Three-Day Prediction of Concrete Compressive

ACI Materials Journal/July-August 2005 231

ACI MATERIALS JOURNAL TECHNICAL PAPER

ACI Materials Journal, V. 102, No. 4, July-August 2005.MS No. 04-069 received April 26, 2004, and reviewed under Institute publication poli-

cies. Copyright © 2005, American Concrete Institute. All rights reserved, including themaking of copies unless permission is obtained from the copyright proprietors. Perti-nent discussion including authors’ closure, if any, will be published in the May-June 2006ACI Materials Journal if the discussion is received by February 1, 2006.

Although there are several procedures predicting concretecompressive strength, reliable methodologies involve either extensivetesting or voluminous databases. This paper presents a simple andefficient procedure to evaluate the activation energy and the rateconstant of concrete. These two parameters can be used for a rapidprediction of the mechanical properties of concrete and particularlythe evolution of compressive strength. They also allow separationof effects due to physical phenomena such as humidity loss. Theprocedure uses an experimentally-determined parameter called“hardening time” as an indicator of equivalent maturity whencomparing two hardening profiles. Test results from specimens ofsix concrete types validate the approach.

Keywords: hydration; maturity; strength.

INTRODUCTIONAt early age, the mechanical properties of cement-based

materials are time-dependent and involve hydration. Thehydration process is a thermally-activated reaction that maybe described by the Arrhenius equation. This equationestablishes the progression of a chemical reaction in terms ofrate of reaction k.1 The integral over time of the rate ofreaction gives the degree of reaction. Two independent andparallel research areas have been generated through applyingdegree of reaction indexes in this research. For the purposesof this paper, they are called “predictions” and “separation ofeffects.” Predictions of mechanical properties of concrete arepossible based on the empirical relationship between thedegree of reaction (hydration) and physical properties suchas compressive strength, tensile strength, and elasticmodulus.2-6 Separation of effects involves decoupling thecontributions to the total deformation of a physical andchemical phenomenon during hardening.7 Unfortunately, theseparation of an effect cannot be done by direct comparison ofdeformation time-histories, measured in concrete pours thatare hardening in different environments. The effects of thetemperature after similar elapsed times of hydration changewith the thermal expansion coefficient (TEC), and thiscoefficient depends on the degree of hydration.8 To performpredictions and separate effects, knowledge of maturityindexes is required. Maturity indexes need to be determinedexperimentally for each concrete type. This article describesa new methodology to determine two common maturityindexes. These indexes lead to the prediction of the evolutionof compressive strength in six different concretes.

RESEARCH SIGNIFICANCEA maturity method is used to predict the compressive

strength evolution of concrete. Values for the activationenergy and the rate of reaction are necessary to implementthis approach. Determination of these values usually requireseither extensive tests or large databases. This has resulted in

limited use of maturity methods. A simple and fast method-ology to determine these values and consequently predictcompressive strength evolution is presented. More timelyknowledge of compressive strength evolution will lead tosavings during construction and improve safety.

BACKGROUNDThe Arrhenius equation states that the rate of a chemical

reaction k increases exponentially with absolute temperature,regardless of the degree of reaction already obtained (refer toEq. (1))

(1)

whereA = frequency factor, s–1;Ea = activation energy (KJ/mole);k = reaction rate;R = gas constant (KJ × mole–1 × K–1); andT = absolute temperature, K.

The degree of reaction is calculated by integrating Eq. (1)over time. The rate of reaction k is constant when the tempera-ture of the hydration process is constant (T = Tr = constantimply k = kr = constant). Equation (2) uses kr to predict thecompressive strength. This empirical equation is widely used.9

(2)

wherekr = rate of reaction at reference temperature Tr;S = compressive strength at age t;Su = ultimate compressive strength;t0 = age at start of strength development, h; andt = time, h.

