ESTIMATION OF THE MODULUS OF ELASTICITY FOR DAM CONCRETE

Transcription

1 ESTIMATION OF THE MODULUS OF ELASTICITY FOR DAM CONCRETE J. Vilrdell, A. Agudo, L. Agulló nd R. Gettu Universitt Politècnic de Ctluny, Deprtent of Construction Engineering, ETSECCPB-UPC, Edificio C-1, Grn Cpitán s/n, Brcelon, Spin. ABSTRACT The odulus of elsticity of d concrete is difficult to deterine directly fro tests due to the necessity for lrge speciens nd testing chines. In order to study the pplicbility of siple elstic odels for predicting the odulus fro stndrd size speciens, tests were conducted on priss of c fbricted with d concrete (xiu ggregte of 120 ). The tests on stndrd c cylinders were de with the ortr nd wet-screened coponents of this concrete. It is seen tht the use of the dt fro these coponents together with estited vlues of the odulus of the ggregtes gives resonble predictions of the oduli of the d concrete. This hs been verified for rnge of ges, fro 7 to 180 dys. Introduction The odulus of elsticity of concrete is preter necessry in structurl nlysis for the deterintion of the strin distributions nd displceents, especilly when the design of the structure is bsed on elsticity considertions. This property is conventionlly esured using stndrdized tests bsed on sll speciens subjected to unixil copression loding. The specien diensions re tken to be t lest three ties the xiu ggregte size of the concrete. Furtherore, epiricl expressions developed fro experientl studies re vilble to estite the odulus of elsticity fro the copressive strength, which is stndrd esure for chrcterizing concrete. The concrete used in the construction of ds is often coposed of binder contining ceent nd high ount of fly sh, nd ggregtes with xiu size rnging fro 80 to 200. The copressive strength of these concretes hs to be esured with lrge

2 speciens, for exple cylinders of c (1). Due to prcticl difficulties in perforing such tests, d concrete is usully wet-screened, reoving ggregtes lrger thn bout 40, nd stndrd cylinders of c re cst nd tested in copression (2). However, this procedure cn result in the overestition of the copressive strength (3); Tuthill et l. (1) suggest tht the strength of the d concrete be tken s 85% of the wetscreened concrete, when specific test dt re lcking. A procedure siilr to tht for the copressive strength hs t ties been dopted for the experientl deterintion of the odulus of elsticity, where tests re perfored on conventionl-size speciens de fro wet-screened concrete (4). More often, the epiricl expressions for conventionl concrete re used to estite the odulus of elsticity fro the copressive strength. Such pproches neglect the effect of ggregte nd specien size on the odulus, which cn be significnt nd vry with the ge of the d concrete (5). In the present work, tests on priss of c de with d concrete (xiu ggregte size = 120 ), nd on cylinders de with the wet-screened concrete (xiu ggregte size = 40 ) nd the ortr of the d concrete (xiu ggregte size = 5 ) were perfored. The objective ws to study the reltions between the oduli of elsticity deterined fro the different speciens, nd to evlute the possibility of using n elstic two-phse coposite odel to estite the odulus of the d concrete. Experientl detils nd results The concrete used in the study corresponds to tht used in the construction of the Llos del Cvll double rch d on the River Crdener in Ctluny, Spin. The noinl coposition of the d concrete hd the following proportions, per cubic eter: Spnish type I 45A (CEN Clss I 42.5R): 130 kg, fly sh: 89 kg, fine snd ( ): 398 kg, corse snd ( ): 234 kg, fine grvel (5-20 ): 392 kg, ediu grvel (20-60 ): 646 kg, corse grvel ( ): 558 kg, plsticizer: 0.55 liters, nd wter: 45 kg. The ggregtes used were obtined long the River Segre ner the loction of the d, nd were identified to be inly liestone. In ddition to the d concrete, the ortr corresponding to this concrete ws fbricted with the coponents up to the grin size of 5 (i.e., excluding the grvels). The d concrete ws lso sieved to reove grvel of size lrger thn 40, nd is denoted s wet-screened concrete. The ortr nd the concretes were fbricted in plnt t the site of the d. Stndrd cylinders of c were cst in steel olds for the ortr nd the wetscreened concrete. Such cylinders could not be cst for the d concrete since the dieter of the cylinder ws lost the se s the xiu ggregte size of 120.

