Predicting One-Day, Three-Day, and Seven-Day Heat ofHydration of Portland Cement

Ahmadreza Sedaghat, P.E., S.M.ASCE1; Natallia Shanahan, S.M.ASCE2; and A. Zayed, M.ASCE3

Abstract: This paper aims to develop empirical equations predicting one-day, three-day, and seven-day heat of hydration of portland cementat 23°C and water to cement ratio of 0.5. Isothermal conduction calorimetry was implemented to measure the heat of hydration of portlandcements for up to seven days. X-ray diffraction was used to study the mineralogy and also for quantification of phase composition of portlandcements. Particle size distribution of cements was measured using a laser scattering particle size analyzer. Blaine fineness of cementswas measured using a Blaine permeability apparatus in accordance with the standard test methods for the fineness of hydraulic cement byair-permeability apparatus procedure. The results indicate that the one-day, three-day, and seven-day heat of hydration of a specific portlandcement ground to different finenesses is changing linearly with the cement mean particle size. This research shows that the mean particle sizeis a suitable measure of cement fineness to correlate with major phases of portland cement (C3S, C3A, C2S, C4AF) in developing equationspredicting the heat of hydration of cements at one, three, and seven days. DOI: 10.1061/(ASCE)MT.1943-5533.0001220. © 2014 AmericanSociety of Civil Engineers.

Author Keywords: Portland cement; Heat of hydration prediction; Isothermal conduction calorimetry; Blaine fineness; Particle sizedistribution; X-ray diffraction.

Introduction

Heat of hydration is a property of portland cement and a directresult of chemical reactions between cement and water. The amountof heat released is dependent upon the cement composition, cur-ing temperature, water to cement ratio, and cement fineness.The phases mainly responsible for heat generation are tricalciumsilicate (C3S), dicalcium silicate (C2S), tricalcium aluminate(C3A), and tetracalcium aluminoferrite (C4AF) (Odler 1998;Sedaghat et al. 2013, 2014; Zayed et al. 2013; Swaddiwudhiponget al. 2002).

High temperature resulting from heat of hydration (thereonreferred to as HOH) of cement can affect the hydration process,and consequently the kinetics of development of the mechanicalproperties of concrete (Kaszyńska 2002). While the current re-search correlates the heat of hydration with the cement fineness andmineralogical composition, others related the same property to thestrength development in cement paste. Kumar et al. correlated theHOH with the compressive strength of the cement paste and devel-oped a linear relationship for the strength prediction based on theheat release (Kumar et al. 2013a). One of the main reasons trigger-ing the interest in HOH of cement is its implication in thermalcracking in concrete. The high temperature gradient between the

inner core and the outer surface of a concrete element is knownto result in large tensile stresses that may exceed tensile strength,thus leading to early-age thermal cracking in mass concrete(Schindler 2002). Cement fineness is a critical component affectingthe HOH of portland cement; the primary reason for contractorsto resort to finer cement is its high early strength and faster con-struction operations (Bentz et al. 2008). Higher cement finenessprovides higher surface area for cement to react with water, there-fore resulting in an increase in rate of heat liberation at early agesand higher internal temperature in the concrete elements (PortlandCement Association 1997). Additionally, small particles can serveas nucleation sites for precipitation of hydration products. Thiseffect has also been illustrated with the addition of mineral admix-tures, such as fine limestone, to portland cements. Chemical com-position and interfacial properties of the mineral admixture maydetermine its tendency to serve as an efficient nucleant and/orparticipation of its dissociated ions in chemical reaction with thecalcium silicate hydrate product (Oey et al. 2013). Kumar et al.noted that smaller particles have higher nucleation rates possiblydue to experiencing higher grinding action and consequent highlydamaged surface (Kumar et al. 2012a). Adjustment of cement ormineral fineness interground or blended together may provide asolution to maintain the early age properties similar to portlandcement while providing the desired strength and reducing theclinker factor of portland cements (Kumar et al. 2013b).

ASTM C1702, Isothermal conduction calorimetry [ASTMC1702 (ASTM 2010d)], and ASTM C186, heat of solution calo-rimetry [ASTM C186 (ASTM 2010c)] are two available methodsunder ASTM standard specifications to measure the HOH ofcements. Heat of solution calorimetry measures the temperaturerise of the acidic solution resulting from the decomposition of theanhydrous and partially hydrated cement separately. The differencebetween the heat of solution of anhydrous and partially hydratedcement can be calculated as the heat evolved during the hydrationperiod. Considering the experimental circumstances, this methodis labor intensive and requires application of hazardous acidic sub-stances (Poole 2007).

1Ph.D. Candidate, Dept. of Civil and Environmental Engineering, Univ.of South Florida, 4202 E. Fowler Ave./ ENB118, Tampa, FL 33620(corresponding author). E-mail: asedagha@mail.usf.edu

2Ph.D. Candidate, Dept. of Civil and Environmental Engineering, Univ.of South Florida, 4202 E. Fowler Ave./ ENB118, Tampa, FL 33620.E-mail: nkashalo@mail.usf.edu

3Associate Professor, Dept. of Civil and Environmental Engineering,Univ. of South Florida, 4202 E. Fowler Ave./ ENB118, Tampa, FL 33620.E-mail: zayed@usf.edu

Note. This manuscript was submitted on March 10, 2014; approved onOctober 14, 2014; published online on December 8, 2014. Discussion per-iod open until May 8, 2015; separate discussions must be submitted forindividual papers. This paper is part of the Journal of Materials in CivilEngineering, © ASCE, ISSN 0899-1561/04014257(12)/$25.00.

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Isothermal conduction calorimetry has the ability to record theheat flow resulting from the cement hydration, immediately fromthe initiation of reaction of water with cement. The calorimetry pro-vides the user the ability to study the hydration stages from therecorded heat flow curve at the desired hydration age. Isothermalconduction calorimtery maintains the bath temperature constant,therefore, avoiding the effect of temperature change on HOH de-velopment mechanism, contrary to the systems in adiabatic con-ditions in which the temperature change due to cement hydrationprocess may affect the HOH development mechanism. Samplepreparation and operation of the instrument are fairly easy, thoughit requires some basic training. The cumulative heat at any age canbe calculated by the integration of the area under the heat flowcurve versus time (Wadsö et al. 1997; Kumar et al. 2012b; Xu et al.2011; Killoh 1988).

