Practical prediction of time- dependent deformations of concrete

Transcription

1 Prcticl prediction of time- dependent deformtions of concrete Prt v: Temperture effect on drying creep Z. P. Bznt (1), L. Pnul (2) The model for drying creep from Prt II I is here extended for the temperture effect. The bsic, dditive form of the double power lw nd the shrinkge-like term re preserved, but certin coefficients become temperture-dependent to reflect the ccelertion of drying nd of ging. Stisfctory greement with test dt is chieved. INTROUCTION The effects of temperture upon creep of seled nd unseled specimens re known to be considerbly different. Heting increses the rte of moisture loss from the unseled specimens. nd during this process creep is intensified, while fter the moisture loss hs been completed, creep gets substntilly reduced. The model for the temperture effect on creep of seled specimens, which hs been presented in Prt IV. will now be extended to cover the cse of drying nd dried concrete e). PROPOSE FORMULAS From the physicl point of view. for concrete there is nothing specil bout the room temperture, compred to moderte elevted tempertures, such s 4 C. rt) Professor of Civil Engineering, Northwestern University, Evnston, Illinois 621, U.S.A.; Active Member, RILEM. e) Grdute Reserch Assistnt, Northwestern University, Evnston, Illinois 621, U.S.A.; presently Eng., Tippetts, Abbett McCrthy nd Strtton, New York. e) Reference numbers less thn 73 rc found in the preceding prts, Vol. 11, No. 65 (Sept.-Oct. 1978), pp , nd Vol. 11, No. 66 (Nov.-ec.), pp /1979/169/$ 4./ BORAS-UNO Therefore. the bsic formuls for drying creep. eqution (25). must retin the sme form t ll constnt moderte tempertures. lthough the coefficients in the formuls must be expected to vry s before. So. we my use gin eqution (25). i. e.. where C, (I. I ') now includes the effect of temperture on the bsic creep prt nd is defined by eqution (34). Temperture 7 is ssumed to be constnt from the loding time I' but my vry prior to I '. The remining two terms re the sme s in eqution (25) but they now include the effect of temperture. They model the increse of creep during drying:, C ( I ) CfJd,-mllk ' S (.1) d I, t. t (J = E Ie" Gsh ex d t. I (J (43) nd the decrese of creep fter drying (predreid specimen) : (44) The mgnitude of the creep Illcrese III eqution (43) is determined by (45) 169

2 Vol N 69 - Mteriux et Constructions in which LIT' is reduced time lg of loding fter heting (I' to): where Tsh (7) is the vlue of T,h for temperture T nd k = 1 for T = To. The shrinkge-like time function III eqution (43) is defined s, ( lotsh(t)(k)1 4)-(d ll lj Sd(l, t)= ;----- I-t (47) The temperture-dependent prmeters in these expressions re k = (_OO )4J -1.j l T k=(k;)5/4. 1 ( 93.5 )41-1 Kl = 1 +.4[ (48) (49) where T = bsolute temperture (K). while the remining coefficients re given by the previous expressions: Tsh by equtions (4). (5). (9) nd (48): <Pd by equtions (31) nd (32). c. 1 by eqution (37). 11 by equtions (17) nd (18). I;' by eqution (35). m by eqution (16). k;, nd k;; by eqution (29). Cd nd c p by eqution (3). nd f,shcx by equtions (6) nd (7). Eqution (48) replces eqution (8) s more ccurte generl expression for k. Finlly. function Sp(l. to) giving the effect of drying time on the decrese of creep fter drying is (5) where LIT represents the reduced time lg which. however. differs from LIT' in tht it is tken up to the current time I rther thn the loding time I': i. e.. de t' - t It I - t' LlT= to h-[i (] = :(T ) + T'h(h' (51) where the lst expression pertins to step-wise temperture history, with step from