PREDICTION OF THE MODULUS OF ELASTICITY OF HIGH STRENGTH CONCRETE *

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1 Irnin Journl of Siene & Tehnology, Trnstion B, ngineering, Vol. 9, No. B Printed in The Islmi Republi of Irn, Shirz University PRDICTION OF TH MODULUS OF LSTICITY OF HIGH STRNGTH CONCRT * D. MOSTOFINJD ** ND M. NOZHTI Dept. of Civil ng., Isfhn University of Tehnology (IUT) Isfhn, I. R. of Irn mil: dmostofi@.iut..ir bstrt The predition of the mehnil hrteristis of onrete ording to its omponents properties hs been of gret interest. In the urrent study, ttempts hve been mde to extrt some experimentl models to predit the modulus of elstiity of high strength onrete bsed on some known hrteristis of the onrete mix. To do so, 4 mix proportions inluding different rtios of sili fume, i.e., SF/CM =,,, nd perent, wter to ementitious mterils rtios, i.e., W/CM =.4,. nd.4, nd types of orse ggregtes, i.e., limestone, qurtzite nd ndesite were seleted. 4 ylindril speimens were st, ured nd tested fter 7, 8 nd 9 dys. Regrding different rtios of sili fume nd different rtios of W/CM, the reltionship of modulus of elstiity of orse ggregte nd onrete t different ges ws disussed nd some empiril equtions were proposed. Speil emphsis ws pid on two proposed models, the omprehensive model nd the simple model. The redibility of the models ws verified using some independent experimentl dt. Keywords High strength onrete, model, modulus of elstiity, sili fume. INTRODUCTION The reltionship between the modulus of elstiity of onrete nd its omponents hrteristis hs been of deep interest for ivil engineers nd reserhers for long time []. For norml strength onrete ( f 4MP), the modulus of the elstiity of onrete my be preisely expressed s funtion of the ompressive strength of onrete []. It is the wy tht most ntionl nd interntionl odes re used to express the modulus of elstiity of onrete; for instne, the merin Conrete Code (CI 8) expresses qs. () nd () [, 4], nd the Cndin Conrete Code (CS.) expresses q. () [] for the evlution of the modulus of elstiity of onrete. =, for. f 4 MP ()..4w f = 47 f (CI 8M9) () = 4 f (CS) () where f (MP) nd (MP) re 8dy ylindril ompressive strength nd modulus of elstiity of onrete, respetively; nd w (kg/m ) is the unit weight of onrete. However, the forementioned equtions re not pplible to high strength (HS) onrete, where mehnil properties of onrete intrinsilly depend on some other prmeters, i.e., the wtertoementitious mterils rtio, the sili fume perentge used, the type of ggregtes, et [6]. Nevertheless, still most existing expressions for the predition of the modulus of elstiity of HP/HS onrete re bsed on its ompressive strength; some of them re s follows with the sme prmeters s before [9]: Reeived by the editors pril, 4; finl revised form Mrh 4, Corresponding uthor

2 D. Mostofinejd / M. Nozhti ( f 69) w = for f 8MP, (CI 6 & Mrtinez) (4). w = 9f 4. for f 8MP, (Norwegin Code & Smeplss) () ( ). = f + 8, (CB) (6).67 f for f 7 MP =, (Grdner & Zho) (7). 9f for f 7 MP ( f 69) W = +., (CS) (8) Some reserhers hve tried to ount for the role of orse ggregtes in the estimtion of the modulus of elstiity of HS onrete; therefore they reommended qs. (9) [] nd () [6] s follows: f t t = 8( ), for f 8 7(MP) (9.) f 8 =.4 + f, for f 8 7(MP) (9.) 8 8 = 47C f, for f (MP) () where in qs. (9), (MP) 8 nd t (MP) re the modulus of elstiity of onrete t 8 dys nd t test time, respetively; (MP) is the modulus of elstiity of ggregtes, nd f 8 (MP) nd f t (MP) re the onrete ompressive strengths t 8 dys nd t test time, respetively. Furthermore, in q. (), C is n empiril oeffiient to ount for the type of orse ggregtes nd is tken equl to.9,.97 nd.8 for limestone, qurtzite nd grnite, respetively. On the other hnd, nother method for the estimtion of the modulus of elstiity of onrete my be the utilizition of formuls used for omposite mterils; i.e., it ould be expressed s funtion of hrteristis of onrete omponents, minly mortr nd ggregtes. Some of these formuls re s follows []: Voigt m m = g + g (Voigt model) () g m g = + (Reuss model) () R euss m = ( + ) (Hirsh Dougill model) () Hirsh Voigt R euss = ( + ) (Popovis model) (4) Voigt Popovis Reuss g g g = + ( m + ) (Counto model) () Counto m Hshin ( m + ) + ( m) g = ( m + ) ( m) g m (Hshin model) (6) g m g Bhe m = (Bhe nd NepperCheistensen model) (7) Irnin Journl of Siene & Tehnology, Volume 9, Number B June