Effect of cement phase composition on HOH has been exten-sively studied by several researchers. Woods et al. (1932) devel-oped equations predicting the HOH of cements at the ages of 3,7, 28, 90, and 180 days based on the measured HOH of 13 cementsusing solution calorimetry. The HOH equations were defined asa linear regression of major phases of C3S, C3A, C2S, and C4AF.The fineness of cements used to calibrate the equations falls withinthe range of 1,390 to 1,670 cm2=g determined by a sedimentationdevice. The study concluded that fineness of cement does not havesubstantial effect on the generated heat. Good linear correlationswere indicated between the HOH at 3 days, 180 days, and 1 yearages and the amount of C3Sþ 2.1C3A, separately (Woods et al.1932, 1933). Comparison of measured and predicted HOH in termsof oxide composition for four commercial cements indicates thatthe equations can overestimate the HOH by 11 Cal=g at the agesof 3, 7, and 28 days and by 5 Cal=g at the age of 180 days (Woodset al. 1932).

Lerch and Bogue (1934) work on HOH shows a significanteffect of cement fineness on HOH at the ages of one, three, andseven days while it is less drastic at the ages of 28 days and up.

Verbeck and Foster (1950) established relationships betweenthe HOH of cements and their composition at several ages rangingfrom three days up to 6.5 years. The least-squares method wasimplemented to fit the experimental data to the proposed equationsassuming linear and independent relationship between cementphases of C3S, C3A, C2S, C4AF, SO3, and HOH. Significant dis-crepancy between measured and predicted heat by his methodscan be observed for Type III and Type IIIA cements at ages of threeand seven days. Although the relationships were established basedon the main phases of cements affecting the heat at varied ages,the fineness was not incorporated into the proposed equations as asignificant factor affecting the HOH.

Poole (2009) developed several equations based on the valuesof HOH of individual compounds as outlined in Lea’s Chemistryof Cement (Odler 1998), data provided by CCRL and U.S. ArmyCorps of Engineers, and the data taken from the Verbeck andFoster’s (Verbeck et al. 1950) research study. One of the equationspredicting the seven-day HOH was developed as a linear functionof C3S, C3A, C2S, C4AF and Blaine fineness based on the datataken from Verbeck and Foster’s research study. It should be notedthat these cements have variable phase compositions with theBlaine fineness in the range of 285 to 490 m2=kg. Poole’s analysisindicates approximately 0.4 J=g increase/decrease in seven-dayHOH per unit m2=kg change (increase/decrease) of Blaine fineness.Poole concluded that Blaine fineness has an effect on seven-dayHOH, but a relatively large change in cement fineness is requiredto make a change in the seven-day HOH of cements. Bentz (2010)studied the change in seven-day HOH of a cement with three fine-nesses of 302, 387, and 613 m2=kg. He reported approximately

0.46 J=g of change in HOH, per unit m2=kg change of Blaine fine-ness, when the Blaine fineness changed from 302 to 387 m2=kg,however this change was 0.07 J=g, per unit m2=kg change ofBlaine fineness, when the Blaine fineness changed from 387 to613 m2=kg. The change in seven-day HOH, on average, occurredas 0.18 J=g, per unit m2=kg change of Blaine fineness, when theBlaine fineness changed from 302 to 613 m2=kg. It is understoodfrom these research studies that the effect of Blaine fineness onseven-day HOH is strongly dependant on the phase compositionof the cements studied as well as the range of the cement Blainefineness in which the cements HOH are examined.

Bentz et al. (2009) conducted several HOH experiments onType I/II portland cement using isothermal conduction calorimetryat (w/c)s of 0.325, 0.35, 0.4, and 0.425. It can be observed thatthe pastes prepared at (w/c) of 0.35, 0.4, and 0.425 show similarHOH at one day while this heat is 10% less for the mix preparedat (w/c) of 0.325. HOH of cement pastes prepared at (w/c) of 0.4shows 1.7% and 2.9% slightly less HOH, respectively, at threeand seven days, relative to the pastes prepared at (w/c) of 0.425.The HOH of pastes prepared at (w/c) of 0.35 and 0.325 relativeto the paste prepared at (w/c) of 0.425 shows respectively, 3.4%and 16.9% less HOH at three days and respectively 7.4% and23.5% less HOH at seven days. As it is evident from the findings,HOH of cement paste is drastically influenced at (w/c) of 0.325while this impact is gradually fading out as the (w/c) approaches0.425. It is well established in the literature that the cement pastesprepared at lower (w/c) <0.42may undergo self-desiccation processsince not sufficient water is available for continuation of hydrationprocess (Young et al. 2002). Bentz et al.’s findings are consistentwith the results provided by Pane et al. in regards to impact of(w/c) on HOH of cement paste (Pane et al. 2005).

This paper aims to establish equations predicting one-day,three-day, and seven-day HOH of portland cements using cementphase composition and fineness at constant water to cement ratioof 0.5 and constant isothermal bath temperature of 23°C. Blainefineness and particle size distribution of candidate cements [asreceived and ground Cements (1)–(4)] was measured, and theirsuitability as a measure of cement fineness to develop the HOHequations was studied. Validation of the proposed equations wasconducted by comparing the HOH of eight as received portlandcements (Cements A–H) measured by isothermal conduction calo-rimetry with the calculated heat using the proposed equations. Thesuitability of the proposed equations to predict the HOH was ex-amined using statistical analysis and by establishment of pairedcomparison t-test confidence intervals on the predicted and mea-sured HOH. The proposed equations can be used to identify port-land cements with high HOH that have the potential to causethermal cracking in mass concrete elements. Also the proposedequations can be implemented to correlate the HOH with otherproperties of portland cement for the prediction of physical andchemical properties and quality control of manufactured portlandcement and concrete (Bentz et al. 2012).

