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0 ne hundred years ago, engineers were debating whether density, aggregate gradation, or water­cement ratio cont:rols the strength of concrete. To­

day, those debates have been settled, but the factors that con­trol the behavior of concrete in compression remain contro­versial. The debate has now shilled to the roles played by cement paste, the interfacial transition t...one between paste and aggregate, and the relative stiffness of the components. \Vhile all three ingredients play significant roles, the prop­erties of cement paste and the heterogeneous nature of the material appear to be the key factors in the response of con­crete in compression.

This article highlights some of the research that demon­strates the roles played by the various constiruents, with em­phasis on microcracking, inlerfacial bond strength, nod mod· els of concrete. The reader is directed to Reference I for a more complete discuss ion o f the subject.

Microcracking Prior to the pione.ering microcracking studies at Cornell Uni­versity in the early 1960s. the reasons why concrete re.~ponds in a nonlinear fashion in compression were not clear.2·' The material consists of cement paste and aggregate, both of which, it was believed. behave as linear elastic bri llle mate­rials in compress ion. As illustrated in Fig. I , the studies showed that microcracks (observable with a light micro­scope) exist around coarse aggregate particles prior to load­ing. With the application of compressive slrcss, Lhcsc bond microc.racks remain stable until the compressive stress reaches about 30 percent of the ultimate va lue. At higher stresses, bond micrm:rucking increases until about 70 per­cent of ultimate, at which point micl'ocracks move into the mortar, connecting the coarse aggregate particles, while bond cracks continue to increase.. Th e rate of microcracking progresses at an increasing rate up to and past the strain cor­responding to the peak stress. The early srudies demonstrated that a nearly linear relationship exists hctwccn the applied compressive strain and the total amount of microcracking.

lnterfacial bond strength During the.~e early studies. microcracking appeared lo pro­vide a clear answer as to why concrete has a nonlinear stress­strain cutve. With the preponderance of bond cracking, it seemed clear that interfacial bond strength between cement paste and aggregate must play an impo11ant role in concrete behavior. This conclusion led to the development of a num­ber of tests in· which the bond strength between coarse ag­gregate and cement paste was modified, with the goal of observing the effects on concrete s1rength. First. coarse ag­gregate particles were coated with soft coating materials to produce a rc<luclion in bond strength. As expected. the re~ suiting concrete strength was reduced s ignifieantly.6•7 Uo­fornmately, the soft materials had the undesired effect of is<>·

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~;i·~- ,,,,------~1~-~:;L ~sv:: V'I O 0. 012 t;:; 0 -

STRAIN STRAIN

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Fig. 1 - Cracking maps and stress-strain curves for concrete In loaded unlaxlal compresslon.5

lating the coarse aggregate from the surrounding cement paste -- causing the coarse aggregate to look more like holes than a solid constituent. Thus, the use of soft coa1 ings proved to be inadequate as an experimental tool for measuring the ef­fects of interfacial bond strength .

T he soft coatings were then replaced by hard coatings that signi ficantly reduced intcrfacial bond strength but did not substantially reduce 1he e ffective stiffness of the aggregate particles.& \'lhe.n these coatings were used, substantial dif­ferences in concrete behavior were also expected. However, as shown in Fig. 2, the initial stiil.iless of the concrete was unatlected and compressive strength was reduced only about 10 percent, indicating that interfacial bond strength plays a measurable but not dominant role in the behavior of con­crete in compression.

Models for concrete If inlerfacial bond strength does not play the dominant role in the non linear behavior of concrete, the question arises -what aspect of concrete response causes the nonlinear stress­strain relationship that is so well known for tbjs material'! This question can be partially answered by observing the extent to which the constituents of concrccc behave in a man· ncr that is similar lo that of the full composite. Fig. 3 com­pares the stress ·strain curves of concrete., mortar. and ce· mem paste. with a water-cementitious materiaJ ratio (w/cm) of 0.5.9 The sand-cement ratios of the concrete and mortar are identical. As demonstrated in r ig. 3, when mortar is loaded in compress ion, it has a somewhat higher compres­sive slrcngth und a lill le more ductility than concrete but, otherwise. possesses a similar stress-strain curve. Thus. mortar can be considered a good model for concrete. The differences in the behavior of the two materials, however, provide useful information.

Concrete International

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vation, however, is that the results fall in a relatively narrow band, independent of the use of silica fume or superplasticizer, indicating that any increase in inlcrfacial bond strength provided by silica fume has little measurahle effect on the compressive strength of the concrete. In facl, for tests at seven and 28 days, lhc materials containing silica fume exhibit the low­est ratio of concrete to mortar strength.