3 Therefore, lrger pristic speciens of c were cst fro the d concrete using linted plywood olds. Note tht the height/width rtio ws equl to 2 in both the specien geoetries. The speciens were loded in unixil copression in 4.5 MN servohydrulic crushing chine with n MTS 458 closed-loop controller. The cylinders were loded t the piston displceent rte of /s nd the priss t rte of /s, producing the se noinl xil strin rte. The rtes corresponded to tht needed to rech filure in the cylinders fter bout 4 inutes. In the cylinder tests, the loding ws stopped t intervls corresponding to 10% of the filure stress in order to record the defortions. In the priss, the loding ws stopped t intervls of 10% of the filure stress obtined in the wet-screened cylinders, in the 7-dy tests, nd t intervls of pproxitely 500 kn, in the others. The tests were perfored t 7, 28, 90 nd 180 dys fter csting. The defortion of ech cylinder ws esured through 3 strin guges plced in the iddle long the xis. The lengths of the strin gges were 30 nd 120 for the ortr nd wet-screened concrete, respectively. For the priss, reference discs were glued on two opposite verticl fces s shown in Fig. 1, nd DEMEC-type echnicl extensoeter, of 15 c gge length, ws used to nully obtin the displceent between djcent discs. The defortions of the strin gges were de through coputer-bsed dt cquisition syste. FIG. 1 The configurtion of reference discs for defortion esureent Typicl stress-strin curves for the three terils t different ges re presented in Fig. 2 -c. The curves re plotted lost until filure in the cse of the cylinders, nd until lod of 2 MN for the priss (Fig. 2c; note the different scles). It cn be seen tht until the

4 stresses of t lest 30% of the xiu, the curves re prcticlly liner. Therefore, the odulus of elsticity ws tken s the verge slope of the curves between 10% nd 30% of the xiu stress.

5 FIG. 2 -c Stress-strin curves for () ortr, (b) wet-screened concrete nd (c) d concrete, t different ges

6 The verge vlues of the odulus obtined for ech teril, long with the coefficient of vrition in prentheses, re given in Tble 1. It cn be seen tht the vlues of E increse with ge in ech teril. Moreover, the odulus of the d concrete (E dc ) is higher thn tht of the wet-screened concrete (E wsc ), which is higher thn tht of the ortr (E or ); i.e., E dc >E wsc >E or. Also, the odulus increses with decrese in the pste content, s expected. The vribility of the results in the cse of the ortr (deterined with stndrd cylinders) is sll, while the vrition of the d concrete results (deterined with priss) is uch higher. The copressive strengths obtined fro the c cylinders re presented in the se tble, long with the coefficients of vrition. The priss could not be loded to filure since the cpcity of the chine ws exceeded in soe cses. TABLE 1. Test Results Age (dys ) (3.1 %) 37.2 (5.0 %) 42.2 (11.0 %) Modulus of elsticity (GP) Mortr Wetscreened D concrete concrete (1.9 %) (20.4 %) (18.2 %) (2.9 %) (4.2 %) (14.2 %) (4.6 %) (1.2 %) (16.1 %) Copressive strength (MP) Mortr Wetscreened concrete (0.2 %) (0.9 %) (4.2 %) (4.2 %) (1.1 %) (2.3 %) (1.8 %) (2.3 %) Prediction of the Elstic Modulus of the D Concrete Since it is prcticlly cubersoe to test lrge speciens, it is proposed here tht the elstic odulus obtined fro conventionl speciens (15 30 c cylinders) of ortr nd/or wet-screened concrete, long with the odulus of the grvel, be used to estite the odulus of elsticity of the d concrete. A siple coposite odel is used for this purpose. Most coposite odels for describing the elstic behvior of two phse terils re bsiclly cobintions of prllel nd series phse rrngeents, s shown in Fig. 3 for the odels of Hirsch nd Counto (6). For pplying these odels, the bsic ssuptions re tht () concrete is three-diensionl cobintion of two hoogeneous nd isotropic phses: the trix phse nd the corse ggregtes; nd (b) ech phse behves linerly in the liner elstic regie of the concrete. Also, it is necessry to know the ix proportions of the concrete, the unit weights of the ggregtes or their volue frctions, nd the

7 odulus of elsticity of ech phse.

