A NEW ANALYSIS OF THE RESTRAINED RING SHRINKAGE TEST

Transcription

1 RILEM Workshop on Long-Trm Prforman of Cmntitious Barrirs and Rinford Conrt in Nular Powr Plants NUCPERF 9 Marh 3 April, 9, Cadarah, Fran A NEW ANALYSIS OF THE RESTRAINED RING SHRINKAGE TEST Briffaut Matthiu 1,, Bnoudjma Farid 1, Torrnti Jan-Mihl 1,3, Nah Gorgs 1, 1 ENS Cahan/CNRS UMR8535/UPMC/PRES UnivrSud Paris, Cahan, Fran Institut d radioprottion t d sûrté nuléair, Fontnay-aux-Rs, Fran 3 Univrsité Paris Est, LCPC, Paris, Fran riffaut@lmt.ns-ahan.fr Astrat: At arly-ag in msiv onrt struturs, raking may our during hardning. Indd, hydration is an xothrmi hmial ration (tmpratur in onrt may ovrom 6 C). Thrfor, if autognous and thrmal strains ar rstraind, omprssiv strsss and thn tration strsss ris, whih an xd th onrt strngth. This raking may inr signifiantly th onrt wall prmaility. Th rstraind shrinkag ring is a good mthod to dtrmin th haviour of onrt (dlayd strain and raking) du to th autognous and drying shrinkag. In this tst, svral oupld phnomna our simultanously. Morovr, dirt strain murmnts in onrt ar diffiult to prform. Thrfor, a good analysis of th rtraind ring shrinkag tst is ndd and two mthods ar hr ompard. Th first on is a 1D analytial mthod whih h n prviously dvlopd y [Mong 3]. Th sond on is d on an axisymtri finit lmnt alulation (Ct3M od, dvlopd y th Frnh atomi nrgy ommission) with th us of thrmo-hmo-lti-damag modl [Bnoudjma and Torrnti 8]. W also ompard th finit lmnt alulation and th analytial analysis dvlopd y [Wiss 1]. Sin svral phnomna our simultanously, th ojtiv is to highlight whih matrial paramtrs hav a signifiant influn on th rsults of finit lmnt alulations. 1. INTRODUCTION At arly-ag in msiv onrt struturs, raking may our during hardning. Indd, hydration is an xothrmi hmial ration (tmpratur in onrt may ovrom 6 C). Thrfor, if autognous and thrmal strains ar rstraind, omprssiv strsss and thn tration strsss ris, whih an xd th onrt strngth. This raking may inr signifiantly th onrt wall prmaility. Th rstraind shrinkag ring is a good mthod to dtrmin th onrt haviour (dlayd strain and raking) du to th autognous and drying shrinkag ut an ffiint (invrs) analysis of this tst is ndd aus th onrt strains and strsss (whih ar not uniform) ar not otaind dirtly. Indd, only orthoradial strains in th ring ar gnrally murd. 37

2 RILEM Workshop on Long-Trm Prforman of Cmntitious Barrirs and Rinford Conrt in Nular Powr Plants NUCPERF 9 Marh 3 April, 9, Cadarah, Fran. RESTRAINED RING TEST PRESENTATION This tst w initially dsignd to rv th onrt raking of a ring spimn whih w t around a rigid or (gnrally in stl): only th raking ag w sil and th strsss gnratd y rstraind shrinkag ould not ddud. Thn [Paillir and Srrano 1976] and [Swamy and Starvids 1979] optimizd th ring dimnsions and addd instrumntation in ordr to mur strains on th stl ring. Finally, [Grzyowski and Shah 1989] plad strain gags on th stl ring in ordr to ddu th strsss in th onrt ring. This tst onfiguration offrs svral advantags and partiularly th fat that th strsss ar slf gnratd y rstraind shrinkag and spimn gomtry. Indd, no additional omplx load systm is ndd (fig. 1: Ring tst gomtry for onrt) Conrt without hydrous xhang Air onditiond room ( C) Strsss profil Ris R Brs: width m Ro 7m Figur 1: Ring tst gomtry 7m 5 m [Wiss and Shah, ] us a fratur mhanis approah to haratriz th influn of th gomtry and spially th onrt ring width. Rntly, [Hsin and Wiss 4] showd that this tst allows for dtrmining ily th rsidual strsss at th intrfa twn th rs and th spimn y an analytial formula. 3. ONE DIMENSIONAL ANALYSIS [MONGE, 3] [Mong, 3] propd a simplifid on dimnsional analysis of th rstraind ring tst with a paralll rhologial hain. ξ) onrt η(ξ) onrt K rs ε Ft(ξ) with η(ξ) dhpot visity ξ) spring stiffnss Ft(ξ) tnsil strngth ε autognous shrinkag strain K rs quivalnt rs modulus ξ hydration dgr Figur : Paralll rhologial hains for th modlling of th ring tst Th gloal quilirium of th systm givs us th quation (1): df df with F onrt for in onrt; F ring for in th rs ring (1) onrt ring 38