3 Predition of the modulus of elstiity of where nd m re the modulus of elstiity of orse ggregtes nd mortr, nd volumetri perentges of orse ggregtes nd mortr, respetively.. OBJCTIV g nd g m re the The objetive of this study hs been better nd lerer understnding of the role of the min omponents of onrete, i.e., mortr nd orse ggregtes, nd their intertion in the modulus of elstiity of HS onrete. The omplementry objetive of the study hs been the extrtion of some experimentl models for the predition of the modulus of elstiity of HS onrete. To hieve the objetives, the urrent study onduted series of experiments on high strength onrete mixes with different SF/CM nd W/CM, nd different orse ggregtes; nd proposed some models for predition of the modulus of elstiity of HS onrete. ) Mterils. TST PROGRM The mterils used in the tests re s follows: Portlnd ement type I, ording to STM C. Sili fume, with speifi weight of. nd purity of t lest 99% ( SiO 99 %). Superplstiizer from sulphonted melmine formldehyde ording to STM C494TypeF. Fine ggregtes from limestone with purity of more thn 9% ( CCO 9%), grding within STM C, fineness modulus of.66, speifi weight of.476, bsorption of.% nd moisture ontent of.%. Corse ggregtes from limestone, ndezite nd qurtzite with grding fitted on urve no. 8 of STM C nd mximum ggregte size of 9. mm. The other hrteristis of the ggregtes re shown in Tble. Tble. Physil hrteristis of orse ggregtes Physil hrteristis Limestone ndesite Qurtzite Speifi Weight Unit weight ( kg m ) bsorption (%) The ompressive strengths nd the modulus of elstiity of limestone, ndesite nd qurtzite were determined using ylindril ores of mm from the sme soures s orse ggregtes. Tble shows the ompressive strengths ( f ) nd the modulus of elstiity ( ) of the speimens (eh figure is the verge of two tests), while the stressstrin urves of the speimens re shown in Fig.. Tble. Mehnil hrteristis of orse ggregtes Mehnil hrteristis Limestone ndesite Qurtzite f (MP) (GP) It is observed in Fig. tht the ompressive strength of qurtzite is onsiderbly higher thn tht of limestone nd ndesite, nd the ompressive strength of ndesite is lmost the verge vlue of those of qurtzite nd limestone. However, the modulus of elstiity of qurtzite is onsiderbly higher thn tht of ndesite, while the modulus of elstiity of ndesite is only little more thn tht of limestone. June Irnin Journl of Siene & Tehnology, Volume 9, Number B

4 4 D. Mostofinejd / M. Nozhti Compressive Strength (MP) Qurtzite ndesite Limestone..4.6 Strin Fig.. Stressstrin urve of ggregtes b) Mix designs Fortyfive onrete mixes were designed ording to the weight method reommended in CI [] nd its ppendies; however, bsed on the studies rried out by other reserhers, some modifitions were pplied, i.e., the orse ggregtes were inresed up to %. The onrete mixes were mde with three different types of orse ggregtes, i.e., limestone, ndesite nd qurtzite, five different sili fume to ementitious mterils rtios, i.e., %, %, %, % nd %, nd three different wter to ementitious mterils rtios, i.e.,.4,. nd.4. The generl hrteristis of the mixes re tbulted in Tble, while the speil hrteristis of eh mix ontining prtiulr type of orse ggregtes re shown in Tble b. Tble. Generl hrteristis of mix designs Mix No W/CM (%).4..4 Sili Fume (%) Cement (kg/m ) Sili Fume (kg/m ) Fine gg. (kg/m ) Superplstiizer (%)..6.4 Tble b. Speil hrteristis of mix designs with limestone C L L L L4 L L6 L7 L8 L9 L L L L L4 L Wter, (kg/m ) C (kg/m ) with ndesite C Wter, (kg/m ) C (kg/m ) with qurtzite C L L L L4 L L6 L7 L8 L9 Q Q Q Q Q 4 Q Wter, (kg/m ) 7 6 C (kg/m ) Irnin Journl of Siene & Tehnology, Volume 9, Number B June

