h,T) i alld - moitur Cmnt prmability /A 42.5 N it i a nonlar - funtion 45 S rlativ Limn humidity [-4mm] h tmpratur 858 T (Bažant 8 & Gravl Najjar 972). Limn Th moitur [5-2mm] ma 945 balan rquir 984 that Admixtur variation Glnium 27 tim ma pr.5 unit Watr - 7 76.3 volum onrt ( ontnt w) b qual divrgn moitur flux J 2.2 Conrt ampl Sampl = ar J mad from a gl bath for ah (2) mnt t typ. Primati ampl ar mad tard mould with a volum qual (4 4 6) m 3. Prior atg, Th ontat ontnt blok w an (i.. b xprd tud) ar a plad um ah mould vaporabl follow hrkag w (apillary volution., vapor, Aftr un-moldg, adorbd ) ampl ar urd non-vaporabl undr at (hmially 2 C durg bound) ix month bfor w u. n (Mill Thrfor, 966, w an Pantazopoulo onidr that & hydration Mill 995). pro It i i raonabl omplt that aum onrt that mirotrutur vaporabl will no i longr a funtion vary ignifiantly rlativ humidity, (Baroghl h, Bouny dgr 994, hydration, Baroghl αbouny, t dgr al. 999). ilia Morovr, fum ration, onrt α, ar i.. -aturatd w =w (h,α,α ) at = ag-dpndnt nd maturation. orption/dorption iorm (Norlg Mjonll 997). Undr thi aumption by ubtitutg Equation Equation 2 on 2.3 obta Control d-aturation pro Conrt d-aturation i a hydrauli pro whih atr h mov by man apillary prur. + ( D h) = Capillary prur i dfd α& + a α& + diffrn w& n btwn liquid ga prur: (3) h t h α α whr / h i lop orption/dorption iorm Pap = Pliq (alo Pga alld moitur apaity). () Th govrng quation (Equation 3) mut b ompltd by appropriat boundary itial ondition. Sution i rlatd dra ontnt, o Th rlation btwn amount vaporabl that, aftr quilibrium, mallt por rma -aturatd. rlativ humidity i alld adorption iorm if maurd with rag rlativity Klv law rlat apillary prur urrnt humidity dorption iorm oppoit tmpratur rlativ humidity: a. Ngltg ir diffrn (Xi t al. 994), followg, orption iorm will b ud with rfrn RT Pap = ρ both w ln( rh orption ) dorption ondition. (2) By way, Mw if hytri moitur iorm would b takn aount, two diffrnt whr rlation, ρ w vaporabl i dnity (funtion v rlativ humidity, tmpratur) mut [kg/m b ud 3 ]; aordg R i prft ign ga ontant variation [J/mol.K]; T i rlativity tmpratur humidity. [K]; Th M w hap i molar orption ma [kg/mol] iorm for HPC rh i i rlativ flund humidity. by many Th paramtr, ra pially apillary tho prur that flun will b xtnt ir du rat an ra hmial tmpratur ration, or a turn, dra dtrm rlativ por humidity. trutur Th por variation iz ditribution lad (--mnt phyial fft upon ratio, onrt. mnt hmial ompoition, SF ontnt, urg For tim a tmpratur mthod, lo tmpratur, 2 C, it mix i additiv, gnrally admittd t.). In that litratur (Baroghl variou Bouny 994, formulation Baroghl an Bouny found t al. 999, drib Ma t al. orption 27, Yurtda iorm 23): normal b onrt - for rlativ (Xi t humidity al. 994). valu Howvr, from 45% %, prnt papr ma d-aturation mi-mpirial mhanim xprion i liquid propod by Norlg Mjornll (997) i adoptd bau it movmnt xpliitly aount du apillary for prur. volution hydration ration - for lowr rlativ SF ontnt. humidity Thi valu, orption diffuion iorm rad vapor i ma phnomnon ladg tranport. Morovr, an ra tmpratur du oalld rmal ativation (Caré 28, Choka