3 RILEM Workshop on Long-Trm Prforman of Cmntitious Barrirs and Rinford Conrt in Nular Powr Plants NUCPERF 9 Marh 3 April, 9, Cadarah, Fran If strsss ar sumd uniform in oth matrials ( rs width; onrt width; onrt strss; rs strss), Eq. (1) lads to: d Krsdε d d with () d dε whr ε is th lti onrt strain and ε is th rs strain dε dε dε dε with t ε t ε total strain ε i rp strain : dε d ε lti strain : dε autognous shrinkag strain (3) dt η( with t tim Sin th two matrials ar in paralll in this approah, oth strains ar th sam: t d d (4) dε dε dε dε dt K η( thn K rs rs Krs d dt K η( rs dε With th quations (6) (7) and (8) for th numrial rsolution (Crank-Nihlson shm): n1 n d, n 1 n and dt (6) By suming th following laws for th matrial paramtrs, a η( ξ) ηξ, ξ ξ ξ and R Ro R Ris K E with ξ mhanial ) E ξ ξ rs R o R R thrshold; ξ maximal hydration dgr; η final visity dε au κ dξ Ι whr κ is a onstant paramtr. (11) (5) (9) An analytial quation for th volution of th onrt strss is finally otaind: n 1 a K rs dε n K n K dt dt η( K K dt η( With quation (), th rs strain an also alulatd. (13) 4. FINITE ELEMENT ANALYSIS Th modl usd is dsrid in [Bnoudjma, Torrnti, 8]. Th tmpratur volution is otaind from th rsolution of th hat quation and th us of a hmial affinity: th nrgy alan quation is solvd, whih inluds th hat rl du to th hydration ration. This modl taks into aount th thrmal and autognous strains and also th i rp strains. Finally, an isotropi lti damag modl is usd d on Mazars on, slightly 39

4 RILEM Workshop on Long-Trm Prforman of Cmntitious Barrirs and Rinford Conrt in Nular Powr Plants NUCPERF 9 Marh 3 April, 9, Cadarah, Fran adaptd to arly ag. This adaptation onsists to link th mhanial damag thrshold to th hydration dgr (through th volutions of Young s modulus E and tnsil strngth f t ): a ξ ( t) ξ E and ξ( t) ξ (15) ft ( ft ξ ξ ξ ξ whr a and ar matrials paramtrs whih ontrol th volution rat [D Shuttr, ]. 4.1 Comparison twn 1D and FE (axisymtri) rsults For th omparison twn th prvious modl and th axisymtri finit lmnt alulation, th i rp is modlld only y on dhpot Strains (µm/m) modl 1D viso-lti modl 1D lti Modl Ctm lti Modl tm viso-lti Tim (h) Figur 3: Brs ring strains volution du to th autognous shrinkag Th rsult shows us an important distintion twn th two modls. This is proaly du to th fat that th hypothsis of onstant strss in th two matrials is not orrt. Morovr, du to rstraind shrinkag in oth vrtial and orthoradial dirtions, th strss stat is multiaxial. Nvrthlss, w an noti that th strain du to th rlaxation is quit similar for th two modls (aout 19% of th lti strain for th 1D modl and % for th axisymtri modl). 4. Comparison twn FE (axisymtri) rsults and analytial rsults [Wiss and Hsin, 3] [Wiss and Hsin, 3] hav dvlopd an analytial mthod to analys th rstraind shrinkag ring tst whih allows for prditing onrt strsss. This mthod is d on th alulation of a virtual prssur Δp l applid on th stl ring y onrt shrinkag (whih omprsss th stl ring): Δε (16) Δpl C1R CR E rs 4