With the exception of controlled laboratory conditions, thetemperature of the hydration process changes during thereaction and then Eq. (2) becomes inapplicable. To overcomethis difficulty, it is sufficient to change the time-history intoa degree of reaction history. This can be done using theequation of Freisleben-Hansen and Pedersen.10 Observingthat hydration of cement is a chemical reaction, the Arrhenius

k AEa–

RT---------exp=

S kr t,( ) Sukr t t0–( )

1 kr t t0–( )+------------------------------=

Title no. 102-M25

Three-Day Prediction of Concrete CompressiveStrength Evolutionby Marco Viviani, Branko Glisic, and Ian F. C. Smith

ACI Materials Journal/July-August 2005232

law is integrated to describe cement hydration through a newindex called equivalent age (Et)

(3)

whereEt = equivalent age, h;Q = activation energy divided by gas constant, Ea/R;t = time, h;t0 = time at hydration start, h;T = temperature of concrete, K; andTr = reference temperature, K.

Et is the integral in time of the ratio between the rates ofreaction k1 and kr of two specimens of the same concretetypes. One is a fictitious specimen and is assumed to be keptat a constant temperature Tr (generally 20 °C in Europe and23 °C in the U.S.).

The other specimen is real and has a temperature profile T1= T1(t). At every time t*, the real specimen has an equivalentage Et,1(t*). This means that at the time t*, it has the samedegree of reaction that the reference process will have aftera total time Et,r(t*), being cured at T = Tr. Where time isconverted in equivalent age, the temperature of the processassumes the value T = Tr. Thus, if T = Tr = constant, Eq. (2)is applicable (refer to Eq. (4)) for cases when temperaturevaries during hydration.

(4)

whereS = compressive strength at age t;Su = ultimate compressive strength;kr = rate of reaction at reference temperature Tr;Et = equivalent age at time t ; andEt0 = equivalent age at start of strength development.

The equivalent age is of great interest for predictions andfor separation of effects because it allows direct comparisonsof concrete pours (or specimens) that are hydrating atdifferent speeds (Fig. 1). Moreover, when used in predictions,it takes into account the so-called cross over effect ofconcrete,9 which affects predictions made with other degreeof reaction indexes.9,11-13

The procedure explained in the following allows thecalculation of the activation energy and can be used todetermine the datum temperature without modification.

Et t( ) Q 1T--- 1

Tr

-----– exp td

t0

t

∫=

S kr Et,( ) Sukr Et Et0–( )

1 kr Et Et0–( )+--------------------------------------=

Hardening timeA long gauge fiber-optic (FO) deformation sensor has

recently been developed.14 The FO sensor is particularly suit-able for concrete because of its robustness, temperaturecompensation, insensibility to magnetic fields, and aprecision of 2 µm. Moreover, FO sensors follow the defor-mation of fresh concrete without disturbing the strain field ofthe host material.15 The stiffness and the thermal expansioncoefficient (TEC) of the FO sensor are influenced mainly bythe characteristics of the protective tube. For instance, theaxial stiffness of standard FO is very low because it is housedin a plastic protective tube. Glisic proposed a new sensorcalled FO “setting” sensor with a higher axial stiffness usinga protective tube made of stainless steel15,16 (refer to Fig. 2).The setting sensor, once embedded in concrete together witha standard sensor of the same gauge length, leads to determi-nation of the hardening time (refer to the following). Whenconcrete is placed, the standard sensor measures the swellingof concrete while the stiff sensor is not initially influenced bythe deformations of the concrete matrix; therefore, the differ-ence between deformations measured by the two sensorsincreases.

Marco Viviani is an assistant at the Applied Computing and Mechanics Laboratory(IMAC), Swiss Federal Institute of Technology in Lausanne (EPFL), Switzerland. Hisresearch interests include predictive modeling of hardening materials and themonitoring of structures.

Branko Glisic is Head of the Solution and Service Department of Smartec SA, Manno,Switzerland. His research interests include the development of smart sensors forstructural health monitoring and industrial engineering applications.

Ian F. C. Smith is a professor and Director of the Applied Computing and MechanicsLaboratory (IMAC-EPFL). His research interests include measurement systems,active structures, and applied computing in civil engineering.

Fig. 1—Concept of equivalent age.

Fig. 2—Standard and stiff FO sensors.