w ( h, α, α ) = G ( α, α ) + 26, Gall t al. 26, Ihida t al. 27, Jo & ( g α α ) h Rhardt 22, Noumouw t al. 996), whih (4) alrat vaporation ondnation pro. Indd, proprti ( liquid g α α ) h vapor K ( α, α ) hang with tmpratur (vioity dra for liquid, ra for vapor). Hn, tranfr proprti uh a prmability diffuion ar d- pndnt whr on tmpratur. firt trm (gl iorm) rprnt phyially Th d-aturation bound (adorbd) pro i tudid hr at ond thr fixd trm (apillary tmpratur iorm) (2 C, rprnt 5 C 8 C). apillary Tmpratur. Thi xprion rlativ humidity i valid only ar both for low ontrolld ontnt ug SF. limati Th offit hambr. G rprnt Fixd rlativ amount humidity valu pr ar: unit rh=98%, volum rh=9%, hld rh=8%, gl por rh=7% at % rh=6%. rlativ humidity, Thy hav bn it an hon b xprd approah (Norlg two aturation Mjornll 997) dgr a for ah matrial (S w =.8 S w =.6). G ( α, α ) = k α + k α (5) vg vg 2.4 Maurmnt produr: ma, hrkag aturation dgr whr k vg k vg ar matrial paramtr. From Thr maximum kd amount maurmnt pr unit ar volum arrid that out an tudy fill all por d-aturation (both apillary pro por a a funtion gl por), tmpratur: an alulat ma Kvariation, a on obta hrkag atura- on tion dgr. Ma volution ovr tim i maurd with an auray +/-.g. w.88α +.22α G Shrkag i maurd undr ontrolld ondition: K ( α, αt=2±5 C ) = rh=4±5%. Shrkag ma- (6) urmnt u a lar trur with an auray on miromtr (Garia Boiv 2). Dryg hrkag i dfd a diffrn btwn tal Th matrial paramtr k vg k vg g hrkag augnou hrkag. Augnou an b alibratd by fittg xprimntal data rlvant hrkag i maurd on primati ampl, whih fr (vaporabl) ontnt onrt at ar prottd from dryg by wrappg m adhiv alumum (Yurtda 23). variou ag (Di Luzio & Cuati 29b). At quilibrium at ah impod rh-valu, 2.2 aturation Tmpratur dgr volution i alulatd with Equation (3): Not that, at arly ag, hmial ration m m aoiatd dry Sw = with mnt hydration SF ration (3) ar xormi, mat mdry tmpratur fild i not uniform for non-adiabati ytm vn if nvironmntal whr tmpratur m i ma i ontant. at onidrd Hat ondution rh-valu, an m at b i aturatd dribd ma, onrt, obtad at aftr lat maturation for tmpratur undr xdg durg ix C month, (Bažant m dry & i Kaplan drid ampl 996), ma, by not whih Fourir i timatd law, whih ug rad poroity maurmnt ( tion 2.5). Hn, dorption iorm ah onrt q = λ Ti timatd a a funtion tmpratur (7) rlativ humidity (i.. a a funtion apillary prur). whr q i hat flux, T i abolut tmpratur, λ i hat ondutivity; thi Prodg FraMCoS-7, May 23-28, 2
2.5 Charatrization itial onrt proprti Charatrization itial onrt proprti (poroity prmability) i mad at drid tat, ordr avoid any fft partial ontnt. Thi tat i obtad aftr dryg an ovn at 6 C until ontant ma. Thi tmpratur 6 C i hon limit onrt miro-rakg. Poroity i maurd ug ma variation a ampl btwn itially aturatd tat drid tat (AFPC-AFREM). Rult ar an avrag 58 ampl for ah onrt. Prmability ah onrt i maurd with an rt ga (argon) on on drid ampl plad a triaxial ll with a onfg prur P onf = 5 MPa (Skozyla 23). Apparnt prmabiliti ar maurd a a funtion ga jtion prur. Th valuation Klknbrg fft (Klknbrg 94) allow alulation matrial tri prmability. Morovr, tiffn ah onrt i timatd by maurg drad