Experimental

Four ASTM portland cements [Cements (1)–(4)] with differentmineralogical composition were selected. The cements wereground separately with ethanol 200-proof absolute 99.5% pure inan airtight jar using McCrone micronizing mill (McCrone Micro-scope and Accessories 2012) for 1.5, 3, 6, and 9 min to obtainvaried finenesses. Ethanol was chosen as a slurry liquid to lessenthe effect of grinding heat on temperature sensitive phases, includ-ing gypsum. Each grinding mix contained 6 g of cement and 10 g

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of ethanol for optimum grinding efficiency. Wet grinding assistsin homogeneity of the ground cement as well as reducing theoxidation and deformation of crystal lattice structure (McCroneMicroscope and Accessories 2012; Hurst et al. 1997). After thegrinding operation, the slurry mix was vacuum filtered with anultrafine Durapore membrane filter with 0.45 μm mesh, and aBuchner funnel was used to extract the ethanol from the mix(Stutzman 1996). The ground cements were then oven dried at43°C for 90 min to remove as much ethanol as possible from themix and then desiccated for 24 h. It was understood that 43°Coven drying of ground cement does not have phase shifting effect,due to temperature, on gypsum since conversion from gypsum tohemihydrate or anhydrate occurs at higher temperatures (Hudson-Lamb et al. 1996). At the time of removal of ground cements fromdesiccators, they were manually ground with a spatula to a homog-enous soft powder and stored in dry, watertight plastic containersuntil testing.

Blaine fineness of cements was measured by an air permeabilityapparatus conforming to ASTM C-204 [ASTM C204-07 (ASTM2010e)]. Particle size distribution of cements was determined usinga Horiba laser scattering particle size analyzer (LA-950) in tripli-cate runs on all the samples (Horiba Instruments Incorporated2012; Horiba Scientific 2013). Describing the laser diffractionmethod, when light hits a cement particle, the diffracted light isgenerated from the particle. Based on the light-scattering theory,the diameter of cement particle is determined based on the scatteredlight strength while the particle’s circumference length and theincoming light’s wavelength are compared. Particle size diameterparameter α (α ¼ πD=λ) and particle refractive index dictate thescattered light strength. Before conducting the measurements,HORIBA instrument was adjusted to obtain 5,000 data measure-ments per second with 15 iterations. Refractive index of 1.7–1.0iwas specified for the diffraction measurements of cement particles.This value was obtained from the “Certification of SRM 114q:Part II (Particle size distribution), NIST Special Publication260-166” conforming to the HORIBA LA-950 user’s manual. Theparticle size distribution measurements were conducted in auto-matic mode and on dry cement powder, implementing a smallnozzle at 0.3 (MPa) of air pressure. Maximum standard deviation[on cumulative volume (%)] on difference of average of three runsand each run of laser diffraction measurement for each sample wascalculated as 0.6% indicating very insignificant deviation andstrong repeatability of the measurements.

ATAMAIR isothermal conduction calorimetry manufactured byTA instruments was implemented to measure the HOH of cementsin accordance with ASTM C-1702, Method A, internal mixing,[ASTM C1702 (ASTM 2010d)] at 23°C isothermal bath temper-ature. Internal mixing provides the user the ability to record theHOH of cements immediately from the time of mixing of waterwith cement. Internal mixing was conducted by 10 s of water in-jection into the admixer ampoule followed by 60 s of manual con-stant uniform internal mixing (13 full turns) using the designatedadmixer. Further detailed information regarding this methodologyis available in Sedaghat et al. (2013). Room temperature was main-tained close to the calorimetry bath temperature to avoid any inter-ruption of heat exchange between the water in the admixer syringeand the surrounding environment at the time of lowering the ad-mixer into calorimetry. Water-to-cement ratio of 0.5 was selectedto avoid self-desiccation of cement paste (Young et al. 2002). Allthe HOH measurements were performed in duplicate runs to en-sure the precision of results. It is noteworthy that all the duplicateruns have less than 1% heat difference from the average of the tworuns at one-day, three-day, and seven-day hydration ages. HOHmeasurements are interestingly repeatable and heat flow curve

generated from the first and second runs, for each specimen,overlap throughout the complete hydration period with the maxi-mum 30 (μW=g) heat flow deviation from each other at any hydra-tion age (with the exception of the first 15–20 min of initial stageof hydration). It should be noted that shape of the heat flow curve atthe initial stage of hydration may be affected by the speed of in-ternal mixing using the designated admixer, though the cumulativeheat shall merge for both first and second runs after approximatelyan hour from the hydration process initiation. Fig. 1 clearly showsthe repeatability of the HOH measurements as indicated by trans-parent overlapping of the first and second heat flow runs for twospecimens used in this study.

Mineralogy of cements was studied using X-ray diffraction.The diffractometer used in this study was a PANalytical CubixPro (PANalytical, Westborough, Massachusetts) coupled withPANalytical X’Pert Industry and HighScore Plus software pro-grams for crystalline phase analysis. Software programs imple-ment Rietveld refinement simulation for phase analysis andquantification. The instrument was equipped with acceleratingdetector, capable of collecting a suitable X-ray pattern scan forquantification purposes, in less than 6 min. The X-ray tubewas operated at a current of 40 mA and a voltage of 45 KV. The2θ scan range was set for 5–60° using a step size of 0.012°. TheX-ray pattern of each sample was obtained in triplicate runs. ForCements (1)–(4), the quantity of each crystal phase was deter-mined as the average of the Rietveld refinement result of threeruns of as received cements and 12 runs of ground cements, indi-vidually, for each cement. For Cements A–H, the quantity of eachcrystal phase was determined as the average of the Rietveld refine-ment result of three runs of as received cement, individually, foreach cement.

Results and Discussion

X-ray Diffraction and Phase Quantification ofCements (1)–(4)

X-ray patterns of Cements (1)–(4) were measured and their crystalphase quantification (using Rietveld refinement simulation) weredetermined in our research lab. The X-ray patterns are shown inFig. 2. Rietveld refinement simulation allows direct quantificationof portland cement crystalline phases. Improved repeatability andreproducibility of the results can be observed from the methodand prior research (Le Saoût et al. 2011). This method uses full

Fig. 1. Evaluation of repeatability of heat-flow measurements

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profile fitting simulation to calculate the quantity of each phaseassociated with the peaks at specific 2θ locations. It is noteworthythat implementation of automatic software (PANalytical X’PertIndustry; HighScore Plus) eases the use of the Rietveld methodby iteratively comparing the X-ray pattern of the portland cementsample to the X-ray pattern of each reference phase in the data base(ICDD or ICSD) (Scrivener et al. 2004).