8 FIG. 3 Multiphse odels of Hirsch nd Counto The odulus of elsticity of the concrete is given by the expressions in Equtions 1 nd 2 for the Hirsch nd Counto odels (Fig. 3), respectively (6). The Hirsch odel is configured with the reltive proportions of the prllel (unifor strin odel) nd series (unifor stress odel) coponents s x:(1-x).

9 E c (V,V, E, E = x ) V E 1 +V E V +(1- x) E V + E 1 E c (V, E, E )= 1 V E V V 1 E + E where E c, E nd E re the elstic oduli of the coposite, trix nd ggregte, respectively, nd V nd V re the volue frctions of the trix nd ggregte. In the clcultions tht follow, vlue of x = 0.5 ws used in the Hirsch odel, following other works (6,7), which corresponds to n equl distribution of the prllel nd series phses. As explined erlier, the oduli of the ortr nd the wet-screened concrete hve been obtined experientlly using stndrd size speciens. Since the river grvels were ixes of different inerlogies, predoinntly liestone, rnge of odulus of elsticity vlues is possible; the rnge used here for the predictions is GP (8). With these vlues, the oduli of the d concrete is clculted nd copred with the experientl dt. By tking the trix phse s the ortr nd the ggregte phse s the grvel of 5-40, the prediction of the wet-screened concrete odulus, denoted s WS(M), cn be obtined fro the odels. Siilrly, with the trix phse s the ortr nd the ggregte phse s the grvel of 5-120, the prediction cn be de for the d concrete, denoted s D(M). Alterntively, the wet-screened concrete cn be considered s the trix phse nd the grvel of s the ggregte phse to predict the odulus of the d concrete, denoted D(WS). The results of these three siultions re given in Tble 2 for the ge of 90 dys, which is usul reference ge for d concretes. The vlues in prentheses re the errors with respect to the experientlly obtined dt given in Tble 1. Note tht the error is clculted s the difference between the prediction nd the experientl dt, expressed s percentge of the ltter (where positive sign indictes tht the predicted vlue is lower thn the ctul vlue). TABLE 2. E c Predictions (in GP) of the Two Models for Different Aggregte Moduli, t 90 dys

10 odel Hirsch odel Counto odel siultion WS(M) D(M) D(WS) WS(M) D(M) D(WS) prediction (error %) with E = 35 GP 31.0 (+11.7) 32.1 (+25.4) 35.1 (+18.3) 31.1 (+11.6) 32.1 (+25.3) 35.1 (+18.3) prediction (error %) with E = 50 GP 36.4 (-3.5) 39.6 (+7.9) 38.7 (+9.8) 36.5 (-3.7) 39.6 (+7.7) 38.8 (+9.7) prediction (error %) with E = 65 GP 40.8 (-16.2) 47.8 (-13.2) 41.7 (+3.0) 40.9 (-16.3) 47.8 (-13.2) 41.9 (+2.5) It cn be seen fro the tble tht the predictions of the Hirsch nd Counto odels re prcticlly identicl. This ws true for ll the ges studied here. Therefore, further coprisons re de only with the Hirsch odel. The predictions of the Hirsch odel t different ges re given in Tble 3. It cn be seen tht the best predictions for the wet-screened concrete, WS(M), re obtined with n ggregte odulus of 50 GP. At this vlue the d concrete oduli re lso best estited with both siultions D(M) nd D(WS), using the experientl dt fro the ortr nd wet-screened concrete, respectively. Tble 3. Predictions of the Hirsch odel for different ggregte oduli nd the corresponding errors, for wet-screened nd d concretes Age (dys) E (GP) WS(M) D(M) D(WS) 7 dys (-2.0 %) 27.6 (8.8 %) 27.3 (9.8 %) (-19.3 %) 33.9 (-11.9 %) 30.2 (0.3 %) (-33.4 %) 39.1 (-29.0 %) 32.6 (-7.7 %) 28 dys (18.1 %) 29.9 (19.6 %) 34.6 (7.0 %) (4.1 %) 36.9 (1.0 %) 38.2 (-2.6 %) (-7.5 %) 42.7 (-14.7 %) 41.2 (-10.5 %) 90 dys (11.7 %) 32.1 (25.4 %) 35.1 (18.3 %) (-3.5 %) 39.6 (7.9 %) 38.7 (9.9 %)