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Going back to Fig. 3, it can be concluded that most of the nonlinear behavior of concrete can be ascribed to its mortar constituent. But now Lhc 4uestion arises as to what causes mortar to be nonlinear. The an­swer lies in the cement paste, a material that exhib­its neither bond nor mortar microcracking. As shown in Fig. 3 and even more clearly in Fig. 5, cement paste is not a linear-elastic material, but a highly non­linear material in its own right.9·l4 It is a material that, at the same wlcm. is generally stronger in com­pression than either mortar or concrete and has a sig­

nificantly greater strain capacity than either of the

MICROSTRAIN

Fig. 2 - Stress-strain curves for concrete as influenced by coating aggregates.8

6000

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······-··· Paste ------- Mortar - - - - Concrete

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-0.004 -0.002 0.000 0.002 0.004 0.006 0.008 0.010 Transverse Strain Longitudinal Strain

Fig. 3 - Stress-strain curves for concrete, mortar, and cement paste with a wlcm of 0.5. 9

If mortars and matching concretes are tested in compres­sion, the combined effects of interfacial bond strength and the heterogeneity caused by the coarse aggregate can he mea­sured. Fig. 4 shows the results for a se-

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materials containing aggregate. The lower strength of mor­tar and concrete results from stress concentrations induced in the cement paste constituent of these materials due to dif­ferences in elaslic properties of aggregate and paste. Failure of the paste-aggregate interface also contributes, but to a lesser degree.

As with concrete, the nonlinear behavior of cement paste can be tied to microcracking, but microcracking that requires a scanning electron microscope, rather than a light micro­scope, to be observed. As demonstrated in several studies, the density of these microcracks is two orders of magnitude greater than that of the bond and mortar microcracks ob­served in concrete. 15· 18

Qualitatively, however, the microcracks in cement paste are much like the microcracks in concrete. In cement paste, microcracks form principally in the lower density phases (calcium silicate hydrate) adjacent to or between the harder phases (unhydrated cement particles and calcium hydrox­ide), behavior on the microscopic level thal matches the larger microcracks in concrctc.17·lo

0.33

ries of mortars and concretes cast us­ing two different w/cm and tested at ages of three, seven, and 28 days. 10 The materials differ in that one-third of the test specimens contain no admixtures, one-third contain superplasticizcr, and one-third contain both superplasticizer and silica fume. It is well known that silica fume increases the strength and density of the interfacial transition zone, as well as the bond strength be­tween cement paste and aggrcgate. 11

· 13 Fig. 4 compares ratios of concrete strength to mortar strength as a func­tion of mortar strength. The ratios range from 74 to 61 percent, dropping as mortar strength increases. At three days, the mortars containing silica fume exhibit lower strengths than the

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corresponding mortars without silica fume, while at seven and 28 days, the mortars containing silica fume exhibit the highest strengths. The key obser-

August 1999

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4000 6000 8000 10000 12000

Mortar Streng1h ( psi )

Fig. 4 - Ratios of concrete strength (f/) to mortar strength (fm ') as a function of mortar strength (NA= no admixtures; SP= superplasticizer; SF= superplasticizer and silica fume).10

83

40

Fig. 5 - Stress-strain curves for cement pastes with wlcm of 0.47 to 0.71. 14

Finite element studies Experimental studies to evaluate the contributions made by interfacial bond strength and paste strength suffer from the disadvantage that it is rarely possible to change only one property of concrete. For example, the addition of silica fume increases both intcrfacial and paste strength. One of the prin­cipal advantages of finite element analysis lies in the fact that one property can be changed at a time. An excellent example of the application of the procedure involves a physi­cal model of concrete. 19 The two-dimensional model con­sisted of nine cored aggregate cylinders imhcdded in a mor­tar matrix (Fig. 6). The compressive strength of the physical model was about 85 percent of the compressive strength of its mortar constituent. The physical model behaved in a non­linear fashion (solid curve in Fig. 6) and exhibited microcracking (observed using x-rays) at the interface and through the mortar constituent. In the initial finite element studies of the model, an attempt was made to match the non­linear stress-strain curve using bond an<l mortar microcracking as the only nonlinear behavior. 19 As shown in Fig. 6, a match could not be obtained, and the resulting stress-strain curve exhibited little deviation from a linear response. Also as shown in Fig. 6, a later finite clement study successfully matched the experimental behavior by model­ing the actual nonlinear behavior of the mortar constituent. 20

The key observation is, again, that the nonlinear behavior of concrete is dominated by the nonlinear behavior of its mor­tar constituent.