To quantify the crystal phases for each cement, 12 crystal phasesof alite (C3S), belite (C2S), ferrite (C4AF), tricalcium aluminate(C3A), periclase (MgO), arcanite (K2SO4), free lime (CaO), por-tlandite (CaðOHÞ2), calcite (CaCO3), gypsum (CaSO4 · 2H2O),hemihydrate (CaSO4 · 0.5H2O), and anhydrite (CaSO4) werespecified. The peaks corresponding to major crystalline phasesare labeled and the quantities are indicated accordingly. The quan-tities of major phases are ranging from 58.7–68.9% (for C3S),3.1–10.3% (for C3A), 8.2–19% (for C2S), and 6.9–13.3% (forC4AF) between Cements (1)–(4) as outlined in Table 1.

Particle Size Distribution of As-Received and GroundCements (1)–(4)

Particles size distribution of as-received and ground Cements(1)–(4) used to establish the proposed HOH equations are shownin Fig. 3 and summarized in Table 2.

The laser scattering particle size analyzer, implemented in thisstudy, determines the cement mean particle size based on theEq. (1) (Horiba Instruments Incorporated 2012)

Mean diameter ¼P½ qðJÞ · XðJÞ�

PqðJÞ ð1Þ

J = particle diameter division number; qðJÞ = frequency distri-bution value (%); and XðJÞ = Jth particle diameter range’srepresentative diameter (μm).

The mean particle size for Cement (1) changes from 12.90 to5.53 μm, for Cement (2) from 14.35 to 5.21 μm, for Cement(3) from 15 to 3.82 μm, and for Cement (4) from 13.15 to 6.17 μm.The span indicating the width of the particle size distribution curvecan be calculated based on Eq. (2) (Horiba Scientific 2013)

Span ¼ D90 −D10

D50

ð2Þ

D90, D50, and D10 refer to the diameters which 90, 50, and 10%of the cement bulk (by volume), respectively, is smaller than that.

Fig. 2. X-ray patterns and Rietveld refinement quantification of as received and ground cements: (a) Cement (1); (b) Cement (2); (c) Cement (3);(d) Cement (4)

Table 1. Major Phase Composition of Cements (1)–(4)

Identifier C3S C3A C2S C4AF

Cement (1) 60.6 6.5 14.2 11.8Cement (2) 58.7 10.3 13.7 6.9Cement (3) 68.9 5.0 8.2 7.9Cement (4) 59.8 3.1 19.0 13.3

Note: Values are in percent.

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As summarized in Table 2 and shown in Fig. 3, the methodof grinding implemented for this study narrowed the particlesize distribution curve; therefore, the range of cements’ particle sizebecomes closer to the mean. It is observed that grinding has adistinguishing effect on D90 for cements ground for nine minutesas D90 appeared as 9.23, 8.92, and 10.43 μm for Cements (1),(2), and (4), respectively, while it is 5.59 μm for Cement (3).Cement (3) contains the highest C3S amount of 68.9% and low

C2S and C4AF amounts of 8.2 and 7.9%, respectively amongall the ground cements. Also, D10 for Cements (2) and (3) groundfor nine minutes is reported as 1.7 and 1.8 μm, while it is 2.25 and2.44 μm for Cements (1) and (4), respectively. Cements (2) and (3)have lower sum amount of C2S and C4AF compared to Cements (1)and (4). It is understood that grindability of cement is related topacking density of each individual phase. C3S crystals show elon-gated habit; and are less densely packed compared to C2S crystals.Brittle index calculated from the measurements of the impressionmade in each phase by Vickers microindenter conducted by DavidLawrence (Lawrence 1998) indicates the highest brittle index of4.7 for C3S followed by 2.9 for C3A and 2 for C2S and C4AF.Brittle index is defined as the ratio of elastic strain energy to irre-versible strain energy, corresponding to the peak point of the σ − εcurve (Brandt 2009). It is perceived that cements with high amountof C3S and low amounts of C2S and C4AF have higher grindabilitypotential.

Development of Proposed Heat of Hydration Equations

TAMAIR isothermal conduction calorimetry was implemented tomeasure the HOH of cements at w=c ¼ 0.5 and isothermal bathtemperature of 23°C. The heat flow pattern obtained from the calo-rimetry can be used to study the hydration stages of the portlandcement. Integration of the area under the heat flow curve can bespecified as the cumulative heat at varying hydration ages and usedto develop the equations predicting the HOH at one-day, three-day,and seven-day hydration ages.

Initially, the effect of cement fineness on HOH was studied bymeasuring the Blaine fineness of Cements (1)–(4) in the as receivedand ground forms in accordance with ASTM C204 specification.The HOH of Cements (1)–(4) (in as received and ground forms) isplotted versus the Blaine fineness and is shown in Fig. 4 and sum-marized in Table 3. Each line in the figure depicts different grinds

Fig. 3. Particle size distribution of As received and ground cements: (a) Cement (1); (b) Cement (2); (c) Cement (3); (d) Cement (4)

Table 2. Particle Size Distribution of as Received and GroundCements (1)–(4)

IDMean(μm)

Median(μm) Span

D10(μm)

D50(μm)

D90(μm)

Cement (1), as received 12.90 10.45 2.03 3.61 10.45 24.86Cement (1), 1.5 min ground 9.42 8.77 1.40 3.74 8.77 16.00Cement (1), 3 min ground 8.34 7.78 1.38 3.40 7.78 14.11Cement (1), 6 min ground 6.39 6.00 1.33 2.71 6.00 10.69Cement (1), 9 min ground 5.53 5.23 1.33 2.25 5.23 9.23Cement (2), as received 14.35 10.78 2.46 3.21 10.78 29.74Cement (2), 1.5 min ground 9.86 9.08 1.45 3.79 9.08 16.92Cement (2), 3 min ground 7.85 7.31 1.39 3.13 7.31 13.27Cement (2), 6 min ground 5.98 5.66 1.35 2.38 5.66 10.02Cement (2), 9 min ground 5.21 4.90 1.47 1.70 4.90 8.92Cement (3), as received 15.00 11.11 2.68 2.43 11.11 32.21Cement (3), 1.5 min ground 9.75 8.94 1.47 3.68 8.94 16.79Cement (3), 3 min ground 7.45 6.99 1.33 3.20 6.99 12.46Cement (3), 6 min ground 5.14 14.93 1.44 1.59 14.93 8.70Cement (3), 9 min ground 3.82 3.97 0.95 1.80 3.97 5.59Cement (4), as received 13.15 10.67 2.22 2.63 10.67 26.30Cement (4), 1.5 min ground 11.97 10.25 1.21 4.60 10.25 16.96Cement (4), 3 min ground 8.65 7.90 1.81 1.76 7.90 16.08Cement (4), 6 min ground 7.53 7.00 1.41 2.98 7.00 12.83Cement (4), 9 min ground 6.17 5.80 1.38 2.44 5.80 10.43

