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Concrete is a heterogeneous material. This is composed of rock, sand, cement and water. Chemical admixtures and supplementary cementitious materials (SCMs) can also be added to the concrete to get desired properties. When water is added to cement, a chemical reaction begins which is called hydration. The cement hydration products are responsible for binding the concrete components together and for the strength gain. There are several other important physical properties besides strength those are results of the cement hydration and have impact on the concrete performance. Among these are dimensional stability, porosity, and permeability.
Activation energy of a chemical reaction represents the relationship of the chemical reaction rate to the reaction temperature. In the case of cement hydration, several chemical reactions happen simultaneously. The term apparent activation energy (Ea) is used to represent the average temperature dependence of multiple chemical reactions. Various physical property such as heat evaluation of hydration, amount of chemical bond water, chemical shrinkage, amount of Ca(OH)2 and strength are at least partially a function of the cement degree of hydration and can therefore be used to calculate Ea. Different methods and calculation techniques are used to determine Ea. The value of Ea depends on the experimental method and calculation techniques used.
This chapter contains a literature review which serves to provide the necessary background in concrete technology, and presents the chemical composition and hydration process of different cementitious systems. This chapter also includes a brief description of various supplementary cementing materials and chemical admixtures used in this study. A brief discussion on chemical shrinkage and factors that influence chemical shrinkage is also presented here. As Ea depend on the experimental methods and calculation techniques, a summary of different methods and calculation techniques used to quantify Ea is also included.
2.1.1 Cement Composition:
Limestone, clay, and shale are the basic ingredients of Portland cement. Clinker is the result of combining these ingredients at a very high temperature. Finally, portland cement is manufactured by grinding and mixing the clinker with gypsum. The gypsum controls the rate of set and can be partly replaced by other forms of calcium sulfate. Clinker normally contains four major phases; alite(Ca3SiO5), belite(Ca2SiO4), tricalcium aluminate (Ca3Al2O6), and tetracalcium aluminoferrite (Ca2AlFeO5).
Alite is the most abundant component of modern portland cement (PC) clinkers. It accounts for 50- 70% of the total mass of clinker. Alite is tricalcium silicate (Ca3SiO5), which is modified in composition and crystalline structure by incorporation of foreign ions, especially Mg2+, Al3+ and Fe3+ (Taylor 1990). Alite is mostly responsible for the early strength gain of cement. Belite constitutes 15- 30% of modern PC clinkers. It is an impure version of dicalcium silicate (Ca2SiO4). It reacts slowly with water and contributes little in the early strength gain; but plays a major role in the concrete's long-term strength development. 5-10% of the normal PC clinker is tricalcium aluminate (Ca3Al2O6), sometimes called aluminate. It reacts rapidly with water and can cause undesirable rapid setting unless some set-controlling agent like gypsum is added. 5-15% of the PC clinker is tetracalcium aluminoferrite (Ca2AlFeO5), sometimes called ferrite. Its rate of reaction to water is high in initial period and dependent on the composition and other properties.
Researchers have been using shorthand notation for simplicity to describe cement compounds. Universally accepted shorthand notations are CaO=C, SiO2=S, Al2O3=A, Fe2O3=F, MgO=M, K2O=K, Na2O=N, SO3=, H2O=H, TiO2=T, P2O5=P, and CO2= (Taylor 1990, Mindess 1981) The compounds typically found in cement and their shorthand are presented in Table 2-1.
Table 2-1: Typical compound composition of Portland cement 
Dicalcium silicate Tricalcium aluminate
Calcium sulfate dihydrate (Gypsum)
2.1.2 Cement Types:
There are different types of cement used, some of which have special purposes. Specifications for the cement types are in general, based on some certain chemical compositions or physical properties such as specific surface area, and partly on performance test, such as setting time and compressive strength developed under standard condition. According to ASTM C150  there are five types of cement. Blended cement is also widely used for construction purpose. Blended cement is the mix of two or more types of cementitious materials (portland cement, fly ash, ground granulated blast-furnace slag, silica fume, or natural pozzolans). Blended cement need to fulfill the requirement of ASTM C595 and C1157. In this study a Type-I cement was used.
Table 2- : Portland cement classification 
High early strength
Low heat of hydration
High sulfate resistance
2.1.3 Hydration of Cement:
Hydration starts as soon as water is added to cement. When water is added to cement, various components of cement are dissolved at a different rate and start reacting with each other. These reactions are exothermic , which means that heat is liberated during the reaction. Due to the reaction between various dissolved ions in the pore water, new compounds are produced. These compounds give cement strength, rigidity, durability and toughness. For portland cement, there are three primary classes of compounds in cement that react during the early-age hydration; Calcium silicates (referred to as silicates), Calcium aluminates (referred to as aluminates), and Calcium sulfates (referred to as gypsum).