A similar model was then used to study the effect ofinter­facial bond strength on compressive responsc.21 •22 As shown in Fig. 7, the model demonstrated that using perfect interfa­cial bond strength increased compressive strength by only four percent. Using zero bond strength decreased compres­sive strength by 11 percent. Thus, at ils very greatest, the full effect of interfacial bond strength in the model ( 4% + 11 % --' 15%) just matches the actual reduction in strength due to the addition of the coarse aggregate to the mortar in the physical model (Fig. 6). For nonnal ranges ofinterfacial bond strength, this effect would be much less than the effect of the increased heterogeneity caused by the addition of coarse aggregate.

Conclusions Overall, one can conclude that relative to concrete and mor­tar, cement paste is a stronger, more ductile material in com­pression, and that the addition of aggregate tends to reduce both strength and strain capacity. The bond strength between

84

Stress, psi

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-1000

Mortar ~ I Aggregatemt-----;;-,'"--I T

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Fig. 6 - Stress-strain curves for concrete model.20

-- Normal lnterfacial Str. --- Infinite I nterfaclal Sir. ---- Zero Tensile and Cohesive

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Fig. 7 - Stress-strain curves for finite element models of concrete with different values of mortar-aggregate bond strength. 21

•22

cement paste and aggregate also plays a significant role in the behavior of concrete in compression. However, its effect is generally less important than the prope1ties of the cement paste constituent and heterogeneous nature of the material.

References I. Darwin, D., "The lnterfacial Transition Zone: "Direct' Evidence on

Compressive Strength," Microstructure of Cement-Based Systems/ Bond­ing and fnlerfaces in Cemenritio11s Materials, S. Oiarnond ·et al., Eds., Materials Research Society Symposium Proceedings, V. 370. 1995, pp. 4 19-427.

2. Hsu, T. C., and Slate, F. 0 ., "Tensile S1rength between Aggregate and Cement Paste or Mortar," Journal of the American Concrete Institute, Pro­ceedings V. 60, No. 4, Apr. 1963, pp. 465-486.

3 . Hsu , T. C.; Slate, F. O . ; Sturman, G. M. ; and Winkr. G ., "Micronacking of Plain Concn:te and the Shape of the Stress-Strain Curve," Journal of the American Concrete lns1in1te, Proceedings V. 60, No. 2, Feb. 1963, pp. 209-224.

4. Slate, F. 0., and Olscfski, S., "X-Rays for Study oflntemal Strnclure and Mierocracking of Concrete," Journal of the American Concrete Insti­tute, Proceedings V. 60, No. 5. May 1963, pp. 575-588.

5. Shah, S. P., and Slate, F. 0., ' ' Internal Minocracking Mortar-Aggre-

Concrete International

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g., te Bond nod the Strcss-Stroin Curve of ConCl'cte." Tl,t• Str11(·twv <1/Con­t 'rt-te1 A. I:!. Orook:;, and K. Newman. eds .. Cement anJ Concrete Associa­tion. Londoo. 196S, pp. 83-92.

6. Shah, S. P., an.d Chundr.i. S .. "Critical Stress. Volume Change .. and Micrucrucking of t'oncrcte,·· Journal nf the. American Cuncn:h: ln..-.tilutc, Proceedinf?S V. 65. No. 9. Sept. 1968. pp. 710-781.

7. Ncr rcr-C-hrls1cnscn. P .. and Nielson, T. r. 11., "Modal De1ermin.,1to11 of the Eff~l of Bond between Coarse. Aggr<.·gate and Morrnr on the: Com­pressive $1rcng:th of Concrete/' Jollrnal of 1he An~ri1.11.n Concrete Lnsti• ,u1e. Proceedings V. 66. No. l. Jan. 1969. pp. t,9•12.

8 . .Da1win. 0 .. and Slate. F. 0 .. "Effect of Paste • ,,ggregate 8011d Strength on Bchn\'i()r of Concrc1e:· Joum11/ vf Mmerlals, AST~t. V. 5. No. I. Mar. 1970. pp. 86-98.

9. Ma11in. J. L.; Omwin. L>.; and l"crry, It fl .• ··Ccme.it P:t$1C, ~fol1:tr

:lnd C'onc,1.!le under (vlonotonjc, Sust3ined and C:yclic Lo.1ding." SM R,.. ptJrl No. 31. Uni\ters-ily of Kansas Ccnler for Rcsear<:h, Lawrence. Kans.a.,:;, Oct. 1991. 1<,1 pp.

10.Cong. X.: Gong. S.: 0 .-uwin. O.; and McCahe. S. L. . .. Role of Silica Fume in Comprcssi\•c S1:rcngth of Cement Paste, MtJth1r nnd Concrc1c," AC! Ma,erials Joumai. V. ll9. No. 4, July-Aug. 1992, pp. 375-3R1.