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of the same cement while the cement composition remained con-stant. Coefficients of determination (R2) based on linear regressiontheory are shown, for each cement, in the figure. Coefficients ofdetermination (R2) are in the range of (0.75–0.94), (0.69–0.86),

and (0.64–0.83) for one-day, three-day, and seven-day hydrationages, respectively. Based on the (R2) provided, it is unlikely thata strong linear correlation will be found between the HOH andthe Blaine fineness.

Fig. 4. Cement heat of hydration versus Blaine fineness: (a) Cement (1); (b) Cement (2); (c) Cement (3); (d) Cement (4)

Table 3. Measured Blaine Fineness, Mean Particle Size; One-Day, Three-Day, and Seven-Day Heat of Hydration for As-Received and GroundCements (1)–(4)

IDBlaine fineness

(m2=kg)Mean particlesize (μm)

Measured one dayHOH (J=g)

Measured three dayHOH (J=g)

Measured seven dayHOH (J=g)

Cement (1), as received 417 12.90 207 298 350Cement (1), 1.5 min ground 479 9.42 262 356 397Cement (1), 3 min ground 497 8.34 264 359 403Cement (1), 6 min ground 628 6.39 290 384 420Cement (1), 9 min ground 703 5.53 297 385 415Cement (2), as received 405 14.35 216 350 386Cement (2), 1.5 min ground 444 9.86 273 383 407Cement (2), 3 min ground 542 7.85 320 402 423Cement (2), 6 min ground 648 5.98 349 413 432Cement (2), 9 min ground 816 5.21 350 415 435Cement (3), as received 426 15 217 306 340Cement (3), 1.5 min ground 463 9.75 273 367 390Cement (3), 3 min ground 550 7.45 306 387 409Cement (3), 6 min ground 675 5.14 341 401 419Cement (3), 9 min ground 876 3.82 362 417 436Cement (4), as received 414 13.15 204 274 326Cement (4), 1.5 min ground 392 11.97 207 295 346Cement (4), 3 min ground 573 8.61 250 328 367Cement (4), 6 min ground 555 7.53 267 348 377Cement (4), 9 min ground 638 6.17 279 360 385

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The cement mean particle also has the potential to correlate withthe HOH to develop the equations predicting the HOH. In priorresearch, mean particle size was noted as an approximate averageof D10, D50, andD90 (Azari 2010). To examine the implementationof mean particle size as a measure of cement fineness, the deter-mined HOH of as received and ground Cements (1)–(4) at one-day,three-day, and seven-day hydration ages is plotted versus mean par-ticle size and is shown in Fig. 5. Each line in the figure depicts thedifferent grinds of the same cement while cement composition re-mained constant. Coefficients of determination (R2), based on thelinear regression theory, are shown in the figure for each cement. Asit is evident from the figure, R2 ranges from 0.92 to 0.99 for all theCements (1)–(4) at one-day, three-day, and seven-day hydrationages. The slope of the line is steeper for one day HOH relativeto three and seven days indicating that cement fineness has moresignificant effect on one day HOH compared to three and sevendays. It can be concluded from the calculated R2 that, in orderto develop the equations, mean particle size is a better parametercompared to Blaine fineness to correlate with the HOH. Accord-ingly, Eq. (3) can be offered as a general linear regression equationpredicting one-day, three-day, and seven-day HOH of portlandcements

CumulativeHOHðat 1; 3; or 7 daysÞ¼ ðHOHÞInterceptþ Slope × ðmean particle sizeÞ ð3Þ

The hydration of portland cement consists of a series of reac-tions between cement phases and water. The HOH of cements ismainly controlled by the four major phases of C3S, C3A, C2S,and C4AF (Odler 1998). As indicated in Fig. 5, HOH of a specificcement is a linear function of mean particle size at ages of one,

three, or seven days, individually; also the change in slope and(HOH) intercept, for each cement, is the reflection of cementmineralogy. In this regard, the (HOH) intercept and slope for eachcement can be defined as a linear regression of C3S, C3A, C2S, andC4AF phases, for each hydration ages of one, three, and seven days,as indicated in Eqs. (4) and (5). In this regard, Solver command inMicrosoft Excel 2010 and also the least-squares method can beused to determine and optimize the coefficients (A1 through D1

and A2 throughD2) based on the actual intercepts and slopes results(as shown in Fig. 5) for Cements (1)–(4) at three hydration ages ofone, three, and seven days. Solver command in Microsoft Excelfunctions based on the generalized reduced gradient (GRG2) algo-rithm for optimizing nonlinear problems code.

ðHOHÞ Intercept ¼ A1ðC3SÞ þ B1ðC3AÞ þ C1ðC2SÞ þD1ðC4AFÞð4Þ

Slope ¼ A2ðC3SÞ þ B2ðC3AÞ þ C2ðC2SÞ þD2ðC4AFÞ ð5Þ

Coefficients of determination (R2) for actual versus calculated(based on optimized coefficients) intercepts and slopes, forCements (1)–(4) as indicated in Table 4, show an interesting fit

Fig. 5. Cement heat of hydration versus mean particle size: (a) Cement (1); (b) Cement (2); (c) Cement (3); (d) Cement (4)

Table 4. R2 Coefficients of Determination for Actual versus CalculatedIntercepts and Slopes for Cements (1)–(4)

Parameters Intercept Slope

One-day heat of hydration 0.88 0.85Three-day heat of hydration 1 1Seven-day heat of hydration 0.98 1

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(R2 > 0.98) for Cements (1)–(4) for hydration ages of three andseven days.