5 Predition of the modulus of elstiity of ) Csting nd uring For the ompressive strength test of onrete, ylindril speimens of mm were used ording to STM C9. The molded speimens were stripped fter 4 hours, ured in wter until hours before testing, nd pped ording to STM C67 to obtin smooth nd level surfes. d) Test proedure nd results The test mhine ws eletrohydruli with pity of kn. The verge loding rte ws.8 MP/se. The strin on the speimens ws mesured using Deme guge with guge length of.8 mm ( in). The results re tbulted in Tbles 4, 4b nd 4 for limestone, ndesite nd qurtzite orse ggregtes, respetively; where the prmeters f 7, f 8, f 9, 7, 8 nd 9 re the ompressive strengths nd the modulus of the elstiity of onrete t 7, 8 nd 9 dys, respetively. Tbles 4, 4b nd 4 show tht with ny type of orse ggregtes used in this study, the mximum ompressive strength of onrete hieved by % substitution of sili fume for ement if W/CM =.4, nd by % substitution of sili fume if W/CM =. or.4. Thus, it ould be onluded tht the optimum perentge of substitute sili fume is not onstnt, nd inreses with the derese of W/CM. However, it my be stted tht within the onventionl rnges of W/CM vritions, the optimum perentge of substitute sili fume is bout % to %. In ddition, Tbles 4, 4b nd 4 demonstrte tht the optimum sili fume perentges for obtining the mximum omprehensive strength re not neessrily the sme s those for obtining the mximum modulus of elstiity. It mens tht the modulus of elstiity of HS onrete my not be diretly proportionl to its omprehensive strength in some ses. Tble 4. Compressive strength nd modulus for mixes with limestone orse ggregtes Mix No. L L L L4 L L6 L7 L8 L9 L L L L L4 L f (MP) f (MP) f (MP) (GP) (GP) (MP) Tble 4b. Compressive strength nd modulus for mixes with ndesite orse ggregtes Mix No f (MP) f (MP) f (MP) (GP) (GP) (MP) June Irnin Journl of Siene & Tehnology, Volume 9, Number B

6 6 D. Mostofinejd / M. Nozhti Tble 4. Compressive strength nd modulus for mixes with qurtzite orse ggregtes Mix No. Q Q Q Q4 Q Q6 Q7 Q8 Q9 Q Q Q Q Q4 Q f (MP) 7 f (MP) 8 f (MP) 9 (GP) 7 (GP) 8 (MP) PRDICTION OF TH MODULUS OF LSTICITY ) Bsed on onrete ompressive strength To predit the modulus of elstiity of onrete bsed on its ompressive strength (s mesured in the tests), the results of the modulus of elstiity nd ompressive strengths of the speimens were orrelted with regression. The resulting urves re shown in Figs., b, nd, for onrete mixes with limestone, ndesite nd qurtzite orse ggregtes, respetively. The following expressions n be derived from the urves, where R is the oeffiient of orreltion..6 Limestone HPC. f, = R =.87 (8). ndesite HPC 8 f, = R =.8 (9). Qurtzite HPC.7 f, = R =.88 () b) Bsed on SF/CM, W/CM nd ge of onrete To ount for three essentil prmeters in HS/HP onrete, i.e., the mount of sili fume, the wtertoementitious mteril rtio, nd the ge of onrete, in the predition of the modulus of elstiity of onrete, multiple regression ws utilized in test results. ordingly, the following expressions extrted for the predition of the modulus of elstiity of HS/HP onrete using limestone, ndesite nd qurtzite orse ggregtes, respetively. Notie tht in the expressions, is the modulus of elstiity of onrete in GP, t is the ge of onrete in dys, nd SF/CM nd W/CM re the rtios of sili fume nd wter to ementitous mterils, respetively. C Limestone HPC t ( + SF ) CM =, R =.9 ().8 ( W ) CM C ndesite HPC t ( + SF ) = CM,.9 ( W ) CM R =.8 () C Qurtzite HPC t ( + SF ) = CM,.7 ( W ) CM R =.9 () Irnin Journl of Siene & Tehnology, Volume 9, Number B June