After concrete hardens, both sensors measure only thedeformation of the concrete matrix and the differencebetween the deformations measured by the two sensorsremains constant (Fig. 3). The hardening time is defined asthe time when the derivative of the difference between thedeformations measured by setting and standard sensorsbecomes zero.

EXPERIMENTAL INVESTIGATIONSDetermination of the activation energy Ea

Originally, hardening time was intended to be an equivalentof setting time. Studies of the mechanism of force transmissionbetween sensors and concrete-matrix indicate that hardeningtime depends on the degree of concrete hydration. Thisdegree is unknown and will be denoted as α = α*. Values forhardening time depend on the following factors• Degree of reaction (types of concrete, temperature of

hydration, and time); and• Sensors features (thermal expansion properties and

stiffness).The strategy adopted for determining the activation energy

uses two specimens of the same type of concrete. Bothspecimens have the same dimensions. They are monitoredwith a stiff and a soft sensor. Aside from their stiffness, eachpair of sensors has the same features. One specimen iswrapped with glass wool. The glass wool acts as insulationand keeps the temperature of this specimen at a higher levelthan the temperature of the other specimen. This induces ahigher rate of reaction in the insulated cylinder. Thetemperature is measured in both specimens (Fig. 4). Thedegree of reaction, in terms of equivalent time Et, is expressedthrough Eq. (3). For both specimens, at the hardening time, thedegree of reaction index Et has the same value. Temperatureprofiles are inserted in Eq. (3) for each specimen and theintegral is calculated to the hardening time. As a result, twoequations with two unknown values (Et and Ea) are obtained.Resolution leads to determination of the activation energy Ea(refer to Fig. 4).

Predictions of compressive strengthThe activation energy is necessary but not sufficient for

determining the rate constant kr (Eq. (1)). The value of kr isneeded to predict mechanical properties (Eq. (4)). The valueof kr can be determined if two compressive tests using stan-dard specimens of the same composition, humidity,boundary conditions and temperature histories, areperformed at different equivalent ages Et. This allows deter-mination of kr through the application of Eq. (4) (Fig. 5).Compressive tests have been carried out after 48 and 72 h

(with exception of Test 1 where test are made at 24 and 72 h).The 24-h test has not been found to be representative forslowly hydrating concrete.

COMPARISON OF PREDICTIONSAND EXPERIMENTAL RESULTS

Hardening time, activation energy, and rate of reaction wereevaluated and applied to six different types of concrete (referto Table 1 to 6) using the procedure presented previously. Fivewere concrete types commonly used in civil engineering.They were made with different types of aggregate. Airentrainers, high-range water-reducing admixtures, anddifferent types of cements were used (refer to Table 1 to 6).The results shown in Fig. 6 to 11 have been obtained withinthe first 72 h. All predictions obtained were realistic andacceptable without any correction according to the criteriagiven in the code TEX-426-A (refer to Table 7 and 8). Thequality of the prediction was verified after 7, 21, and 28 days.The maximum deviation between predicted and tested valuesof each test is presented in Table 8. Zero equivalent age in

Fig. 3—Hardening time.

Fig. 4—Determination of activation energy Ea.

Fig. 5—Determination of rate of reaction kr , frequencyfactor A, and ultimate compressive strength Su.

234 ACI Materials Journal/July-August 2005

Fig. 6 to 11 does not always refer to the pouring time. Becausepoured concrete temperature is influenced by ambienttemperature in the initial phases, the zero equivalent age istaken to be the point where cooling (if it occurs) slows to avariable rate. If no cooling occurs, the zero time is taken to bethe batching time.