After determining the coefficients of A1 through D1 and A2

through D2, Eqs. (4) and (5) can be incorporated into Eq. (3) todevelop the HOH Eqs. (6)–(8) for one-day, three-day, andseven-day hydration ages.

1 DayHOH ðJ=gÞ ¼ ð476 − 13.35 MPSÞC3S

þ ð1,290 − 58.41 MPSÞC3A

þ ð99 − 6.94 MPSÞC2S ð6Þ

3 DayHOH ðJ=gÞ ¼ ð521 − 6.84 MPSÞC3S

þ ð933 − 0.55 MPSÞC3A

þ ð127þ 20.04 MPSÞC2S

þ ð534 − 88.55 MPSÞC4AF ð7Þ

7 DayHOH ðJ=gÞ ¼ ð517 − 6.53 MPSÞC3S

þ ð1,099 − 11.73 MPSÞC3A

þ ð35.18 MPSÞC2S

þ ð722 − 78.59 MPSÞC4AF ð8Þ

Mean particle size should be noted as μm and the quantity of eachphase must be inputted as a fraction. Validation of the proposedEqs. (6)–(8) is discussed in the following section.

Eqs. (6)–(8) can be combined into a more general expression aspresented in Eq. (9). To develop Eq. (9), each coefficient inEqs. (6)–(8) was plotted as a function of time and the correspondingsecond order polynomial equations was fitted into the data points todefine each coefficient as a function of time (day), subsequently,each coefficient was placed in the general format of Eqs. (6)and (7) or Eq. (8) to develop Eq. (9).

HOHD ¼ f½−3.92ðD2Þ þ 38.17ðDÞ þ 441.75�− ½0.53ðD2Þ − 5.37ðDÞ þ 18.19�MPSgC3S

þ f½36.67ðD2Þ − 325.17ðDÞ þ 1,578.5�− ½5.29ðD2Þ − 50.08ðDÞ þ 103.2�MPSgC3A

þ f½−7.63ðD2Þ þ 44.5ðDÞ þ 62.13�− ½1.62ðD2Þ − 19.96ðDÞ þ 25.28�MPSgC2S

þ f½−36.67ðD2Þ þ 413ðDÞ − 377�− ½−7.79ðD2Þ þ 75.45ðDÞ − 67.66�MPSgC4AF ð9Þ

where D corresponds to the hydration age (1, 3, or 7 days).

Validation of Proposed Heat of Hydration Equations

Validation of the proposed Eqs. (6)–(8) is conducted by comparingthe measured HOH of eight as received commercial portland ce-ments (Cements A–H) with the predicted heat by the proposedEqs. (6)–(8). The Blaine fineness, mean particle size, mineralogicalcomposition and HOH of the cements were determined usingthe same experimental procedures and instruments used to char-acterize Cements (1)–(4). The pertaining data are summarizedin Table 5.

The paired-comparison t-test hypothesis (Montgomery 2005)was implemented to determine the 95% confidence interval on pre-dicted [by Eqs. (6)–(8)] and measured HOH of Cements A–H asoutlined in Table 6. The difference between predicted and measuredHOH of Cements A–H, at hydration ages of one, three, and sevendays, is shown in Fig. 6.

The proposed Eq. (6) one day HOH prediction; Eq. (7) threeday HOH prediction; and Eq. (8) seven-day HOH prediction over-estimate the HOH, on average, by þ3, þ1, þ1 J=g, respectively.The standard deviation of predicted minus measured heat at hydra-tion ages of one, three, and seven days are calculated as 9, 3, and6 J=g, respectively.

Table 5.Measured Blaine Fineness, Mean Particle Size, X-Ray Rietveld Phase Quantification: One-Day, Three-Day, and Seven-Day Heat of Hydration of AsReceived Cements A–H

Cement identifier

Blainefineness(m2=kg)

Meanparticlesize (μm)

C3S C3A C2S C4AFMeasured one day

HOH (J=g)Measured three day

HOH (J=g)Measured seven day

HOH (J=g)Expression %

A 612 10.05 61.7 6.9 14.0 12.7 252 341 385B 530 10.27 58.8 11.2 13.3 5.9 286 383 407C 575 8.65 58.6 2.9 20.1 13.4 252 329 368D 494 10.41 61.9 5.2 15.8 9.6 252 342 384E 389 14.45 57.4 4.5 11.4 13.2 177 234 278F 392 13.01 61.3 6.1 11.3 10.4 211 297 345G 414 13.69 68.3 4.3 8.9 9.6 206 303 343H 405 15.59 63.5 5.6 13.7 12.6 189 270 328

Table 6. Statistical Analysis on Cements A–H for Evaluation of Proposed Eqs. (6)–(8)

Hydrationage

Average of“predicted minus

measured” heat (J=g)

Standard deviation of“predicted minus measured”

heat (J=g)

R2 of “predictedversus measured”

heat (J=g)

Paired comparisonT-test lower

confidence limit

Paired comparisonT-test upper

confidence limit

One day 3 9 0.95 −5 10Three days 1 3 1 −2 4Seven days 1 6 0.98 −4 6

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The 95% confidence interval on predicted and measured HOHwere calculated as ½−5,10�, ½−2,4�, and ½−4,6� for hydration agesof one, three, and seven days, respectively. It is understood thatthe smaller 95% confidnce interval shows the higher accuracyof the equation to predict the HOH (Montgomery 2005; Sedaghatet al. 2013).

It appears that Eq. (7) can more accuaretly predict the HOH(at three-day hydration age), as it has smaller confidence interval,smaller standard deviation of predicted minus measured heatcompared to Eqs. (6) and (8) implemented to predict the HOHat one-day and seven-day hydration ages, respectively.

It is concluded that all three of the proposed Eqs. (6)–(8) showgood accuracy to predict the HOH at hydration ages of one, three,and seven days, while Eq. (7) appears to be a better predictor ofHOH relative to the other two proposed equations.