11 (-16.2 %) 46.1 (-7.2 %) 41.7 (3.0 %) 180 dys (12.5 %) 33.2 (21.4 %) 35.6 (13.4 %) (-2.6 %) 41.0 (2.8 %) 40.3 (4.5 %) (-15.2 %) 47.8 (-13.2 %) 43.4 (-2.8 %) It cn lso be seen tht the use of reltively wide rnge of elstic odulus vlues (35-65 GP) for the ggregtes leds to errors coprble to the vritions norlly seen in experientl dt. This iplies tht when ctul dt for the ggregtes re lcking or when their inerlogy cnnot be deterined with exctitude, it is possible to pproxitely predict the d concrete odulus using resonble rnge of elstic odulus vlues for the ggregtes. The prediction D(WS) fro the experientl dt of the wet-screened concrete is uch better thn D(M) obtined fro the ortr dt. The error is generlly less thn 15% (except in one cse), which is the ccepted error in prediction foruls for the elstic odulus. Obviously, the error in D(WS) is lower since the reltive contribution of the unknown ggregte odulus is lower thn in the prediction bsed on the ortr. When n pproprite ggregte odulus is used, the two predictions re quite siilr, s seen in the cse of E = 50 GP (Fig. 4). Note tht in Fig. 4, the bullets nd the error brs denote the en vlues nd the stndrd devitions, respectively.

12 FIG. 4 Predictions with the Hirsch odel nd E = 50 GP It cn lso be seen in Tble 3 nd Fig. 4 tht t 7 dys the errors of the predictions bsed only on the ortr dt re reltively high. This cn be ttributed to the presence of wek interfces, whose contribution is not tken into ccount explicitly in the odels. This effect is lower in the prediction D(WS) bsed on the wet-screened concrete dt, king it uch ore relible for prcticl purposes, even t erly ges. As entioned erlier, the configurtion of the Hirsch odel used here hs equl proportions of the prllel nd series coponents. A ore generl tretent, considering this proportion s x:(1-x), cn be de to optiize the vlue of x. It ws seen here tht incresing the vlue of x with ge (i.e., incresing the prllel or unifor defortion coponent) decreses the error in the predictions of E dc de fro the dt of the ortr. The trends for the other siultions were inconclusive.

13 Conclusions 1. Dt fro stndrd speciens of ortr nd wet-screened coponents of d concrete cn be used in siple elstic odels (e.g., odels of Hirsch nd Counto) long with estitions of the ggregte oduli, to obtin stisfctory predictions of the elstic odulus of d concrete. This is prcticlly useful since the testing of the d concrete requires lrge size speciens nd testing chines. 2. For prcticl purposes, the use of dt fro wet-screened concrete is recoended for predicting the elstic odulus of d concrete, especilly when the ggregte odulus is unknown. 3. The elstic odulus of d concrete is predicted better with elstic coposite odels t lter ges (ore thn 28 dys), probbly due to the lower contribution of wek interfces. Acknowledgents Prtil funding fro Spnish DGICYT Grnts PB , AMB nd PB to the UPC is grtefully pprecited. The uthors thnk the Junt d Aigües (Generlitt de Ctluny) nd INARSA for their help in prepring the speciens nd for stiulting discussions with the. The experientl work ws conducted with the ssistnce of Miguel A. Mrtín t the Structurl Technology Lbortory of the UPC. References (1) L.H.Tuthill, G.S.Srkri, nd C.J.Cortright, Trnsctions of the Tenth Interntionl Congress on Lrge Ds (Montrél, 1970), Vol. IV, , ICOLD, Pris, (2) R. Sánchez Trejo, Qulity Control of Concrete, Report for the Coittee on Mterils for Ds, Bulletin 47, ICOLD, Pris, (3) A.M.Neville, Properties of Concrete, Longn Scientific & Technicl, Hrlow, UK, (4) ACI Coittee 207, Mss concrete, Report ACI 207.1R-87, Aericn Concrete Institute, Detroit, (5) J. Sores de Pinho, J. Mor nd C.A. Florentino, Trnsctions of the Sixteenth Interntionl Congress on Lrge Ds (Sn Frncisco, 1988), Vol. III, , ICOLD, Pris,1988. (6) S. Mindess nd J.F. Young, Concrete, Prentice-Hll, Inc., Englewood Cliffs, N.J., (7) F.P. Zhou, F.D. Lydon nd B.I.G. Brr, Ce. Concr. Res., 25, No. 1, 1995, pp (8) P. Alejos nd M. Fernández, Mterils nd Structures, 28, No. 184, 1995, pp