7 Predition of the modulus of elstiity of 7 (GP) 48 LimestoneHPC =. f 8 xpe r ime ntl 6 Liner 4 ( i t l) f ( MP) (GP) ndesitehpc xpe r im e ntl Liner 8 ( i t l) f. ( MP) = 8 f. Fig.. Modulus of elstiity versus ompressive strength of onrete (Limestone C) Fig. b. Modulus of elstiity versus ompressive strength of onrete (ndesite C) (GP) QurtziteHPC =. 7 f 4 xpe r ime ntl 8 Liner 6 ( i t l) f. ( MP) Fig.. Modulus of elstiity versus ompressive strength of onrete (Qurtzite C) ) Bsed on ll possible prmeters Sine onrete is bsilly omposite mteril inluding two omponents, i.e., mortr nd orse ggregtes, it is quite rtionl to express its bsi hrteristis s funtion of the hrteristis of its omponents. On the other hnd, the mortr hrteristis in HS/HP onrete re bsed on the prmeters like wtertoementitious mterils rtio (W/CM), sili fume to ementitious mterils rtio (SF/CM), nd the ge of mortr (t). Therefore, to ount for ll possible prmeters in estimtion of the modulus of elstiity of onrete, it is logil to express it s funtion of the modulus of elstiity of orse ggregtes, (GP), nd the essentil hrteristis of mortr, i.e., W/CM, SF/CM, nd the ge of onrete, t (dys). Tking into onsidertion ll four forementioned prmeters nd utilizing multiple regression in test dt, the following expression ws derived for the predition of the modulus of elstiity of onrete, (GP)... t ( + SF CM ).8 ( W CM ).8 8 =, R =.8 (4) It is worthy to notie tht lthough four different prmeters re engged in the preeding eqution, the orreltion oeffiient within 4 ylindril onrete speimens is eptble. Therefore, q. (4) ould be ounted s relible omprehensive expression for the predition of the modulus of elstiity of high strength onrete. June Irnin Journl of Siene & Tehnology, Volume 9, Number B

8 8 D. Mostofinejd / M. Nozhti Nevertheless, sine it is not prtil to determine the modulus of elstiity of orse ggregtes to substitute in q. (4), q. () is proposed for the predition of the modulus of elstiity of onrete s simple expression, when the modulus of elstiity of orse ggregtes is unknown ( + SF CM ).8 ( W CM ) t =, R =.7 () It is evident tht the ury of q. () is less thn tht of q. (4); however it my be more pplible in most of the ses.. VLUTION OF TH CRDIBILITY OF TH PROPOSD MODLS To verify the ury nd the redibility of the proposed equtions for the predition of the modulus of elstiity of high strength onrete, four new high strength onrete mixes with different W/CM nd SF/CM were designed nd mde in the lbortory; nd the modulus of elstiity of the speimens were determined t 8 dys. Furthermore, high strength onrete mixes were extrted from the experiments of other reserhers. The hrteristis of the whole HS onrete mixes re shown in Tble [, 6, 8, 4]. The modulus of elstiity for ll onrete mixes ws lulted bsed on the omprehensive model (q. (4)), nd the simple model (q. ()), nd ompred with the experimentl dt s shown in Tble. The results showed tht the bsolute error for estimtion of the modulus of elstiity of HS onrete bsed on the omprehensive model is 8.6%; while it is 4.% bsed on the simple model. Tble. Comprison between the lulted modulus of elstiity from the proposed omprehensive nd simple models nd some seleted experimentl dt No. Soure of Dt Type of C D mx (mm) (GP) t (dy) SF/CM W/CM (GP) (GP) rror (%) (GP) rror (%) IUT limestone IUT limestone IUT qurtz IUT ndesit Giio et l. 99 [] grnite Giio et l. 99 [] bslt Giio et l. 99 [] limestone Blbki et l. 99 [] limestone Blbki et l. 99 [] limestone Blbki et l. 99 [] qurtz Blbki et l. 99 [] ndesit Khyt et l. 99 [8] limestone Khyt et l. 99 [8] limestone Irvni 996 [6] sndstone Irvni 996 sndstone Irvni 996 [6] sndstone Irvni 996 [6] sndstone Irnin Journl of Siene & Tehnology, Volume 9, Number B June