bulk modulu K b two drid ampl prlimary plad id a triaxial ll (Rouglot 29), with P onf varyg btwn 3 25 MPa. In ory poromhani, dvlopd (Couy 24), drad bulk modulu K b rlat volumtri tra variation onfg prur variation ( P onf ) (quation (4)) whn r i no variation trtitial prur (por prur i uually t at atmophri prur, i.. drad ondition). P onf ε v = (4) Kb whr ε v i volumtri tra variation. Fally, poroity ditribution i maurd by mrury truion poroimtry (MIP) ug onrt ampl l than m 3 at drid tat (Fig. ). poroity ditribution I poroity ditribution Por diamtr [µm]...3.2.. Figur. Poroity ditribution onrt maurd by mrury truion poroimtry (MIP). Prlimary haratrization onrt i prntd Tabl 2..35.25.5.5 d/dlogd [ml/g] Tabl 2. Poroity, ga J prmability = D ( h, T ) h drad bulk modulu onrt at drid tat. I Th proportionality offit D(h,T) Poroity [%] 8 2 Intri prmability moitur [m 2 ] prmability 5. -8 2. it -8 i a nonla Drad bulk modulu K b GPa] rlativ 3 humidity h 2 tmpratur & Najjar 972). Th moitur ma balan Comparion btwn that both variation onrt tim how that ma I onrt volum i l porou onrt mor ( prmabl ontnt w) b q than on. divrgn Thi i du moitur pozzolani flux J addition mnt whih du a thnr poroity, but with a highr tal poroity (Prlot t al. = J 26, Lobt 23, Kourouni t t al. 27). Rult drad bulk modulu K b how that I onrt prnt Th a mor ontnt dformabl w an b matrix xprd a than onrt, vaporabl whih i lk w highr (apillary wa poroity for vapor, I onrt. adorbd ) non- (hmially bound) w n (Mil Pantazopoulo & Mill 995). It i ra 3 EXPERIMENTAL aum RESULTS that vaporabl i a fu rlativ humidity, h, dgr hydration All rult ar avrag dgr maurmnt ilia fum ration, arrid αout, i.. w =w on thr primati = ampl ag-dpndnt at ah tmpratur orption/dorption for ah onrt. (Norlg Mjonll 997). Undr thi aum by ubtitutg Equation Equati obta 3. Dorption iorm Figur 2 3 prnt dorption iorm a a h funtion tmpratur, rptivly + ( D h) for = α& I + α& + w h t h onrt. α α Saturation dgr Sw Saturation dgr Sw..9.8.7.6.5..9.8.7.6 whr / h i lop orption/ iorm (alo alld moitur apa govrng quation (Equation 3) mut b by appropriat boundary itial onditi Th rlation btwn amount I 2 C I 5 C I 8 C rlativ humidity i alld.4 iorm if maurd with rag.3 humidity dorption iorm th.2. a. Ngltg ir diffrn (Xi t al.. followg, orption iorm will b 2 4 6 8 rfrn both orption dorption Rlativ Humidity rh [%] By way, if hytri Figur 2. Dorption iorm I onrt a a funtion tmpratur. iorm would b takn aount, two rlation, vaporabl v rlativ humi b ud aordg ign varia rlativity humidity. Th hap iorm for HPC i flund by many p pially tho that flun xtnt hmial ration, turn, dtrm 2 C 5 C 8 C.5 trutur por iz ditribution (ratio,.4 mnt hmial ompoition, SF.3 urg tim mthod, tmpratur, mix.2 t.). In litratur variou formulatio. found drib orption iorm. 2 onrt 4 6 (Xi t 8al. 994). Howvr, th Rlativ Humidity rh [%] papr mi-mpirial xprion pro Figur 3. Dorption Norlg iorm Mjornll onrt (997) a i a funtion adoptd b tmpratur. Prodg FraMCoS-7, May 23-28, 2
