SPLITTING CONCRETE COVERS - A FRACTURE MECHANICS APPROACH

Transcription

1 Factue Mechanics of Concete Stuctues, Poceedings FRAMCOS-2, edited by Folke H. Wittmann, AEDIFICATIO Publishes, D Feibug (1995) SPLITTING CONCRETE COVERS - A FRACTURE MECHANICS APPROACH K. Noghabai Division of Stuctual Engineeing, Lulea Univesity Lulea, Sweden Technology Abstact splitting capacity of concete cylindes subjected to an inne pessue ae investigated expeimentally, theoetically and numeically. Thee types of concete ae tested: Nomal, high and vey high stength concete, (NSC, and VHSC with a compessive stength of 57, and 157 espectively). Refeence cylindes with no confining spial einfocement ae compaed to cylindes including a spial. Two analytical models based on non linea factue mechanics (NLFM) ae evaluated. A good coespondence is obseved. Finite element (FE) analysis ae successfully pefomed based on the discete cack, the smeaed cack and the inne softening band (ISB) concepts. The factuing behaviou of a cylinde is vey adequately captued specially by the ISB appoach. 1 Intoduction Consideing the pactical limitation on the concete cove, the poblem of splitting constitutes an impotant estiction on fo instance the ultimate bond capacity of einfoced concete stuctues. The splitting phenomenon 1575

2 is also dangeous, as it manifests a vey bittle behaviou. This is accentuated when concete of high stength is utilized. Theoetical splitting models have been deduced based on NLFM, which also take into account the confining effect of spial einfocement. The models ae hee veified by a socalled membane splitting test, whee concete ings of diffeent mixtues ae subjected to an inne hydostatic pessue until collapse. In ode to investigate the coectness of the assumptions of the theoetical models and to acquie insight in the factuing behaviou of a ing subjected to inne pessue, FE-analysis have also been caied out. Thee diffeent appoaches have been used: The discete cack appoach, the smeaed cack appoach and the inne softening band appoach, see Klisinski et al. (1995). 2 Theoy - Splitting models Tepfes (1973) adopted a limit analysis to the splitting failue of concete coves fo assessing the ba-to-concete bonding capacity. Howeve, it was poved expeimentally (see e.g. Reinhadt, 1992 and Rosati et al., 1992), that the stength citeia alone is not sufficient fo an accuate pediction. An additional enegy citeion is equied, incopoating the cohesive qualities of cacks due to aggegate intelocking afte the stength limits ae eached. To descibe such post-peak, tensile (softening) mateial behaviou of concete, Hillebog et al. (1976) intoduced NLFM in eseach on cementitious mateials by poposing a constitutive law based on the stess - cack opening.displacement (COD) elation along a so-called fictitious cack. Reinhadt (1992), Van de Veen (1990), Rosati et al. (1992) and Noghabai et al. (1993) incopoated the fictitious cack model in the patlycacked-elastic-ing concept established by Tepfes (1973), each of them assuming an appopiate constitutive law that govens the softening. Hence, the concete ing is consideed to consist of one intact, elastic oute ing and one cacked, softening inne ing with a hydaulic pessue, Pb' acting on the cicumfeence of the inne hole, see Fig. 1. With sufficient concete cove, the ultimate pessue will be eached fo a citical cack depth, i. Hee we will only compae the models of van de Veen ( 1990) and Noghabai (1993, 1995). The geneal featues of these two models ae pesented in Fig. 1. Due to lack of sufficient data, the exponent k in van de Veen's model will be set to and the citical stess-fee cack width we = 5.14 Gfl fct fo all cases, admitting the fact that this is only validated fo a nomal stength concete. 1576

3 Elastic ing + Cacked, softening ing Confining effect of spial einfocement,'()',\ I....,_ \ I 1 I \ '... ~ f \ I \ I Vi -i -i o -~t+ :, s=lfct cacks un-cacked pat J s i I at F=fspial'Aeq E E A p~ = s s eq z i leq Aeq = Equivalent steel cylinde aea n cacks van de Veen 1 Noghabai et al. van de Veen Noghabai et al. Steel stains Noghabai et al. (1993, 1995): van de Veen (1990): 2 ---i ~ Pb =!j. ( o - i J + n l ch -n:. I n l ch - n: b J + E s A eq. [ l + l ch ( s -.) ( 2 n: 1 s - n l eq ) ] fct b /+/ 0 l '2J I n:. b l l.- (n: -n l) n ch - n: i s eq 1 s ch P _!!. i f. ( o-i 2 + (i -b). l _ 1 b. + s eq. l + s z s 2 '2 f ( ct b +. b 514 n l ch s E c. 1 0 l 1. Geneal featues of two splitting models, deived fom Noghabai (1995) 2 n: (.' - ) Jk 1 E A [ ( 2 n: - n (.' - )