Toto T t time I. ANAL YSIS OF PROPOSE FOR:1ULAS The term Co (t, t ') hs the sme form s before [eqution (34)] becuse it describes the bsic creep prt. Coefficient <P, chrcterizing the creep increse due to drying, diminishes s the time lg t' - to between the strt of loding nd the strt of heting increses. i. e.. s the specimen gets closer to hygrl equilibrium t the strt of loding. Becuse t higher tempertures the new hygrl equilibrium gets estblished fster, the dependence of <P upon t' - to must evidently involve temperture. The simplest possible pproch is to define n equivlent or reduced time lg LIT' for vrious tempertures. (In fct. the use of reduced time seems to be the only proper choice becuse the ccelertion of drying by heting is instntneous. without memory effects.) The reduced time is introduced by the integrl in eqution (46) for generlly vrible temperture. wheres the lst expression in eqution (46) pplies for. step-wise temperture history which equls T lj from the time. 1, of drying exposure to certin intermedite time. [;. nd given constnt elevted temperture T from time / to the time of loding. ['. Coefficient k is chosen to be 1. t reference temperture To = 23 C nd to grow with temperture. Since t high tempertures k; is lrge. eqution (46) will give reltively lrge reduced time lg LIT' even if the ctul time lg I' -/(, is smll. For concrete loded long enough time fter the strt of drying, the drying creep term Cd (I. 1'.1 ) must vnish. i. e.. <P=O. which is indeed properly indicted by eqution (45). Mrechl's tests [75] (see lso [76] nd [77]) re n exmple of reltively long time lg I' -I o. which cused the response to be rther different from other dt. Without eqution (45) such differences could not be modeled. Temperture ffects not only the mgnitude of the drying creep term (<p) but lso the rte of development of this term nd the dependence of this rte on size. This is modeled by coefficient k [eqution (48)]. which enters the clcultion of Tsh (7) ccording to equtions (4)-(5) (Prt I). Without coefficient k;. LIT' would be proportionl to k; (becuse Tsh is proportionl to 11k;). This dependence is, however. insufficient nd coefficient k serves to intensify the dependence of LIT' upon-t. mking LIT' in effect proportionl to (k )2.25. This models the fct tht the effect of heting before loding upon the mgnitude of the drying creep term ppers to be stronger thn the effect of heting upon the rte of development of the drying creep term, given by the shrinkge-squre hlf-time in eqution (47) for Sd (I. I '). The fct tht k; enters through Tsh in eqution (47) utomticlly gives the temperture influence upon the size-dependence of the drying creep term; however, this dependence must further be djusted by coefficient (k;)l /4. giving the overll dependence s (k;)5 /4. The optimum dependence of coefficients k; nd k upon T hs not come out to be of the ctivtion energy type. Nevertheless, the reduced time pproch, i. e., the use of LIT' nd LIT. is in greement with the rte-process theory (ctivtion energy model). Temperture ffects, however, not only the rte of the drying creep term, governed by Tsh in eqution (47), but lso the time shpe of this term. At higher temperture, the rise of Sd(t, t') in time is more grdul, nd so the exponent in eqution (47) ought to get smller upon heting. This is chieved by correction of coeffi-. cient Kl in the exponent of eqution (47). In Prt I, eqution (8), the ctivtion energy concept ws ssumed to describe the temperture dependence of coefficient k;. However, it ppered tht ccording 17