3.. J = D ( Influn h, T ) h tmpratur () For rh>9%, tranport i maly du prmation liquid Th proportionality. Th ra offit tmpratur D(h,T) lad i alld a dra moitur vioity, prmability whih ra it i a nonlar prmability. funtion On rlativ rh<9%, humidity two h omplmntary tmpratur phnomna T (Bažant ar & Najjar prdomant. 972). Th Tranport moitur by ma diffuion balan i alratd that with variation tmpratur tim bau a loal ma ra pr unit rquir vapor volum prur onrt rmal ( ontnt agitation w) b qual molul divrgn du an ra moitur flux tranfr J proprti. Th volution aturation dgr with rlativ humidity at 2 C 5 C ar imilar. Howvr, = Jw an noti that bhavior at 8 C (2) i t vry diffrnt. Th d-aturation ra fatr for a tmpratur Th ontnt 8 C w than an b for xprd two or a tmpratur. vaporabl Suh volution at w 8 C uggt that r um (apillary, i vapor, a poibl adorbd dhydration ) CSH. non-vaporabl (hmially Similar trnd bound) with tmpratur w i alo dribd n (Mill 966, by Pantazopoulo S. Poyt, who & idntifid Mill 995). dorption It i raonabl iorm aum a that I onrt vaporabl by man aturatd i a funtion alt olution rlativ (Poyt humidity, 29). h, dgr hydration, α, dgr Influn ilia onrt fum ration, ompoition α, i.. w =w (h,α,α ) = Conidrg ag-dpndnt dorption orption/dorption iorm at idntial iorm tmpratur (Norlg Mjonll how 997). that Undr I thi onrt aumption prnt lowr by ubtitutg aturation Equation dgr whatvr Equation 2 on rhvalu obta i. For tan, at 2 C, targt valu S w =.8 i obtad for I onrt at rh=98%, for onrt, at rh=6%. Indd, h biggr mirotrutur giv a highr + ( D h) = α& + α& + w& n (3) prmability h t valu h for α I onrt α whih lad a highr ma lo than. Morovr, poroity ( ontnt) CSH i mor important onrt than I, that i why, whr / h i lop orption/dorption iorm (alo alld moitur apaity). Th on dryg front rah CSH poroity govrng quation (Equation 3) mut b ompltd al, by appropriat ma lo boundary kti low itial down ondition. for I onrt Th rlation ra btwn for amount onrt (whih vaporabl ha mor CSH-por rlativ ). humidity i alld adorption iorm if maurd with rag rlativity 3.2 humidity Dryg hrkag dorption iorm oppoit Shrkag a. Ngltg i a maroopi ir diffrn onqun (Xi t al. 994), loal omprion followg, orption mnt iorm matrix du will b an ud ra with rfrn apillary both prur. orption Figur dorption 4 5 ondition. how dryg By hrkag way, if at quilibrium hytri a a funtion moitur apillary iorm prur would b takn tmpratur, aount, rptivly two diffrnt for rlation, I vaporabl onrt. v rlativ humidity, mut b ud aordg ign variation 9 rlativity humidity. Th hap orption 8 iorm for HPC i flund by many paramtr, 7 pially tho that flun xtnt rat 6 hmial ration, turn, dtrm por 5 I 2 C trutur por iz ditribution (--mnt I 5 C 4 I 8 C ratio, mnt hmial ompoition, SF ontnt, 3 urg tim mthod, tmpratur, mix additiv, 2 t.). In litratur variou formulation an b found drib orption iorm normal onrt (Xi t al. 994). Howvr, prnt 2 3 4 5 6 7 8 9 papr mi-mpirial maximum diation hrkag xprion [µm/m] propod by Figur Norlg 4. Dryg Mjornll hrkag (997) i I onrt adoptd a a bau funtion it apillary prur tmpratur. apillary prur Pap [MPa] xpliitly 9 aount for volution hydration ration 8 SF ontnt. Thi orption iorm rad apillary prur Pap [MPa] 7 6 5 2 C 5 C w 4 ( h, α, α ) = G ( α, α ) + 8 C 3 ( g α α ) h (4) 2 ( g α α ) h K ( α, α ) 2 3 4 5 6 7 8 9 maximum diation hrkag [µm/m] Figur 5. Dryg hrkag onrt a a funtion apillary whr prur firt trm tmpratur. (gl iorm) rprnt phyially bound (adorbd) ond 3.2. trm (apillary Influn iorm) tmpratur rprnt apillary Shrkag. Thi dformation, xprion i xprd valid only a for a low funtion ontnt apillary SF. Th prur, offit how Gamplitud rprnt ra amount with tmpratur, pially unit volum btwn hld 5 C gl por 8 C. at % Thi uggt rlativ humidity, that, addition an apillary b xprd prur (Norlg variation, Mjornll or 997) mhanim a hav b onidrd. Capillary prur at a an trnal tr applid onrt mirotrutur. Thrfor, thi may G ( α, α ) = k α + k α (5) lad a hrkag vg amplifid vg by rp CSH. Indd, it i blivd that ht CSH lid ovr whr on k anor, o a rlax trnal tr du vg k vg ar matrial paramtr. From maximum apillary amount prur variation. pr unit Hn, volum rp that an CSH fill all i por ativatd (both by apillary tmpratur. por gl por), on an Shrkag, alulat Kmaurd on obta a a maroopi dformation, i n a um miroopi pro volvg mirotrutur, hydrat rp, apillary prur. Th pro ar trongly tmpratur/ w.88α +.22α G aturation dpndant. (6) K ( α, α ) = 3.2.2 Influn ompoition g α α Shrkag volution i alo flund by mnt typ. I onrt, whih rah lowt aturation Th matrial dgr paramtr ompard k vg k vg at a g givn an rlativ b alibratd humidity, by fittg how xprimntal l hrkag. data Th rlvant proportion fr (vaporabl) aturatd poroity ontnt bad onrt matrial at (i.. variou ubmittd ag (Di Luzio apillary & Cuati prur) 29b). i highr than that I. 2.2 Du Tmpratur highr tiffn volution ( tion 2.5.), l amount at a givn rlativ humidity, Not that, I mnt at arly matrix ag, hrk l hmial than ration undr aoiatd apillary with prur. mnt hydration SF ration ar xormi, tmpratur fild i not uniform for non-adiabati ytm vn if nvironmntal 3.3 tmpratur Ma variation i ontant. vru Hat hrkag ondution an b Conidrg dribd rlativ onrt, ma at lat variation for tmpratur v hrkag, not it i xdg poibl C thr (Bažant uiv & Kaplan pha. 996), by Fourir law, whih rad At firt a lpg pha orrpond lo nar ampl urfa, an arly mirorakg, whih ountrbalan hrkag. (7) q = λ T Th ond pha rlat larly ma variation whr hrkag, q i with hat ra flux, T apillary i prur. abolut tmpratur, Th third pha, λ i whih hat prnt ondutivity; an volution thi ma lo without any hrkag volution, i attrib- Prodg FraMCoS-7, May 23-28, 2
utd ir miro-rakg around aggrgat, or a non-lar bhavior mnt matrix. Figur 6 7 prnt dryg hrkag v ma variation a a funtion tmpratur, for I onrt rptivly. rlativ ma variation -. -.9 -.8 -.7 -.6 -.5 -.4 -.3 -.2 -.. - I 2 C I 5 C I 8 C Figur 6. Dryg hrkag vru ma variation I onrt a a funtion apillary prur tmpratur. rlativ ma variation -. -.9 -.8 -.7 -.6 -.5 -.4 -.3 -.2 -.. - 2 C 5 C 8 C Figur 7. Dryg hrkag vru ma variation onrt a a funtion apillary prur tmpratur. 