9 Predition of the modulus of elstiity of 9 Tble ontinued Lrrrd & Bello, 997 Lrrrd & Bello, 997 [] Lrrrd & Bello, 997 [] Lrrrd & Bello, 997 [] itin & Meht, 99 [4] itin & Meht, 99 [4] itin & Meht, 99 [4] itin & Meht, 99 [4] limestone limestone bslt flint limestone dipz grvel grnite bsolute rror omprison of the predited modulus of elstiity of HS onrete s obtined from the proposed models with those obtined from the equtions in the literture (mostly in the Codes) is given in Tble 6. The results show better greement between the predition of the omprehensive model nd the experimentlly mesured modulus of elstiity; while the predition of the modulus of elstiity obtined from the simple model is lso in the rnge of the best preditions bsed on some equtions in the literture. Tble 6. Comprison of the predited modulus of elstiity s obtined from the proposed models with those obtined from the literture No. Soure of Dt f (MP) (GP) xperimentl IUT 68.. IUT IUT IUT Giio et l. 99 [] Giio et l. 99 [] Giio et l. 99 [] Blbki et l. 99 [] Blbki et l. 99 [] Blbki et l. 99 [] Khyt et l. 99 [8] Irvni 996 [6] Irvni 996 Irvni 996 [6] Irvni 996 [6] Compreh. model q. (4) 6. (+.4) 8.6 (+7.) 4. (+4.) 8. (.7) 8.8 (+.8) 4.7 (.7) 4. (+.4) 4. (+.8) 4. (). (4.) 4. (.) Simple model q. () 9. (+.) 4.9 (+6.4) 8.6 (+9.7) 4. (+9.7) 9. (+.) 9. (.) 9. (+.8) 4.7 (+4.) 4.7 (+4.) 4.7 (+.7) 4. (.) 7.7 (+7.8) 4. (+9.) 4.8 (+.) 4.4 (+.9) CI 6 q. (4). (+.) 9.6 (+.) 9. (+.8) 8.8 (9.) 7.4 (.9) 9. (.7).4 (4.) 4. (+6.) 4. (+8.) 4. (+.) 8.8 (4.7). (+9.) 4.8 (+7.) 4. (+4.) 44.8 (+.4), GP ; (rror, %) Norwy q. ().7 (.9) 6.6 (+.6) 6. (+.7) 6. (.8). (9.) 6. (.). (7.6) 8. (.8) 9. (.4) 7.8 (7.8) 6. (.8).4 (+4.) 7.4 (+6.8) 8.4 (+.4) 4. (+) CB q. (6) 4.8 (+9.) 4. (+.9) 44.8 (+7.) 44.6 (+4.) 4.4 (+.7) 44.9 (.4) 9.9 (+.) 47.7 (+9.) 48.4 (+) 46.9 (+4.4) 44.6 (.9) 4.4 (+9.) 46. (+44.7) 47.6 (+.6) 49.6 (+7.8) CS q. (8) 6.4 (+.7) 4.6 (+.9) 4. (+.6) 9.8 (7.) 8. (.) 4. (.6) 4. (.) 4.6 (+8.9) 44.4 (+.) 4. (.7) 9.8 (.).9 (+.) 4.8 (+.7) 4.4 (+7.) 4.9 (+8.) Grdner et l. q. (7) 6. (+.) 9.7 (+.) 9. (+.) 9. (8.9) 7.8 (.8) 9. (.) 4.4 (.8) 4.9 (+4.8) 4.6 (+6.) 4. (+.) 9. (4.).9 (+.) 4.6 (+6.8) 4.8 (+.) 4.7 (+.6) June Irnin Journl of Siene & Tehnology, Volume 9, Number B