3 Z. P. Bznt - L. Pnul k., I +( T3.I5) 4 ( 4 _ 4 ) 1 exp,l- To T ->< Temperture in C Fig Coefficient k s function of temperture. to this concept the vlues of k; t higher tempertures (> 75 C) re much too high. which yields too smll vlues of 'sh nd does not give proper size dependence. The temperture dependence introduced by eqution (48) closely follows the ctivtion energy dependence up to bout 75 C but beyond this vlue k; rises slower (see jig. 35). As in Prt III the decrese of creep fter drying. given by function Cp(t, t', to). is proportionl to the bsic creep term Co (t, t '), becuse the shpe of creep curves fter drying is similr, nd is verticlly scled ccording to the degree of drying reched up to the current time t, s given by the shrinkge-like function Sp(t, to) in eqution (5). COMPARISON WITH TEST ATA Only reltively limited test dt on drying creep of heted concrete exist, nd they mostly del with concretes which re typicl of rector vessels. Five different comprehensive test dt sets vilble in the literture ([73], [63], [74], [7]. [75]) hve been fitted by the preceding formuls (see jig. 36). In these fits, 1/ Eo hs been determined by optimizing the fit of the drying creep dt t room temperture. Thus, the fits shown indicte the bility of the formuls to describe the effect of temperture upon drying creep when there is no error in 1/ Eo. ifferent fits, in which 1/ Eo is lso predicted with formul [eqution (19)], re exhibited in figure 37. The most comprehensive nd consistent dt set is tht of Hickey [73]. A rther unusul curing history (specimens demolded fter 24 hours nd stored therefter t 5 % reltive humidity) ws used in Seki nd Kwsumi's tests [7], nd the totl predictions in figure 37 must be' judged in this light. They re poor becuse the vlue of 1/ Eo determined from bsic creep dt (Prt IV), s well s tht from eqution (19). ws 19% smller (.15 x 1-6/ psi) thn the vlue indicted by the optimum fits from drying creep dt t To (jig. 36). Becuse the erly drying exposure in these tests unusully impired the strength development. the vlue of 1/ Eu ws higher compred to tht from the prediction formuls. Moreover. this cused tht the bsic creep curves J (t, t ') for t' = 29 dys nd 15 dys were unusully close to ech other. The fits re lso rendered more difficult by the fct tht the reltive humidity ws not controlled nd only n pproximte men vlue ws given. The drying creep of heted concrete very strongly depends on the movement of wter. which itself is rther scttered phenomenon. So, highly ccurte formuls re impossible without good model for the diffusion of wter. The tests of Gross [74] were of reltively short creep durtion. In these tests, the curves for 4. 6 nd 8 C re very close to ech other. compred to other dt. For the tests of Arthnri nd Yu [63] the reltive humidities for 2, nd 12 C were not reported nd they hve been, therefore, ssumed to be 7. 25, 3 nd 1 % respectively. Nevertheless. these estimtes must be good enough for higher tempertures (84 nd 12 C) becuse the humidities obtined by heting room ir t constnt moisture content of the ir lwys fll within few percent from zero. The initil elstic deformtion for these tests hd to be estimted. too. which ws done by compring the creep vlues for very short times to the corresponding creep vlues reported for seled specimens of the sme composition. ue to sctter of these dt, the curves for 58 nd 84 C cross ech other, which is illogicl nd mkes it. nywy, impossible to chieve ccurte fits. So. the results must be regrded more in the qulittive sense. Mrechl's tests [75] differed from the other tests minly by the use of long preheting period (15 dys) nd lso by rther smll specimen size. This cused the specimens