3.3. Influn tmpratur Rult how trong flun tmpratur on xtnt itial lpg pha. Shrkag i gratr with tmpratur ra (at 2 C: it i nar.8% for I onrt.5% for, at 5 C maximal valu lpg pha hrkag i about.37% for I.6% for matrial, at 8 C it i narly.4% for I matrial.9% for ). Thi i du rmal ativation, whih alrat vaporationdiffuion pro: rmal ativation du an ra amount nar ampl urfa, whih an bttr vaporat (Choka 26). Th ond lar pha onfirm flun apillary prur upon dryg hrkag. Th ra apillary prur with tmpratur lad mor hrkag dformation. Fally, third pha i only obrvd on volution dryg hrkag at 8 C: it i qual 5µm/m for I onrt 7µm/m for. Thi pha prnt an ra ma lo do not lad ontud hrkag. Hn, w an onfirm that variation apillary prur i not -2-3 -4-5 -6-7 -8-9 - -2-3 -4-5 -6-7 -8-9 - diation hrkag [µm/m] diation hrkag [µm/m] ma gl Jhrkag = D ( h, T ) mhanim. h Th rp rmal ativation CSH, whih xpla diffrn amplitud Th hrkag proportionality dformation offit with D(h,T) tmpratur, might moitur b prmability additional mhanim it a rponibl for thi obrvation. rlativ humidity h tmpratur nonla & Najjar 972). Th moitur ma balan 3.3.2 Influn that ompoition variation tim ma Conidrg am volum tmpratur, onrt it ( i poibl ontnt w) b q ompar onrt divrgn trm hrkag, moitur flux hn, J trm dud miro-rakg. At firt, it an b notid that ond pha i good agrmnt with = prviou J rult, namly that t I onrt ha a highr ma lo a lowr hrkag than Th at am ontnt apillary w an prur. b xprd a Th itial lpg vaporabl pha man that wr i (apillary wa miro-rakg on vapor, onrt adorbd urfa. ) Th I non- ha highr lpg (hmially pha, bound) whatvr tmpratur i. Thrfor, Pantazopoulo thi onrt & Mill dvlop 995). mor It i ra w n (Mil miro-rakg on aum hi urfa that than vaporabl. i a fu Miro-rakg rlativ around humidity, aggrgat h, our dgr durg hydration third pha. Thi dgr pha ilia i mor fum pronound ration, αfor, i.. w =w matrial. = Hn, ag-dpndnt thi onrt orption/dorption i mor miro-rakd around (Norlg aggrgat Mjonll than 997). I. Undr thi aum by ubtitutg Equation Equati obta 4 CONCLUSIONS Our rult how that onrt h dryg i trongly d-pndnt on tmpratur. h Ma t lo h ( αdorption + ( D h) = α& + α& + w pro) rlatd hrkag ra with tmpratur with a ignifiant diffrn btwn 5 C whr / h i lop orption/ 8 C, ompard diffrn btwn 2 C iorm (alo alld moitur apa 5 C. govrng quation (Equation 3) mut b Th tmpratur ra lad highr by appropriat boundary itial onditi vapor prur, n onrt aturation Th rlation btwn amount dgr i lowr than at ambt tmpratur at a rlativ humidity i alld givn rlativ humidity. iorm Shrkag if maurd dformation with rag ra with tmpratur. humidity Hn, dorption rik iorm mirorakg ra th a. with Ngltg tmpratur ir (rmal diffrn dformation dryg). (Xi t al. Rult followg, how orption that hydrauli iorm bhavior not only will b rfrn dpnd on both apillary orption prur dorption but alo, potntially, By on a rmal way, if ativation hytri longtrm rp CSH. iorm would b takn aount, two Bhavior tudid rlation, onrt vaporabl ubjtd v dryg rlativ humi i alo flund b by ud mnt aordg typ. Conrt ign mad varia with a rlativity /A mnt humidity. (blndd Th mnt: hap lkr/bfs/fly iorm ah), prnt for HPC a i flund mirotrutur by many p thnr than pially poroity tho a that I flun (pur lkr xtnt mnt typ) onrt. hmial A a ration onqun,, dpit turn, a dtrm highr tal poroity, trutur por onrt iz ditribution i l prmabl l diffuiv (ratio, mnt than hmial I onrt. ompoition, Du SF ignifiant diffrn urg tim tal mthod, por volum tmpratur, mix por iz ditribution, t.). In litratur I matrial variou prnt formulatio a lowr aturation found dgr drib durg dryg. orption iorm onrt dryg onrt hrkag (Xi i t mor al. 994). important Howvr, than th I onrt. papr Thi diffrn mi-mpirial i du a xprion highr pro amount Norlg at givn Mjornll rlativ humidity (997) i dryg adoptd b a l dformabl matrix bad Prodg FraMCoS-7, May 23-28, 2