The six most important and common chemical reactions in portland cement hydration are (Equation 2.1-2.6)
C3S + 5.3H â†’ C1.7SH4 + 1.3CH Reaction 2.1
C2S + 4.3H â†’ C1.7SH4 + 0.3CH Reaction 2.2
C3A + 3CH2 + 26H â†’ C6A3H32 Reaction 2.3
C3A + C6A3H32 + 4H â†’ 3C4A$H12 Reaction 2.4
C3A + 6Hâ†’ C-A-H Reaction 2.5
3C4AF +33CH2+42H â†’3C4AH12+3CH+3FH3 Reaction 2.6
Calcium Silicates Hydrates (C-S-H) forms with the addition of water to either tricalcium silicate or dicalcium silicate. About 50 to 60% of the total volume of the portland cement reaction products are C-S-H. C-S-H is responsible for strength, durability and stability of hydrated concrete. During these reactions, relatively weak and less dense compound calcium hydroxide (Ca(OH)2) is formed as a byproduct, which may become unstable when exposed to acids.
The second series of reactions involves tricalcium aluminate, C3A. Gypsum (), is added to the cement to control the setting of the hydrated Portland cement. As water is added, ettringite (C6A3H32) forms until the excess calcium sulfate is consumed. Monosulfoaluminate (C4AH12) will then begin to form from the reaction between C3A and ettringite, as shown in Equation 2.4. If there is any unused C3A remaining, the C3A will hydrate as shown in Equation 2.5, to form a calcium aluminate hydrate, C-A-H.
The third series of reactions is the hydration process of tetracalcium aluminoferrite, C4AF, in Portland cement, whose reaction is shown in Equation 2.6
2.2 Supplementary Cementitious Material:
2.2.1 Ground Granulated Blastfurnace slag:
Blastfurnace slag is a by product of iron manufacture. It is formed as a liquid at 1350- 1550oC. The molten slag can be cooled rapidly with water to form small glassy granules which can then be ground and used as an SCM called ground granulated blastfurnace slag (GGBFS). For a wide range of steel producing countries, the composition range of GGBFS is: MgO, 0- 21%; Al2O3, 5- 33%; SiO2, 27- 42%; and CaO, 30- 50% . In the United States, GGBFS is specified according to ASTM C 989, which classifies GGBFS into three grades based on the strength development of a 50% replacement of portland cement by GGBFS The relative proportion of slag and cement used in construction varies widely. Mass concrete constructions have used GGBFS to replace up to 80% of the portland cement, however dosages in the 35-50% range is more typical. The slag reaction is considerably slower then alite, which results in lower early age concrete strength, but may however result in higher later age strength. In one concrete mixture, a replacement of 65% of the portland cement by GGBFS resulted in 50% lower compressive strength at 2 days, but an increase in compressive strength by about 12% at 91 days . GGBFS can increase the workability and finishability of concrete and decrease both the rate and total amount of heat released during hydration.
2.2.2 Fly Ash:
Fly ash is a byproduct captured from the flue gas of coal burning power stations. Fly ash is composed principally of very fine, glassy, spherical particles due to the rapid cooling process. The chemical composition of the fly ash depends on the type of coal burned and the coal burning conditions during production. Anthracitic or bituminous coal gives ash high in SiO2, Al2O3 and Fe2O3 and low in CaO, whereas sub-bituminous or lignite coals give ash higher in CaO and lower in SiO2, Al2O3 and Fe2O3. Small percentages of crystalline materials can also be found in the fly ash such as quartz. However, these materials are largely inert (can cite the dissertation by Ryan Chancey here).
Figure 2-: Scanning electron micrograph of fly ash particles. Note the characteristic spherical shape that helps improve workability (personal contact with Dr. Kyle A. Riding).
Fly ash is classified according to ASTM C 618 , where Class F Class F and Class C fly ash must have a minimum SiO2+Al2O3+Fe2O3 content above 70% and 50%, respectively. Table 2.1 presents typical range of chemical compositions for the two classes of fly ash.
Table 2- Typical Range of chemical composition of fly ash .
Range of Chemical Composition (% by Weight)
Class F Fly Ash
Class C Fly Ash
2.2.3 Silica Fume:
Silica fume is a byproduct of the production of silicon or silicon alloy. Some SiO is lost as a vapor which when cooled, gives very fine solid, particles. The particles are spherical, have an average diameter around 100 nm, and are made up principally of amorphous SiO2. Most of the silica fume used in concrete has been derived from the production of alloys with at least 75 percent ferrosilicon, which yields a SiO2 content in the silica fume of 84 percent or higher . ASTM C 1240  specifies a minimum SiO2 content of 85% of the utilization of silica fume in concrete mixtures. Typically, the specific surface area of silica fume as measured using BET nitrogen adsorption is 20,000 m2/kg . The true density is above 2000 kg/m3 but the bulk density of the freshly filtered powder is only 200 kg/m3. Table 2.2 presents typical range of chemical compositions for silica fume.