t high temperture to lose much of their wter before loding while t lower tempertures the 15 dy period ws not sufficient to produce severe drying of the specimens. This explins why in Mrechl's tests the creep t 7 C ws less thn the creep t 5 C. Figure 38 shows tht the present formultion is cpble of modeling this reverse dependence on temperture; this is chieved by decresing the mgnitude of Cd (t, t', to) by mens of <p, nd by incresing the mgnitude of C p (t, t', to), which is still smll t 5 C but becomes very lrge beyond 1 C. Mrechl's dt show pek vlue of creep t 5 C while the present formuls gve pek t 7 C, which could not be further djusted without cusing the temperture increse of creep to be too smll in fitting other test dt. For this reson the fit of Mrechl's dt is not too good. lthough the behvior predicted is qulittively correct. The initil elstic deformtion for Mrechl's dt ws not reported s prt of the creep dt in [75 ], but temperture dependence of E tht is probbly pertinent to these dt ws reported in reference [62], which ws used in fitting. The reltive humidities nd mix proportions hd to be lso ssumed, which ws done so s to get typicl verge vlues of m, nnd ry.. 171

4 Vol N 69 - Mteriux et Constructions Sek i nd Kwsumi, 197 I I Eo Ips; <1>, m <l>d.338 Cd CT2.29 C T O e T '".' o :.., -?- ou" ", =, t,'" "..", oo IA-rlh--n--ri- n-dyu-,196= r-j.9 O.B.4 I/Eo 15 IO 6 /ps; <1>, n m <l>d -.33 cd C HO '.39 CTOS -.75 CTe Cn2' u.1 '!' >'P ZO (.' 1.1 (j). 1.!, C Hickey, 1967 I leo /ps; <1>, C T n CT -.65 m.298 CTe CTllo 2.84 <l>d Cn4-2.5 cd " = 1 dys.2 Lw.----.L...L...L...L.Ju...LLLIOc---.L..u...L...L.J...J...I-:':!.IOO Seki nd Kwsumi, 197 I/Eo /ps; <1>, ' m <l>d.338 Cd '1.664 Cno.25 Cuo CTTO.713 O J %.'" '2-..,o' o.4.3 I' = 6 dys Mnichl, 197 I I Eo Ips; <1>, C TTo Gross, 1973 I/Eo' /ps; <1>, 3.22 CT2.62 CT O.449 m CT CTeo '=27 dys,.5.4 m '.134 ' t - t' In dys 1 Fig Fits of Tests by Seki nd Kwsumi, 197 [7]; Arthnri nd Yu, 1967 [63]; Hickey, 1967 [73]; Mrtchl, 197 [75]; nd Gross, 1973 [74] (1/ Eo optimized). 172

5 z. P. Bznt - L. Pnul Seki nd Kwsumi, 197 IIEo /psi "', n m "'d cd C T CT Cno <Sl!P 1..9 Arlhnri nd Yu, 1967 lie o Q- 6 /psi "', n m ",f:j. Cno CU CT CTl If).4 - C/l b c: t' = 1 dys 1.1 Hickey, IIEo /psi "', CTS4-O.65 Seki nd Kwsumi, n m II Eo /psi "'d "', n cd ' m -.35 C T sc> -.63,; >d -.338,.. cd r#.7 C no C T4 -O o.s.4.3 O.! 1.Oo (,' 4:> o t' = 6 dys 1 t - t I In dys C T7 -O.713 C.1 1 :I8 e# 1ft 1 1 Fig Fits of Tests for Temperture Effect on rying Creep by Seki nd Kwsumi, 197 [7]; Arthnri nd Yu, 1967 [63]; nd Hickey, 1967 [73] (I/Eo predicted by formul). 173

6 Vol N 69 - Mteriux et Constructions.6 U>... Q.5.!:..:.4..., smoothed dt by Morechl by formul ''-,- " Temperture in C Fig J (t, t') predicted with formuls (solid line) t t -t' =6() dys s function of temperture compred with experimentl test result (men vlues) by Mrechl. APPENIX V Bsic Informtion on Test t Used Hickey's Tests of Temperture Effect on rying Creep (1967) [73]. - Cylinders 6 x 16 in. (152 x 46 mm), in molds for 24 hours t 73 F (23 C); then stripped nd cured in fog room t 73 F (23 C) for 1 month; then exposed to 5 % R.H. t 73 F (23 C) for nother month. One dy before elevted temperture tests the specimens were wrpped with fiberglss insultion (to minimize temperture chnges). Specimens were loded t the ge of 2 months. Immeditely fter loding, the chmber temperture ws slowly incresed to the test temperture over period of bout 24 hours. Wter-cementsnd-grvel rtio.468: 1: 1.775: Cement type V, 332 kg/m3, nd pozzoln 83 kg/m3. Corse ggregte: good qulity mphibole schist river ggregte, mx. size 1 in. (25 mm). 