DISCUSSION OF RESULTSThe methodology presented assumes that the hardening

time is an indicator of the degree of reaction. Tests supportthis assumption for the concrete that was studied. Moremixtures will be tested to clarify the limits of applicability.Constraints on the testing procedure (such as minimumdifference in temperature profiles) could be added for abetter definition of hardening time when necessary. Therelationship between the hardening curve and the degree ofreaction is an important issue for the extension of the

methodology to the general field of hardening materials, andthis will be the subject of further study. The basis of theproposed methodology involves passing from mechanicalproperties of concrete (hardening time) to thermodynamic-chemical properties (activation energy and rate constant) andback again to mechanical properties (compressive strength).Some codified methods use similar concepts by inserting thefinal setting time into maturity-strength equations and

Table 1—Mixture proportions Test 1w/c 0.45

Cement CEM II/A-LL 42.5 R 325 kg/m3

High-range water-reducing admixture 0.9%

Air-entraining admixture 0.1%

Aggregate 0-32 Hüttwangen

Maximum temperature difference 5 °C


Cement CEM I 42.5 R 350 kg/m3


Air-entraining admixture None

Aggregate 0-32 Sergey

Maximum temperature difference 15 °C


Cement CEM I 42.5 N HS 360 kg/m3




Maximum temperature difference 20.2 °C


Cement CEM III/A 32.5 N 360 kg/m3






Cement CEM II/A-LL 32.5 R 360 kg/m3






Cement CEM I 52.5 N 1051.1 kg/m3

High-range water-reducing admixture 35.1 kg/m3

Steel fiber Not available


Silica fume 273.3 kg/m3

Aggregate 0-4 sand of Fontainebleau


Table 7—Verification criteria for maturity prediction*

Verification criteria Adjusting procedure

s* ≤ 0.90ss* ≥ 1.10s Develop new S-M relationship

Three consecutive within0.90s ≤ s* ≤ 0.95s1.05s ≤ s* ≤ 1.10s

Evaluate batching and placement, adjust s-M* relationship if needed

Better correlations S-M relationship accepted*Code: TEX-426-A; s = predicted strength; and s* = independent test results.

Table 8—Maximum error between predicted strength and independent test results

Test

Maximum errors

Day Maximum error, %

1 7 +4.5

2 28 –5.1

3 28 +5.1

4 21 –7.4

5 28 –6.4

6 13 +3.7

Fig. 6—Compressive strength versus equivalent age for TestSeries 1. Calibration strengths of young concrete are usedto predict strength evolution and, this prediction is verifiedby independent test results using cylinders containing moremature concrete.


performing regression analyses. A recently developedmethod17 uses a variant of the setting time to determine theequivalent age and thus helps to determine strength-maturityrelationships.

Maturity methods are still rarely used in practice. This lackof acceptance is partially related to limited experience withthese approaches. Confidence in the methodology presentedherein would be increased through performing morecompressive tests during the early age of concrete. Forexample, using a given pair of compressive-strength values,the value of kr and Su are obtained, and a predictive curve canbe calculated. Using other pairs, an envelope of curves isobtained. A standard apparatus for the application of thismethodology is under development. Due to reusability androbustness of equipment, an inexpensive and in-place appli-cation of the methodology is feasible.

SUMMARY AND CONCLUSIONSCompressive strengths of several widely used concrete

mixtures have been successfully predicted using a procedurethat involves early age deformation monitoring. The same

Fig. 7—Compressive strength versus equivalent age for TestSeries 2. Calibration strengths of young concrete are usedto predict strength evolution, and this prediction is verifiedby independent test results using cylinders containing moremature concrete.



Fig. 10—Compressive strength versus equivalent age forTest Series 5. Calibration strengths of young concrete areused to predict strength evolution, and this prediction isverified by independent test results using cylinders containingmore mature concrete.

Fig. 11—Compressive strength versus equivalent age forTest Series 6. Calibration strengths of young concrete areused to predict strength evolution, and this prediction isverified by independent test results using cylinders containingmore mature concrete.

236 ACI Materials Journal/July-August 2005

procedure has been applied to a special concrete to study theapplicability of the methodology to other types of hardeningmaterials. This methodology allows a fast and accurateprediction of compressive strength on site. Seventy-twohours are sufficient to gather the necessary data and provideaccuracy of less than 8% error. It is also an attractive procedurefor the determination of the activation energy and the rateconstant. Separation of various contributions to deformation(autogenous, thermal, and humidity loss) is thus possiblein-place and in real time. More timely knowledge ofcompressive strength evolution will lead to savings duringconstruction and improve safety.