Table 2- : Chemical compositions of silica fume from the production of elementary silicon and 75% ferrosilicon alloy .
High strength concrete will often include silica fume. The concrete permeability also decreases when silica fume is used. This has increased the use of silica fume for making high performance concrete when durability aspects are essential. Silica fume also decreases the bleeding, workability, and pumpability .
Metakaolin is obtained by calcinations of kaolin clay at moderate temperatures, usually 600 oC-800 oC. Clay minerals lose most of their absorbed water at 100oC -200oC. At 500oC-600oC kaolin clay loss water by dehydroxilization. The obtained material is grounde at an average partial size of 1 to 2 Î¼m; this is about 10 times finer than cement, but still 10 times coarser than silica fume. Metakaolin is used in concrete as an SCM where high strength and low permeability is required.
Partical size 3um
2.3 Chemical Admixture:
Chemical admixtures are ingredients are added to the concrete during mixing which are to achieve certain properties or performance. These admixtures can be natural or manufactured chemicals. Air entrainers, water reducers, and set control agents are the most common admixtures used in the concrete industry. ASTM C 494  includes seven types of admixtures. Of these admixtures, only a water reducer was considered in this study.
Table 2- : List of chemical admixtures according to ASTM C 494 .
Water-reducing and retarding admixtures
Water-reducing and accelerating admixtures
Water-reducing, high range admixtures
Water-reducing, high range, and retarding.
2.3.1 Water Reducing Admixture:
ASTM C 494  defines water reducing admixture (WRA) as the admixture which reduces the amount of water required to produce concrete to a desirable consistency. ASTM C 494  describes two basic type of WRA, low range and high range water reducing admixture. Type A and D are low range water reducing admixtures. Both these admixtures provide at least 5% of water redaction when used in concrete, also has some retarding property typical initial setting time varies from 1-3.5 hour . Type F and G are high range water reducing admixtures. High range water reducers provide at least 12% of water reduction and initial setting time varies at a range of 1-3.5 hour . Low range water reducing admixtures are commonly derived form natural organic materials such as sugars and lignins. High range water reducers can be two types, sulfonated melamine or naphthalene-formaldehyde condensates and polycarboxylates. Water reducers works in two ways, dispersion and ionic repulsion. Water reducing admixture helps dispersing cementitious materials by making the cement partials hydrophilic (Figure 2-2) [39, 40]. Dose of this water reducing admixture can be adjusted to obtain desired range of water reduction and setting time.
Not to Scale
Figure 2- : Dispersion mechanism of water reducing admixture. (a) Charged cement particles trapping water. (b) Cement grains are separated by water reducers and releasing the water to be available for hydration. 
hydrateIt is the internal microscopic volume reduction which is
2.4 CHEMICAL Shrinkage:
Chemical shrinkage is a physical property of cementitious materials, results from hydration. When cementitious materials hydrate the absolute volume of the reaction products (e.g. C-S-H gel and CH) is smaller than the volume of the reactants (C3S and water); this microscopic volume reduction is the chemical shrinkage . The chemical shrinkage is proportional to degree of hydration . Researchers  documented that autogenous shrinkage is triggered by chemical shrinkage and autogenpus shrinkage is equal to the external chemical shrinkage until a self-supporting C-S-H skeleton is strong enough to resist the contracting force (i.e. Set time). Generally self supporting C-S-H starts to form within 5-9 hrs depending on the property of the cement (cement composition, fineness) and curing temperature, the rate of autogenous shrinkage slows down dramatically and the shrinkage vs time curve flattens out and separate from the total chemical shrinkage . After the self-supporting skeleton (roughly at time of set) starts to develop, autogenous shrinkage becomes smaller than the chemical shrinkage and the difference between them is the internal contraction pores .
2.4.2 Factors That Influence Chemical Shrinkage:
The cement composition, supplementary cementing materials, curing temperature, water-cement ratio and sample size are the factors that influence the chemical shrinkage of cementitious materials. Chemical shrinkage reduces with the increase of C3S in portland cement, but if mixed with supplementary cementing materials results varies depending on the mineral admixtures . Silica fume accelerate the chemical shrinkage while slag delays it . As the temperature increases, both the hydration and the chemical shrinkage rate increase . The effect of water to cement ratio and sample size on chemical shrinkage varies. At early ages, the chemical shrinkage is independent of the water-cementious material ratio (w/cm) and sample size , but with time the lower the water-cementious material ratio the lower the chemical shrinkage .