5 RILEM Workshop on Long-Trm Prforman of Cmntitious Barrirs and Rinford Conrt in Nular Powr Plants NUCPERF 9 Marh 3 April, 9, Cadarah, Fran C C 1R R [( 1 υ ) R (1 υ ) R ] is ( R R is [( 1 υ ) R (1 υ ) R ] ( R o ) R ) o with υ rs Poisson s ration and υ onrt Poisson s ratio (17) (18) From ths alulations, th alulations of irumfrntial strsss in onrt an prditd from an xat solution (ylindr sumittd to a prssur) for: Δ Δ C maximal onrt strss (19) C 3R max rsidual pl 3R R R () R R o o Th fr onrt shrinkag is also a paramtr in th modl and th rsults otaind y th analytial mthod and numrial simulations (with th sam mhanial paramtr) ar ompard for diffrnt msh rfinmnts. 1,8 1,6 1,4 Strsss (MPa) 1, 1,8,6,4, Conrt strss Ctm 1FE 1,5mm² Conrt strss Ctm 1FE 6,5mm² Conrt strss Ctm 1FE 5mm² Analytial analysis [Wiss] Tim (h) Figur 4: Comparison twn analytial modl and numrial modl for diffrnt msh sizs. Th rsults show that th ordr of strss givn y th two modls is similar. At th nd, with th smallst msh siz th diffrn twn oth modls is lss than 9%. Anothr alulation (1 FE 1mm²) h n prformd ut th sam numrial rsults than th prvious alulation hav n otaind. Th msh dpndny is du to th strong disontinuity of th strsss profil on th rings intrfa. Although, th finit lmnt alulations ar mor ompliatd than th analytial modl, thy hav a strong advantag. Efftivly, a hmo-thrmal modl an usd to dsri ompltly th haviour of th ring (dilatation first du to th hat rl of th onrt and thrmal dilatation of th rings and thn ontration). Morovr, th analytial modl is usd with an lti law, whr th 41

6 RILEM Workshop on Long-Trm Prforman of Cmntitious Barrirs and Rinford Conrt in Nular Powr Plants NUCPERF 9 Marh 3 April, 9, Cadarah, Fran finit lmnt alulations an prformd with an aging viso-lti law (to tak into aount th i rp). 5. PARAMETRIC STUDY It h n shown that th finit lmnt modl an vry intrsting if th thrmomhanial haviour of th ring tst h to prditd. Nvrthlss, this modl uss svral paramtrs whih an lsifid in thr typs (thrmal paramtrs, thrmomhanial paramtrs, mhanial paramtrs). In this part, a snsiility analysis is undrtakn in ordr to highlight whih paramtrs hav an influn on th prdition of onrt strsss (and thus strains in th mtalli ring). Th ojtivs of th paramtrial study ar to dtrmin whih paramtrs hav to prisly murd and for whih on an approximativ valu is suffiint. 5.1 Thrmal paramtr Th thrmal ondutivity (k) and hat apaity (C) rah quikly (aftr fw hours) a onstant valu [Mounanga, 4] ut th final valu dpnds on th onrt mix and on th xtrnal tmpratur. 1 (a) 1 () Strain (µdf) tim (h) Rfrn k 1.16 W/(m C) k.9 W/(m C) k 1.75 W/(m C) Strain (µdf) Rfrn C4 J/(K.m3) - C 1 J/(K.m3) tim (h) Figur 5: Influn of thrmal paramtrs (a) Conrt thrmal ondutivity; () Conrt hat apaity C 7 J/(K.m3) Th figur 5 shows that th influn of th thrmal onrt ondutivity and th onrt hat apaity an ngltd for ronal valu of ths paramtrs. 5. Thrmo-mhanial paramtr Th thrmal strains ar dirtly linkd to th tmpratur volution though th thrmal dilatation offiint. This paramtr rahs rapidly a onstant valu whih only dpnds on th onrt mix [Loukili, ] [Laplant, Boulay, 94]. 4