ACKNOWLEDGMENTSThis project was supported in its early stages through a project funded by

the Swiss Commission for Technology and Innovation (CTI) and Cemsuisse(Swiss Cement Fabricators Association). The authors are grateful to K.Scrivener, EPFL, for valuable advice and for providing testing support. Wealso express special thanks to P. Gallay who has helped design and buildtesting apparatus.

REFERENCES1. Arrhenius, S., “On the Reaction Velocity of the Inversion of Cane Sugar

by Acids,” Zeitschrift für Physikalische Chemie, No. 4, 1889, pp. 226-232 (astranslated and published in Margaret H. Back and Keith J. Laidler, 1967,“Selected Readings in Chemical Kinetics,” Pergamon, Oxford, 1967).

2. De Shutter, G., and Taerwe, L., “Degree of Hydration-Based Descriptionof Mechanical Properties of Early Age Concrete,” Material and Structure,V. 29, 1996, pp. 335-344.

3. Plowman, J. M., “Maturity and the Strength of Concrete,” Magazineof Concrete Research, V. 8, No. 22, 1956, pp. 13-22.

4. Carino, N. J.; Lew, H. S.; and Volz, C. K., “Early Age TemperatureEffects on Concrete Strength Prediction by the Maturity Method,” ACI

JOURNAL, Proceedings V. 80, No. 2, Mar.-Apr. 1983, pp. 93-101.5. Kee, C. F., “Relation between Strength and Maturity of Concrete,”

ACI JOURNAL, Proceedings V. 68, No. 3, Mar. 1971, pp. 196-203.6. Knudsen, T., “On Particle Size Distribution in Cement Hydration,”

Proceedings, 7th International Congress on the Chemistry of CementEditions Septima, V. II, 1980, pp. I-170–I-175.

7. Turcry, P.; Loukil, A.; Barcelo, L.; and Casabonne, J. M., “Can theMaturity Concept be Used to Separate the Autogenous Shrinkage andThermal Deformation of a Cement Paste at Early Age?” Cement andConcrete Research, V. 32, 2002, pp. 1443-1450.

8. Laplante, P., and Boulay, C., “Evolution du Coefficient de DilatationThermique du Béton en Fonction de sa Maturité aux tout Premiers Âges,”Materials and Structures, V. 27, 1994, pp. 596-605.

9. Carino, N. J., and Lew, H. S., “The Maturity Method: From Theory toApplication,” Proceedings of the 2001 Structures Congress & Exposition,P. C. Chang, ed., ASCE, Reston, Va., 2001, 19 pp.

10. Freiesleben Hansen, P., and Pedersen, J., “Maturity Computer forControlled Curing and Hardening of Concrete,” Nordisk Betong, V. 1,1977, pp. 19-34.

11. Klieger, P., “Effects of Mixing and Curing Temperatures on ConcreteStrength,” ACI JOURNAL, Proceedings V. 54, No. 12, 1956, pp. 1063-1082.

12. Nurse, R. W., “Steam Curing of Concrete,” Magazine of ConcreteResearch, V. I, No. 2, 1949, pp. 79-88.

13. Saul, A. G. A., “Principles Underlying the Steam Curing of Concreteat Atmospheric Pressure,” Magazine of Concrete Research, V. 2, No. 6,1951, pp. 127-140.

14. Inaudi, D., “Fiber Optic Sensor Network for the Monitoring of CivilEngineering Structures,” PhD thesis, No. 1612, EPFL, Lausanne, Switzerland,1997, 182 pp.

15. Glisic, B., “Fibre Optic Sensors and Behaviour in Concrete at EarlyAge,” PhD thesis, No. 2186, EPFL, Lausanne, Switzerland, 2000, 195 pp.

16. Glisic, B., and Simon, N., “Monitoring of Concrete at Very EarlyAge Using Stiff SOFO® Sensor,” Cement and Concrete Composites, V. 22,2000, pp. 115-119.

17. Pinto, R. C. A., and Hover, K. C., “Application of Maturity Approachto Setting Times,” ACI Materials Journal, V. 96, No. 6, Nov.-Dec. 1999,pp. 686-691.

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Three-Day Prediction of Concrete Compressive