matrial, J = D ( h, T ) a hown h by drad bulk modulu maurmnt. () A Th a onluion, proportionality mnt offit typ a wll D(h,T) a boundary i alld ondition moitur prmability larly how ir it i flun a nonlar on funtion dryg pro rlativ humidity phyial h onqun tmpratur on T onrt. (Bažant Thu, & Najjar ordr 972). Th a moitur mhanial ma balan long rquir trm bhavior that variation onrt tim trutur, pro ma pr hav unit volum b takn onrt aount. ( ontnt w) b qual divrgn moitur flux J REFERENCES = J (2) t AFPC-AFREM. Dtrmation apparnt dnity poroity aibl, rommndd produr. ANDRA Th & CEBTP, ontnt 2. w Choi an b xprd rfrn a formulation: um mnt vaporabl CPA- I, mhanial w (apillary proprti, durability, vapor, trnal doumnt adorbd ra ) n C RP CTP non-vaporabl -2/A ( (hmially frnh) bound) w n (Mill 966, ANDRA & LERM, 2. hoi rfrn formulation, trnal doumnt ra n C RP LER -4/A ( Pantazopoulo & Mill 995). It i raonabl aum frnh) that vaporabl i a funtion ANDRA, rlativ 25. humidity, Doir h, 25: dgr rfrn hydration, matrial for αrag, dgr high lvl ilia fum long livd, ration, volum α, 2: i.. mntitiou w =w (h,α matrial, ag-dpndnt trnal doumnt orption/dorption ANDRA n C RPASCM45T2_A, iorm,α ) = (Norlg 25 ( Mjonll Frnh) 997). Undr thi aumption Baroghl Bouny,. 994. Mirotrutural hydrou haratrization by ubtitutg mnt Equation pat ordary Equation high prforman onrt, i national hool road 2 on obta bridg (ENPC) ( frnh) Baroghl Bouny,. Maguy, M. Laabatr, T. Couy, O. 999. hcharatrization idntifiation + quilibrium ( D h) = α& + α& + w& n (3) h tranfr t moitur h proprti α for ordary α high prforman mntitiou matrial. Cmnt Conrt R- arh 29: 225-238 Caré, whr S. 28. / h Efft i lop tmpratur on orption/dorption poroity hlorid iorm diffuion (alo mnt alld pat. Contrution moitur apaity). Buildg Th Matrial 22: quation 56-573 (Equation 3) mut b ompltd govrng Choka, M. 26. Efft tmpratur, mhanial loadg by appropriat boundary itial ondition. ir tration on prmability trutural onrt. Th Thi rlation ntral btwn hool amount Nant ( frnh) vaporabl Couy, O. 24. rlativ Poromhani, humidity Wily. i alld adorption Gall, iorm C. P, if M. maurd Ran, G. Rodriguz, with rag S. 23. Efft rlativity humidity hatg rat on dorption ridual rmo-hydro-mhanial iorm oppoit proprti a high-trngth onrt ontxt nular a. Ngltg ir diffrn (Xi wat rag. Tranation 7 th t al. 994), Intrnational Confrn followg, on Strutural orption Mhani iorm Rar will b Thnology ud with rfrn (SMiRT 7), both Pragu, orption Czh Rpubli, dorption Augut 7-22 ondition. 