Evaluation of Equations Predicting Seven-Day HOHProposed by the Authors of This Paper and AlsoAvailable in the Literature

This section will discuss the equations developed by the authors ofthis paper and also by other researchers to predict the seven-dayHOH of portland cements. Per ASTM standard specifications,ASTM C150 (ASTM 2009) and ASTM C1600 (ASTM 2008) haveset limits per optional physical requirements on seven-day HOH ofcements while ASTM C595 (ASTM 2010b) and ASTM C1157(ASTM 2010a) have set limits per physical requirements on seven-day HOH of cements. ASTM standard specifications assigned theASTM C186 (ASTM 2010c) as the procedure to measure theseven-day HOH of portland cement for standard purposes. Follow-ing this statement, several researchers attempted to predict theseven-day HOH of portland cement based on the cement compo-sition, cement fineness and/or physical properties of cement pasteor mortar.

Poole developed Eq. (10) based on the HOH of individualcompounds published in Lea’s Chemistry of Cement (Poole 2009;Lea 1971). Eq. (10) consists of the four major phases of C3S,C3A, C2S, and C4AF as the main contributors to the seven-dayHOH of cement. This equation does not include the effect ofcement fineness as a variable affecting the seven-day HOH ofcements.

Seven-dayHOH ðJ=gÞ ¼ ð15.55ÞC3Aþ ð2.21ÞC3S

þ ð0.42ÞC2Sþ ð5.82ÞC4AF ð10Þ

Poole (2009) developed Eq. (11) from a stepwise linear regressioncalculation on the seven-day HOH, measured by heat of solutioncalorimetry (ASTM C186), of 38 cements data that he obtainedfrom the CCRL (16 cements) and U.S. Army Corps of EngineersResearch and Development Center (22 cements). He noted that thevariables were incorporated into the equation as long as they werestatistically significant at a probability of 0.05. He concluded thatonly C3S and C3A were found to be statistically significant. Thisequation was the basis to establish the maximum limit of 100 onthe quantity of (C3Aþ 4.75C3A) in ASTM C150 to maintain theseven-day HOH (measured based on ASTMC186) of Type II (MH)and Type II (MH)A under 335 (J=g). The range of the Blaine fine-ness of the cements used to calibrate the equation falls within2,640–4,360 cm2=g. The quantities of the major phases of cements(potential phase composition) were determined using Bogue equa-tions [ASTM C150 (ASTM 2009)].

Seven-dayHOH ðJ=gÞ ¼ ð133.9Þ þ ð9.36ÞC3Aþ ð2.13ÞC3S

ð11Þ

Poole (2009) developed Eq. (12) from the linear regression analysison seven-day HOH data obtained from the Verbeck and Foster’sresearch study (Verbeck et al. 1950) The seven-day HOH was de-termined using the heat of solution calorimetry. Water to cementratio of 0.4 was chosen to prepare the cement pastes. The Blainefineness of the cements used to calibrate the equation falls withinthe range of 2,850–4,900 cm2=g. Poole incorporated Blaine fine-ness as a variable into the Eq. (12) as he found it statistically sig-nificant varibale affecting the seven-day HOH of cement

Seven-dayHOH ¼ 1.98þ ð11.44ÞC3Aþ ð1.53ÞC3S

þ ð0.4ÞBlaine fineness ð12Þ

Poole’s equation indicates approximately 0.4 J=g increase/decrease in seven-day HOH per unit m2=kg change (increase/decrease) of Blaine fineness. Mathematical analysis conducted bythe authors of this paper on four cements with varied finenesses andmineralogical composition (HOH and Blaine fineness of the ce-ments are outlined in Table 3) indicates approximately 0.23, 0.12,0.21, and 0.26 J=g change in seven-day HOH, respectively forCements 1–4, per unit m2=kg change of Blaine fineness. As it isevident from the results, change in seven-day HOH per unit changeof Blaine fineness is significant and influenced by the phase com-position of the studied cements. The results indicate that change inseven-day HOH per unit change in Blaine fineness is less signifi-cant for cements with higher amount of C3A (Cement 2) and issubstantial for cements with lower amount of C3A (Cement 4).

Taylor (1997) developed Eq. (13) from the linear regressionanalysis on seven-day HOH and potential phase composition (de-termined based on the Bogue equations) of several cements. He didnot mention the quantity of the phases of the cements and also theirfinenesses used to calibrate his equation. He noted that the seven-day HOH of the cement pastes were measured using heat of sol-ution calorimetry and at water to cement ratio of 0.4

Seven-dayHOH ¼ ð1556ÞC3Aþ ð222ÞC3Sþ ð42ÞC2S

þ ð494ÞC4AF ð13Þ

The suitability of the proposed Eqs. (8) and (10)–(13) to predict theseven-day HOH of portland cements was assessed by inputtingthe mineralogy and fineness of the Cements A–H, as outlined inTable 5, in each equation and comparing the predicted HOH withthe measured HOH of Cements A–H. The difference between the

Fig. 6. Predicted and measured HOH difference for as receivedCements A–H, using Eqs. (6)–(8)

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predicted (by the proposed equations) and measured seven-dayHOH of portland Cements A–H is shown in Fig. 7.

For each proposed equation, predicting the seven-day HOH,95% confidence interval (based on the paired-comparison t-testhypothesis) (Sedaghat et al. 2013; Montgomery 2005) was deter-mined on predicted and measured seven-day HOH of CementsA–H, as outlined in Table 7. Paired comparison t-test greatly im-proves the precision by making comparisons within matched pairs(blocks of measured and predicted HOH) of experimental cements.This method eliminates the error associated with the differences ofphase composition and fineness between cements, as an additionalsource of variability. The paired comparison t-test confidence in-terval can be calculated using the following equation:

d̄� t0.025;n · Sd=ffiffiffin

p ð14Þ

d∶Average of the difference between predicted andmeasuredHOHof studied cements

t0.025;n∶ t − statistics corresponding to 95% confidence interval

& ðnÞ studied cements

Sd∶ Standard deviation on difference between predicted andmeasuredHOHof studied cements

The average and standard deviation of predicted minus mea-sured seven-day HOH of Cements A–H were calculated foreach proposed equation and are outlined in Table 7. It appears thatEq. (8) overstimate the seven-day HOH, on average, by þ1 J=gwhile Eqs. (10)–(13) underpredict it by −59, −35, −1,and −68 J=g, respectively. The standard deviations of the predicted

minus measured seven-day HOH were calcualted as 6, 37, 34, 25,and 36 J=g for Eqs. (8) and (10)–(13), respectively.