4 3 splitting tests The specimens as in Fig. 2. Concentic holes wee out of the cylindes concete had cued. Thee batches of diffeent concete mixtues wee used accoding to the table in Fig. 2. Fom batch thee cylindes wee poduced: A efeence specimen (no spial einfocement) and two test pieces including spial einfocement made of 0 6 mm defomed ba (Ks400, 5 =2 l 0 GPa), with the same adius,, 5 but with feent pitches, s (28 14 mm, hence Aeq= and m 2 /m). compessive tensile splitting stengths, fee and fespb wee meason concete cubes, 150 mm fo the NSC and HSC concete 100 mm cubes fo concete. The factue enegy, Gp wee...,."""'..."with the dimension 840xl00xl00 mm 3. mens wee wate fo at least 28 days afte pouing. device the inne pessue was exeted to (membane o sleeve) consisted of a steel mandel coated with a polyuethane elastome. Oil was pumped cavity between the inne membane wall using a pessue contolled hydaulic pump (hence, the expeiment was conducted in load-contol). The adial displacement was measued in two othogonal diections, symmetically ove the The mateial paametes of the concete wee detemined conjunction with the pefomance the expeiment and ae summaized in Table 1. Component NSC HSC VHSC Coase aggegate Fine aggegate Cement Silica fume Supeplastisize w/c Fig. 2. The featues of the test specimen. The table shows the concete ecipes (dy mateial [kg/m 3 ]) used in the splitting tests, denominated as: Nomal Stength Concete, NSC, Stength Concete, HSC and Vey High Stength Concete, VHSC. Expected 28-days compessive stengths (of cubic specimens) ae 40, 80 and 140 MPa. 1578

5 1: paametes of the diffeent concete mixtues. the paenthesis denotes days afte Paametes NSC HSC VHSC Notes tube [MP ] 57.0 (40) (49) (51) Mean values of 6 cubes cc a the stengths and 6 tube [MPa] 4.2 (40) 5.6 (49) 8.9 (51) RILEM beams fo the cs pl G 1 [Nmlm] 105 (40) 145 (57) 172 (53) [GPa] 33.8 (74) 39.4 (49) 41.2 (51) deived 33.0 (40)* except fo NSC. fct[mpa] f_ube, to cs pl see van de Veen (1990) Zeh [m] Chaacteistic length *. Re-evaluated value to age coesponding to the time of testing, accoding to CEB-FIB model code following comments can be made on the behaviou (cf. Fig. 4 Stonge and moe bittle concetes give smalle espect to the fee' fespl o NSC is moe ponouncedly affected the use but seems to be less sensitive towads the pitch uvju.lt.ll, highe pitch density does not lead to a splitting capacity of the specimens. No pemonition of failue was peceived in any case. At a...,._,, ui.. the pessue gets too high and a single cack penetates the concete cove and povide enough space fo othe cacks to become visible. state and distibution of the stesses the cylindical specimens influences the fomation of the cacks disegaded the stength concete and ego must be a key issue. It is doubtful whethe such expeiments could be conducted displacement contol. Spial einfocement pobably only affects the peak capacity a specimen and not its oveall stiffness, which is destined as soon as cacks ae tiggeed (at exceed the fct) and ae not initially affected by the spial. 1579

6 4 to a "smeaing-out"._,_._...,... analysis wee geomety. Based on analysed the ISB...,._,._,A.'-'"'~""'"... theoy) and plain elements wee was simulated by a successive incease of of hole. Mesh Element type numbe 8196 A 0392~ inteiface ~ 91 element fe U I"' "\ 0196 ~ ~ ~ Continuation method Regula Newton Raphson Continuation and Riks ac-length methods Fig. 3. FEM appoaches employed in the analysis. 5 Compaison between theoy, expeiments and FE-analysis Continuity in location of the softening bands (cacks) ove element boundaies, ( Klisinski et al., 1995) 4 to 6 show diffeent compaisons between the theoetical models, expeiments and the FE-analysis. 1580

7 40 (j)... o ~u iu1j"'"'""''-'" of ultimate fo the diffeent concetes, obtained fom...,,,.,ij...,... Hu...,...,.,. theoetical models and FEM. VHSCs28 is not to be elied s28 35 ~ -,-~~ 30 sl4 u Cl) z u u:i :::: > /:LineaJ Expeiment Discete 20 Smeaed ISB Compaison between the expeimental and FEM esults. The inlaid illustations and photos show the factued state of the specimens. 1581