23 Garia By Boiv, way, S. 2. if Rmovg hytri young ag moitur onrt: iorm Dvlopmnt would b an takn xprimntal aount, mthod two analytial diffrnt rlation, ontribution vaporabl phyial rmoval v rlativ augnou. humidity, pr mut for road bridg ( frnh) b ud aordg ign variation rlativity humidity. Th hap orption iorm for HPC i flund by many paramtr, pially tho that flun xtnt rat hmial ration, turn, dtrm por trutur por iz ditribution (--mnt ratio, mnt hmial ompoition, SF ontnt, urg tim mthod, tmpratur, mix additiv, t.). In litratur variou formulation an b found drib orption iorm normal onrt (Xi t al. 994). Howvr, prnt papr mi-mpirial xprion propod by Norlg Mjornll (997) i adoptd bau it Ihida, xpliitly T. Makawa, aount K. Kihi, for T. 27. volution Enhand modlg hydration ration moitur quilibrium SF ontnt. tranport Thi orption mntitiou iorm matrial undr arbitrary tmpratur rlativ humidity hi- rad ry. Cmnt Conrt Rarh 37: 565-578 Joo, M. & Rhardt, H.W. 22. Prmability diffuivity onrt a a funtion tmpratur. Cmnt Conrt Rarh 32: 497-54 w ( h Klknbrg,, α, α ) = G ( L.J. 94. α, Th α ) prmability + porou mdia liquid ga. Amrian Ptrolum ( g αintitut, α Drillg ) h Prodution Prati: 2-23 (4) Kourouni, S. Tivili, S. Takiridi, P.E. Papadimitriou, G.D. ( g Tibouki, Z. 27. Proprti α hydration α ) h blndd mnt with tlmakg lag. Cmnt Conrt R- K ( α, α ) arh 37: 85-822 Lobt, A. 23. Influn paramtr ompoition whr mntitiou firt matrial trm on (gl iorm) tranfr proprti. rprnt Thi univrity Toulou ( frnh) Ma, phyially B.G. Wn, bound X.D. (adorbd) Wang, M.Y. Yan, J.J. Gao, X.J. ond 27. trm Dryg (apillary hrkag iorm) mnt-bad rprnt matrial undr apillary ondition Thi ontant xprion tmpratur i valid only varyg for humidity. low ontnt Jour-. nal SF. Th Cha offit Univrity G Mg rprnt Thnology amount 7, 3: 428-43 pr unit volum hld gl por at % Noumouw, A.N. Clatr, P. Dbiki, G. Cotaz, J.L. 996. rlativ humidity, it an b xprd (Norlg Thrmal tr vapour prur high prforman 997) onrt a at high tmpratur. Prodg 4 th In- Mjornll trnational Symp. On utilization high trngth/high prforman onrt, Pari: 56-57 Prlot, G ( α C., α ) rdir, = k αj. Cara, + k α M. 26. Influn mnt (5) vg vg typ on tranport proprti hmial dgradation: Appliation nular wat rag. Matrial Strutur whr 39: 5-523 k vg k vg ar matrial paramtr. From Poyt, maximum S. 29. amount Exprimntal vtigation pr unit volum that fft an fill tmpratur all por (both on apillary firt dorption por iorm gl por), onrt. on Cmnt Conrt Rarh 39, : 52-59 an alulat K Rouglot, T. Skozyla, a on obta F. Burlion, N. Watr dorption hrkag mortar mnt pat: Exprimntal tudy poromhanial modl. Cmnt Conrt Rarh 39: 36-44 w.88α +.22α G Skozyla, F. Couy, O. Lafhaj, Z. 23. On rliability (6) K ( maurmnt α, α ) = prmability htrognou ga jtion. Miro-pul ttg. Frnh rviw Civil Engrg 7, 4: 45-469 Yurtda, I. 23. Couplg dryg mhanial bhavior mnt Th matrial matrix: xprimntal paramtr tudy k mortar, i univrity thnology Lill (USTL) ( vg k vg g an b alibratd by fittg xprimntal data rlvant frnh) fr (vaporabl) ontnt onrt at variou ag (Di Luzio & Cuati 29b). 2.2 Tmpratur volution Not that, at arly ag, hmial ration aoiatd with 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 onrt, at lat for tmpratur not xdg C (Bažant & Kaplan 996), by Fourir law, whih rad q = λ T (7) whr q i hat flux, T i abolut tmpratur, λ i hat ondutivity; thi Prodg FraMCoS-7, May 23-28, 2