10 D. Mostofinejd / M. Nozhti Tble 6 ontinued Lrrrd & Bello, 997 Lrrrd & Bello, 997 [] Lrrrd & Bello, 997 ] Lrrrd & Bello, 997[] itin & Meht, 99 [4] itin & Meht, 99 [4] (.) 4. (.6) 4. (.9) 4. (.6) 4. (+8.7) 4. (+.) 4. (8.) 9. (.8) 9.9 (.4) 9.8 (8.) 4. (+8.) 8.8 (+.) 8.9 (6.) 6. (.) 6.8 (9.) 6.7 (.8) 7. (.) 6. (+.6) 48. (8.4) 4. (+7.7) 4. (.6) 4. (7.9) 46. (+.7) 44.6 (+4.7) 44. (6.) 4. (.) 4.9 (.) 4.8 (6.) 4. (+.) 9.8 (+.4) 4.4 (9.4) 9.6 (.8) 9.9 (.) 9.8 (8.) 4.8 (+7.6) 9. (+.9) bsolute error Sine the experimentl dt used for verifition were seleted from independent studies, it ould be onluded tht both proposed omprehensive nd simple models (qs. (4) nd ()) re relible for the predition of the modulus of elstiity of high strength onrete. 6. CONCLUSIONS. The mximum ompressive strength of HS onrete ws hieved by % substitution of sili fume for ement when W/C ws.4, nd by % substitution of sili fume for ement when W/C ws. or.4. The optimum sili fume perentge does not seem to be onstnt, nd inreses when the rtio of W/C dereses.. To hieve the mximum modulus of elstiity of HS onrete, the optimum sili fume perentge is not neessrily equl to tht for hieving the mximum ompressive strength.. The reltionship between the modulus of elstiity of HS onrete nd its ompressive strength n be expressed by qs. (8), (9), nd () for limestone, ndesite nd qurtzite orse ggregtes, respetively. 4. Regrding onrete s omposite mteril, omprehensive model s expressed in q. (4), or simple model s expressed in q. () n be used for the estimtion of the modulus of elstiity of HS onrete with eptble ury. RFRNCS. Lrrrd, F. & Bello,. (997). The influene of ggregte on the ompressive strength of norml nd highstrength onrete. CI Mterils Journl, 94(), Blbki, W., itin, P. C. & Bllivy, G. (99). On prediting modulus of elstiity in highstrength onrete. CI Mterils Journl, 89(), 7.. Puw,. (96). Stti modulus of onrete s ffeted by density. CI Journl, Proeedings, 7(6), CI Committee 89, (99). Building ode requirements for reinfored onrete, Metri System, merin Conrete Institute, Detroit.. CS.94, (99). Design of onrete strutures. Cndin Stndrd ssoition, Rexdle, Ontrio, Cnd. 6. Irvni, S. (996). Mehnil properties of highperformne onrete. CI Mterils Journl, 9(), CI Committee 69, (998). Stteofthert report on highstrength onrete. CI Mnul of Conrete Prtie, Prt. 8. Khyt, K. H., Bikley, J.. & Hooton, R. D. (99). Highstrength onrete properties derived from ompressive strength vlues. Cement, Conrete, nd ggregtes, CCGDP, 7(), CB/FIP Model MC9, (997). uropen Stndrd for Design of Conrete Strutures, p Prrott, L. J. (969). Prodution nd properties of highstrength onrete, Conrete, (), CI Committee 89, (998). Stndrd prtie for seleting proportions for norml. Hevyweight, nd Mss Conrete, CI Mnul of Conrete Prtie, Prt. Irnin Journl of Siene & Tehnology, Volume 9, Number B June

11 Predition of the modulus of elstiity of. Giio, G., Roo, C., Violini, D., Zppitelli, J. & Zerbino, R. (99). Highstrength onretes inorporting different orse ggregtes. CI Mterils Journl, 89(), Blbki, W., itin, P. C. & Bllivy, G. (99). On prediting modulus of elstiity in highstrength onrete. CI Mterils Journl, 89(), itin, P. C. & Meht, P. K. (99). ffet of orseggregte hrteristis on mehnil properties of highstrength onrete. CI Mterils Journl, 87(), 7. June Irnin Journl of Siene & Tehnology, Volume 9, Number B