11. RcJ;Ourd. M .. "Mic-ro.s!nu.:1ure uf High Stn.-ng1h Cement Oa!-ed Ms­lerials.,'' l le1)' High Sm!n.gth Cemem-Bti.1ed M<1t<•rfo/11·. M,u~1iul Re~rch Sodc.ty ~ymposium Proccctiing5, V. 42, 1985. pp. 3-17.

12. De.ntur. A., a11d Cohl~n. M. 0 .. "Btl'cct ofConden..,;ed Silica Fumco.n 1he Microstruclurc oflntcrfaciu.t 2one in Porttand Cemcnl Momui.·• Juur. ,wt. A.l'.l)~r. Ceramic Soc .. V. 70, No. IO, 1987. pp. 738-743.

13. Bcnl'ur. A.; Cinldman, A.~ and CohL"n, M. U., 'The Contrihution of 1he Traosi1ioo Zom: lo lhe S1.rcngth of I ligh Qtialiiy Silica Fume Coucn:lt's." Bonding i11 c.·ememitious Compo::it i?.t, Material Rcsetin::h Society Sympo­sium Proceedings, V, 114, 1988. pp. 97-104.

14. Spooner, D. C.; Pomeroy. C. D.: and Dougill, J. W., ··Oamage and F..ncrgy Oii.si1xi1i1:>1i in Ccmeo1 ll llSte-s in Compre.,:;~ic,n," M<~guziru: q{Con­crt'le Re.search (London). V. 28, No. 94. M~r. 1976, pp. 21 -29.

15. Aniogbe. F.. K .. a:td D:i.rwin. 0 ., "Submicrocr.icking in Cemenl Paste and MonM, .. AC/ Mt1tef'ials Journal. V. 34. No. 6, Nov.-Dee. l9$7, pp. 491-500.

16. Aniogb<:. E. K., and Daiwin, 0 .• ·'Strain Dul' to Submicrocrad.:ing in Cemen1 Paste 30(! Monar.'' AC/ Marerlols Journal. V. 85. No. I, Jan.-

,·cb. 1988. pp. 3.11, 17. Oaiwin, D. ond /\bou-Zdd. M. N. "Application of Amonia1ed lm­

:igc Analysi.s 10 1be S1udy or Cement Paste Micros:11, 1<:h.ire." M itl'().Nriu~­rure Qf Ct'ment-Based Sys1ems/8011di11g <111d lnt~rfu,·es i11 C<!mentitiott.'i Matl!rial.t, S. Oiamonci ct :ii., tJ.s .• Materials Research S0cic1y Sym1')(1· siunl Pr01.'!t,.-Ji11gs. V . . nu. IY9S, pp. 3- 12.

18. Uurwin, L>.: Abou-Zeid. M. N.~ artd K~tch;un, K. W.,"Auto1naied Crack Identification for Cemcnl P,1sk : · Cemelll am/ Concrete Rexearch, V. 25, No, ,1, Apr. 1995. pp. 605·6 l 6.

19. Buyuko21urk. 0., "S1res.s.Strain Response ~nd Fracture of a Model of Concrete in Bia., ial l..ooding." Doc1orul Thesis . Cornell Univer~ity. llhaca, N, Y., Jun4! 1970.

20. Darwin, L> .. '"Microscopic Finite Elemen1 Model ofCom.:Tdc-." fo' irst lntcmalional Conference on Mathematical Modding.. ~1. Louis. August 29-Sepiember I, 19 77 (unpublished).

21. Maher. A .. and Uarwin, 0 .. "'A Finite. f:.IC'mcnl Model to Study the MicrQscopic Behavior of Plain Concrete." CRJNC Rqxm SL· 76-02. Uni• ,..crsi1y of Kansa..i. Center for Rdearch. Luwrc-ncc. Kan., November 1976, 83 pp.

22.. Maher. r\ .. o1nd L>arwin, 0 .. ·'Microscopic Finite F.le111ent M01.kl of Curn:n-1c.:· Proceedf,,g:s. First lntcnuuion.111 Confen.·nCQ uo l\·1tuhcoontica\ Modeling. SL l ,<>uis. V. 111. pp. I lOS- 1714,

Sclec1c:d for reu.dcr interest by the edi1ors Mtet' ind1:.-per:id~ot l·xpcrt t\'alua1ion and 1'eco1nmt"nJation.

ACI Fellow David Darwin Is the Deane E. I Aokers Professor ol Civil Engineering and the Director of the Structural Engineering

1 and Materials Laboratory al the University ol Kansas. He is a member and past chai r-man ol ACI Committee 224, Cracking. He now chairs the TAC Technology Transler Committee and serves on several ACI Com­

mittees, 1nc1ua1ng the Publications Committee. He is a re­cipient of the Arthur R. Anderson and ACI Structural Research Awards of the Institute.

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