7 RILEM Workshop on Long-Trm Prforman of Cmntitious Barrirs and Rinford Conrt in Nular Powr Plants NUCPERF 9 Marh 3 April, 9, Cadarah, Fran (a) (a) 1 1 strain (µdf) Rfrn TDC 7.5µm/K TDC 5µm/K -3 TDC 1µm/K -4-5 strain (µdf) Rfrn TDC 7.5µm/K TDC 5µm/K -3 TDC 1µm/K tim (h) -6 tim (h) Figur 6: Influn on thrmo-mhanial paramtrs. (a) Conrt thrmal dilatation offiint; () rs thrmal dilatation offiint In th figur 6, w an rv that th thrmal dilatation offiint h an influn on maximal strains valu. For xampl a variation of 7µm/K (whih is th lowr and th uppr valu of th litratur) on th onrt thrmal dilatation offiint givs a diffrn of 11% on th final strain valu. 5.3 Mhanial paramtrs Th mhanial simulations nd svral matrial paramtrs to murd in ordr to prditiv. Final autognous shrinkag or Young's modulus valus hav, oviously, a strong influn on th rsults. Thrfor, ths paramtrs hav to murd auratly. In this study, th ffts of sondary mhanial paramtrs ar studid. Thus, th variation of th Poisson ratio and th offiint a (for th Young's modulus volution, Eq. 15) h n onsidrd. (a) () 1 1 strain (µdf) tim (h) Rfrn a.45 a.6 a.3 Strains (µdf) Tim (h) Rfrn v. v.15 v.5 Figur 7: Influns of sondary mhanial paramtrs (a) D Shuttr Young s modulus offiint; () Conrt Poisson s ratio Th figur 7 shows that th onrt Poisson's ratio h no influn on th numrial rsults if ronal valus ar usd. On th ontrary, th Young modulus offiint (whih ontrols its volution rat) h a slight influn on th strains volution ut also on th final strain valu. Its rfrn valu (a.45) h n otaind from xprimntal omprssiv tsts on a CEM II. Its maximal valu (a.6) h n otaind y [D Shuttr, ] for a CEM I. Thrfor, it an onludd that th us of CEM I an slightly dr th strains (and thus onrt strss) du to rstraind autognous shrinkag (if all othr matrial 43

8 RILEM Workshop on Long-Trm Prforman of Cmntitious Barrirs and Rinford Conrt in Nular Powr Plants NUCPERF 9 Marh 3 April, 9, Cadarah, Fran paramtrs ar th sam). Howvr, this rsults is not rally ralisti aus th autognous shrinkag for a CEM I mnt typ is mor important than for a CEM II mnt typ [ Boukr, 7] 6. CONCLUSION Th us of finit lmnt simulations for th analysis of th rstraind ring shrinkag w dvlopd in this study. First, w ompard this analysis with two othr analytial mthods and show that for lti laws, th numrial modl and th analytial modl dvlopd y Wiss lad to similar rsults. Morovr, th us of a rhologial hain to rprsnt th rstraind ring tst ovrstimats th strains valus, aus hypothsis soiatd to this modlling ar wrong. Although th numrial modl is mor ompliatd than th Wiss (analytial) on, it is important to not that with a finit lmnt simulation, th tmpratur volution and th viso-lti onrt haviour an takn into aount Sondly, w hav dtrmind whih matrial paramtrs of th finit lmnt modl ould hav an important influn on th final strains or strsss. Th outlook of this work is to prform a rstraind ring tst and to ompar th xprimntal data to th numrial simulations. 7. REFERENCES Bnoudjma, Torrnti, 8 Early-ag haviour of onrt nular ontainmnts Nular Enginring and Dsign, Volum 38, Issu 1, p Boukr, 7 PhD thsis in frnh ; Etud numériqu t xpérimntal du rtrait ndogèn au très jun âg ds pats d imnt av t sans inlusions D Shuttr, G. and Tarw, L., 96 Dgr of hydration-d dsription of mhanial proprtis of arly ag onrt, Matr. Strut. 9 p Grzyowski, Shah, 89 Modl to prdit raking in fir rinford onrt du to rstraind shrinkag. Mag Conrt Rs 4, p Hsin, Wiss, 4 Assssing rsidual strss dvlopmnt and strss rlaxation in rstraind onrt ring spimns. Cmnt and Conrt Compits, 6 :p Laplant, P., Boulay, C., 1994 Evolution of offiint of thrmal xpansion of onrt with rspt to its maturity at vry arly ags. Matrials and Struturs 7, p Loukili, Chopin, Khlidj, L Touzo,. A nw approah to dtrmin autognous shrinkag of mortar at an arly ag onsidring tmpratur history. Cmnt and Conrt Rsarh, Volum 3, Issu 6, p Mounanga, Khlidj, Btian, 4 Exprimntal study and modlling approahs for th thrmal ondutivity volution of hydrating mnt pt. Advans in Cmnt Rsarh, 16, 3, p Paillèr, Srrano, 76 Apparil d étud d la fissuration du éton. Bulltin d liaison du Laoratoir Cntral ds Ponts t Chaussés n.83, Laoratoir Cntral ds Ponts t Chaussés Mong, 3 PhD thsis in frnh ; Fissuration ds Mortirs n Couhs Mins - Effts d l Hydratation, du Séhag t d la Caronatation, LMT Cahan Swamy, Starvids, 79 Influn of fir rinformnt on rstraind shrinkag and raking. ACI Journal prodings, 76[3]:p