It appears that Eq. (8) shows the smallest 95% confidence in-terval of ½−4,6� on predicted and measured seven-day HOH ofcements compared to Eqs. (10)–(13) with the confidence intervalsof ½−90;−28�, ½−64;−7�, ½−22,19�, and ½−98;−38�, respectively.

It can be concluded that the following reasons may result inEq. (8) being a better predictor of seven HOH of portland cementsrelative to the other Eqs. (10)–(13).• Eq. (8) was developed based on the mineralogical composition

[quantitative X-ray diffraction (QXRD), direct method] of theportland cements while Eqs. (10)–(13) were established basedon the potential phase composition (using Bogue equations) ofthe cements. It is well established in the literature that the Bogueequations may cause erroneous results when quantifying themajor phases in portland cement (Stutzman 1996; Taylor 1997).

• Cement mean particle size is incorporated into Eq. (8) as a mea-sure of cement fineness while Eqs. (10), (11), and (13) do notcontain any measure of cement fineness as a variable factoraffecting the seven-day HOH of portland cements.

• HOH of portland Cements (1)–(4) [used to calibrateEqs. (6)–(8)] and also HOH of Cements A–H were deter-mined at water to cement ratio of 0.5 while the HOH of ce-ments used to calibrate Eqs. (10)–(13) were determined atwater to cement ratio of 0.4. Higher water to cement ratio mayprovide more available water for wetting and hydration of port-land cement, though the change of water to cement ratio from0.4 to 0.5 may not significantly affect the HOH of cement pasteat seven day hydration age (Bentz et al. 2009).

• HOH measurements using isothermal conduction calorimteryshows better precision compared to solution calorimetry forboth within laboratory and between laboratory HOH results[ASTM C1702 (ASTM 2010d)].

Conclusion and Proposed Future Work

This paper addressed the development of empirical equationspredicting the heat of hydration of portland cement at one-day,three-day, and seven-day hydration ages. The main results aresummarized as follows:• The proposed equations can be used to identify portland ce-

ments with the potential to cause thermal cracking in mass con-crete elements. Also, the equations can be used to correlate theheat of hydration with other properties of portland cement forquality control and prediction of physical and chemical proper-ties of manufactured portland cement and concrete.

• Cement fineness plays critical role in the heat of hydration ofportland cements.

• Mean particle size is a better measure of cement fineness relativeto Blaine fineness to correlate with the heat of hydration ofportland cement to establish equations predicting the heat atone-day, three-day, and seven-day hydration ages.

Fig. 7. Predicted and measured seven-day HOH difference for asreceived Cements A–H, using Eqs. (8)–(13)

Table 7. Statistical Analysis on Cements A–H for Evaluation of Proposed Eqs. (8)–(13)

Equationnumber

Average of “predictedminus measured”

heat (J=g)

Standard deviation of“predicted minus measured”

heat (J=g)

R2 of “predictedversus measured”

heat (J=g)

Paired comparisonT-test lower

confidence limit

Paired comparisonT-test upper

confidence limit

Eq. (8) 1 6 0.98 −4 6Eq. (10) −59 37 0.22 −90 −28Eq. (11) −35 34 0.30 −64 −7Eq. (12) −1 25 0.74 −22 19Eq. (13) −68 36 0.25 −98 −38

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• Heat of hydration of portland cement at one-day, three-day, andseven-day hydration ages is a linear function of cement meanparticle size when the composition is maintained constant atconstant isothermal bath temperature of 23°C and water tocement ratio of 0.5.

• Equations predicting one-day, three-day, and seven-day heat ofhydration of portland cement can be established based on theportland cement major phases of C3S, C3A, C2S, C4AF, andcement mean particle size.

• The proposed Eqs. (6)–(8) can predict the heat of hydrationat one-day, three-day, and seven-day hydration ages with goodaccuracy for portland cements for which major phases (C3S,C2S, C3A, C4AF) and mean particle size fall within the rangeof Cements (1) through (4) used to calibrate the proposedequations.

Proposed Future Work

The HOH equations developed in this paper can be modified toreflect the effect of combination of (w/c), temperature, cement fine-ness, cement composition and pozzolanic cementitious materialscontent on HOH. The following general equation can be proposed.

HOHðX;Y;ZÞ ¼ A · X þ B · Y þ C · ZX: (w/c), Y = Temperature (°C), Z = Cement fineness (m2=kg or

mean particle size)• A¼ A1 · ðC3SÞþB1 · ðC3AÞþC1 · ðC2SÞþD1 · ðC4AFÞþE1 ·

½CaOðflyashor slagÞ� þF1 · ½SiO2ðflyashor slagÞ� þG1 · ðSilica fumeÞ• B¼ A2 · ðC3SÞþB2 · ðC3AÞþC2 · ðC2SÞþD2 · ðC4AFÞþE2 ·

½CaOðflyashor slagÞ� þF2 · ½SiO2ðflyashor slagÞ� þG2 · ðSilica fumeÞ• C¼ A3 · ðC3SÞþB3 · ðC3AÞþC3 · ðC2SÞþD3 · ðC4AFÞþE3 ·

½CaOðflyashor slagÞ� þF3 · ½SiO2ðflyashor slagÞ� þG3 · ðSilica fumeÞThe quantity of each phase must be input as a fraction.A significant number of HOH experiments need to be con-

ducted to measure the HOH at varied “w=c ¼ 0.3, 0.4 and 0.5,”“temperature = 23, 30, and 40°C,” “Cement fineness = at least 4different cement finenesses,” “four portland cements coveringhigh and low quantities of major phases of C3S, C3A, C2S,C4AF,” “pozzolanic materials (slag, fly ash) = pozzolanic materialswith high and low CaO and SiO2 content,” “silica fume = high andlow quantities.” For this instance, the number of HOH experimentsin duplicate runs will be: N ¼ 2 × 3 × 3 × 4 × 10 ¼ 720. Solvercommand in Microsoft Excel can be implemented to optimize thecoefficients of A1 through G1, A2 through G2, and A3 through G3

based on the known cement composition, cement fineness, (w/c),temperature, pozzolanic cementitious materials content.

It is important to note that development of equations capable ofpredicting the HOH at 28 days is a possible option that requiresextension of the HOH measurements up to 28 days.

References

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