8 Discete Appoach 6 Lfoea o~t\,~&~ ~ ~\~"., : N6n linea : soft,. : l,clt ', of~eni~ g:~- ~\,, ' ',. ' 1.0 Non linea : so~~ 6 Smeaed Appoach ~~- ',,,' 0\,,/ 0 \, ', '' i,~it\ , ' D!SB Appoach 6e-~7Jo,,-, v/ i, ' \ f-,' I \ -,' I \ -,/ : \\ ~ ' ' '., ' ' i,cit ~ ' 870 :,- ~'\.,, - '' '. '. ' D ~ - LO LO 'O Active cacks 6. between the theoetical models (dashed) and the FEM-analysis The figues at the bottom show a typical factuing situation fo each appoach at ultimate pessue (Pb at i,cit). It is poved that model of Noghabai et al. (1993) gives fom the expeimental esults than model of van de Veen see Fig. 4. Also, FE-analysis that a linea softening discepancy 4-6). The tension stiffening effect fo all spial...,,......,,,'v...,,... cases is almost neglected (n leq~ 2 n s in the equations might explain incease in eo fo such cases. oveall compaison between FE-models and expeimental esults...'u,...,"'...,,l:> that the ISB appoach exhibits the most consistent behaviou of models (also cf. the "ISB-ing" in Fig. 6 with the authentic cases shown 1582

9 by photogaphs in Fig. 5). In this context, the theoetical models should be consideed as appoximations to the vey plausible desciption tuing behaviou of a concete ing the FE-models offe, see Fig Discussion diffeences between the models of N oghabai and van de pehaps moe evident by making use of the bittleness numbe, the ultimate (elative) pessue fo diffeent B ae plotted in...,._;,_,... Jl....-'L... scales. This is done fo the efeence cases (no spial), wheefoe numbe of cacks, n, is set to two. The logaithmic expession of see Fig. 1, (which is in fact due to the stain assumptions pat) subdues the contibution the softening ing fo moe concetes, which is both plausible and hamonizes with the expeiments. Quintessential fo this poblem (and specimens of this size and seem to be cack stability and the ole the gadients of the assumed '-''U'-'L.. ~AA ing cuves might play, without offeing futhe poof. 0.8 ' ' Model of Noghabai.. ~t.~i. ( i993, i995j ' logb = Jct o = Iog--- lch n Ec-Gf 7. The ultimate dative pessue given by the diffeent models fo a concete ing (b=18 and 0 =156.5 mm) as a function of B, in log scale. A linea factue mechanics (LEFM) analysis based on Bowie et al. (1972), with one and two existing cacks (i.e. n=l and 2) with an assumed cack length (a) of 0.5 mm, is also included. The hoizontal lines indicated by "Plastic", "Patly-cacked-elastic" and "Elastic" ae accoding to the models of Tepfes (1973). 7 Conclusion vey good coespondence was achieved between expeimental analytical model by Noghabai (1993, 1995). The n-nin.ac' ::>.ll 1583

10 model gives a coect desciption of the bittleness of the splitting failue when applied to high stength concete. The esults ae also veified by means of FEM, whee the analysis based on the inne softening band concept was poved to give the most consistent esults, compaed to the discete cack and smeaed cack appoaches. 8 Acknowledgement The wok was suppoted by "Axel och Magaet Ax:son Johnsons Stiftelse" and the Swedish Council fo Building Reseach. The wok was supevised by Pof. Lennat Elf gen and D. Thomas Olofsson. 9 Refeences Bowie, 0.L. and Feese, C.E. (1972) Elastic analysis fo a adial cack in a cicula ing, Engineeing Factue Mechanics, vol. 4, Hillebog, A., Modee, M. and Petesson, P-E. (1976) Analysis of cack fomation and cack gowth in concete by means of factue mechanics and finite elements. Cement and Concete Reseach, vol. 6, Klisinski, M., Olofsson, T. and Tano, R. (1995) Mixed mode cacking of concete modelled by inne softening band, Computational Plasticity (eds D.R.J Owen, E. Ofiate and E. Hinton), Bacelona, pat 2, Noghabai, K., Olofsson, T. and Ohlsson, U. (1993) Bond popeties of high stength concete, Utilization of High-Stength Concete (eds I. Holand and E. Sellevold), Lillehamme, Noway, Noghabai, K. ( 1995) Splitting of Concete in the Anchoing Zone of Defomed Bas - A Factue Mechanics Appoach, Licentiate Thesis, Lulea Univesity of Technology, Lulea, Sweden. To be published. Reinhadt, H.W. (1992) Bond of steel to stain-softening concete taking account of loading ate. Factue Mechanics of Concete Stuctues (ed Z. Bazant), Elsevie, London, Rosati, G. and Schumm, C. (1992) Modelling of local ba-to-concete bond in einfoced concete beams. Bond in Concete - Fom Reseach to Pactice (eds A. Skuda and R. Tepfes), Riga, Latvia, vol. 3, 12: Tepfes, R. (1973) A Theoy of Bond Applied to Ovelapped Tensile Reinfocement Splices fo Defomed Ba. Dissetation, Chalmes Univesity of Technology, Gotebog, Sweden, van de Veen, C. ( 1990) Cyogenic Bond Stess-Slip Relationship. Doctoal thesis, Delft Univesity of Technology, Delft, The Nethelands. 1584