39-dy strength of specimens 7,7 psi. In clcultions, 28-dy stndrd cylinder strength ws ssumed s 7,5 psi (51. 7 N/mm2). Arthnri nd Yu's Tests of Temperture Effect on rying Creep (1967) [63]. - Slbs 12 x 12 x 4 in. (35 x 35 x 12 mm) cured under wter until 3 dys before loding. Heting begn one dy before loding. Loded t ge of 1 dys, stress 1, psi (6.895 N/mm2). For trnsforming bixil test dt to equivlent unixil ones, Poisson's rtio ws ssumed to be.2. The initil (elstic) vlues of J (t, t') t t-t'=o.ooi dy nd 2, 58, 84 nd 12 C were ssumed to be.25,.273,.288, / psi, nd the corresponding R.H. were ssumed s 7, 25, 3 nd 1 %. Wtercement-snd-grvel rtio.564: 1 : 1.125: 2.625; Thmes river grvel of size (3/16) - (3/8) in. ( mm), ordinry portlnd cement; its content ssumed s 38 kg/ m 3; 28-dy verge cube strength 6, psi (41.4 N/mm2), cold. Gross' Tests of Temperture Effect on rying Creep (1973) [74]. - Cylinders 6 x 18 mm stored in wter up to the 7th dy, then kept under dmp hessin for 4 weeks, therefter in the ir t 5 % R.H. nd 2 e. Specimens were preheted for one dy t the relevnt temperture. Lod pplied t the ge of 9 months; stress-strength rtio.2 (cold strength). Wter-cement-snd-grvel rtio.6: 1: 2.2: Ordinry portlnd cement; its content ssumed s 35 kg/ m 3. Aggregte: Thmes River deposits, mx. size 9.5 mm. 28-dy verge cube strength 42 N/mm2, cold. Seki nd Kwsumi's Tests of Temperture Effect on ryingcreep(197) [7]. - Cylinders 15 x 6mm demolded fter 24 hours nd cured t 2 C nd 5 % R.H.; seled t the top nd bottom. The 4 C specimens were loded t 29 dys nd 1 dys; plced into room of 4 C t 28 nd 97 dys. R.H. ws not controlled, but ws bout 28 % t 4 e. The 7 C specimens were loded t 29 nd 15 dys; plced into the test chmber t the ge of 27 nd 14 dys. R.H. not controlled but ws bout 3 %. Wter-cement-snd-grvel rtio.4 : 1 : : Ordinry portlnd cement, 343 kg/ m 3. Fine ggregte nturl snd from the River Fuji-Gw, corse ggregte from the River Ar-Kw, mx. size 4 mm. Pozzoln ws dded to the mixture. 28-dy verge cylinder strength 445 kp/cm 2 (43.6 N/mm2), cold. Mrechl's Tests of Temperture Effect on rying Creep (197) [75]. - Prisms 7 x 7 x 28 mm cured in wter for 1 yer then heted O. 25 C/ h up to the test temperture. Temperture stbiliztion time 15 dys before loding. Specimens t tempertures 2, 5, 7, 15, 15 C were ssumed to dry t 5, 35, 3,1 nd.1 % R.H. Cement content 4kg/m 3. For fitting, the following ws ssumed: wter-cement-sndgrvel rtio.5: 1 : 1.8: 2.8; nd 28-dy verge cylinder strength 5,5 psi (37.9 N/mm2). The initil (elstic) vlues of J (t, t') t elevted tempertures were evluted using reference [62]. REFERENCES [73] HICKEY K. B. - Creep, strength, nd elsticity oj concrete t elevted tempertures. Report No. C-1257, Concrete nd Structurl Brnch, ivision of Reserch, United Sttes eprtment of the Interior, Bureu of Reclmtion, enver, Colordo, ecember [74] GROSS H. - On high-temperture creep oj concrete. 2nd Interntionl Conference on Structurl Mechnics in Rector Technology, Berlin, 1973, Vol. H, Pper H6/5, T. A. JAEGER, Ed., pub!. by Commission of EuT. Communities. [75] MAREcHAL J. e. - Fluge du beton en jonction de l temperture. Annles de l'institut Technique du Btiment et des Trvux Publics, Vol. 23, No. 266, Februry 197, pp [76] MAREcHAL J. e. - Contribution d I 'etude des propriete,' thermiques et mecniques du beton en jonction de l temperture. Annles de l'institut Technique du Btiment et des Trvux Publics, Vol. 23, No. 274, October 197, pp [77] MAREcHAL J. e. - Fluge du beton en jonction de l temperture. Complements experimentux. Mteriux et Constructions, Vol. 3, No. 18, November-ecember 197, pp