2.5 Apparent Activation Energy:
The apparent activation energy (Ea) of concrete characterizes the sensitivity of concrete properties to temperature . The apparent activation energy of the concrete can be determined by either mechanical, calorimetric means, or any other method that measure the degree of cementitious material hydration . The mechanical method is based on mortar cube strength at six ages cured at three different temperatures . To get a more accurate method for calculation of apparent activation energy, Ma et al.  developed an isothermal calorimetry method. This method can be carried out both in isometric and adiabatic condition. The isothermal condition has proven more affective . In 1999 Zhang  proposed another microwave based technique which is also proven effective for apparent activation energy calculation. Despite the accuracy and effectiveness of both the isothermal calorimetry and microwave technique, they both require sophisticated or expensive technology.
The arrhenius equation is commonly used to characterize the temperature sensitivity of the hydration of cementitious materials, which allows for the calculation of Ea . Arrhenious showed that variation of specific rate of reaction with the temperature can be expressed as follows
R = the natural gas constant (8.314 J/mol/K),
T = temperature (K) at which the reaction occurs,
k = the rate of heat evolution (W),
A = the proportionality constant (same units as k), and
Ea = activation energy (J/mol).
This relationship was developed to describe the reaction rate of salts in solution at different temperatures . The Arrhenius equation was developed to describe the temperature sensitivity of single chemical reactions. Cement hydration however is comprised of several simultaneous chemical reactions. The calculated Ea values are therefore related to the average temperature sensitivity of the combined chemical reactions, hence the addition of the word "apparent".
2.5.1 Methods for Apparent Activation Energy Calculation:
There are various methods that have been used to calculate Ea. These methods vary in the physical property measured, applicability, and ease of use. This portion of the literature review documents several methods that have been used to calculate the apparent activation energy of cementitious materials.
184.108.40.206 ASTM C 1074:
ASTM C 1074  describes how to calculate the activation energy of a cementitious system mortar compressive strength tests. In this method, the mortar strength is measured on 50mm (2 in) mortar cubes at three different temperatures. Compressive strength of a mortar cube at a particular time and temperature is the average of the compressive strength of three cubes. The activation energy is then calculated from the measured strength values.
220.127.116.11 Isothermal Calorimetry:
This method was first proposed by Ma et al.  and further developed by Kada et al . This method is based on the measurement of the cement hydration rate of heat release. As cement hydration is an exothermal reaction, energy is released during the reaction in the form of heat. As the rate of heat released is a function of the rate of hydration, a measure of the cement degree of hydration can be calculated at any time t by measuring the total amount of heat generated till that time. The amount of energy released is measured using a heat flux sensor (usually a peltier sensor) to measure the cooling required to keep the channel at a constant temperature. In this method, amount of heat generated by cement hydration is measuredat different isothermal temperatures. Ea can be calculated from the total heat of hydration and calculation techniques will be discussed later.
18.104.22.168 Setting time:
Calculation of Ea from the setting time was first proposed by Pinto and Hover in 1998 . Initial and final setting is measured at different temperatures to calculate Ea. This method was further validated by García et al.  by using simpler technique. The assumption used is that the initial and final sets are reached after certain level of microstructure develops for any mix, in other word after a certain degree of hydration is achieved. This method follows the same conventional maturity technique that is described in ASTM C1074  where the initial and final set depends on the time and curing temperature.
2.5.2 Calculation Technique
22.214.171.124 Single linear approximation
This method is discussed by Ma et al . This method depends on the first-order approximation of the reaction rate. The reaction rate is calculated using a line fit to the positive slope portion or acceleration region of the isothermal calorimetry plot. This is equivalent to calculating the reaction rate using a first-order differential rate equation . Some researchers have argued that Ea of Portland cement should be dependent on degree of hydration [21,24]. An Ea value that changes with DOH is problematic for practical use in temperature, creep, or strength calculations.
The cementitious system degree of hydration at any time t can be defined as total amount of heat evolved at time t divided by the total amount of heat available to be released based on the cementitious material composition, as shown in the equation (2) [21,24, 30,33,34].
= the degree of hydration at time t,
H(t) = the heat evolved from time 0 to time t (J/gram), and
Hu = total heat available for reaction (J/gram).
The value of degree of hydration varies from 0 to 1, where 0 means no hydration and 1 means complete hydration.
The value Hu is a function of cement composition and amount and type of supplementary cementing materials (SCMs) and may be calculated as follows .
Pslag = slag to total cementitious content mass ratio,
PFA = fly ash to total cementitious content mass ratio,
PFA-CaO = fly ash CaO to total fly ash content mass ratio,
Pcem = cement to total cementitious content mass ratio, and
Hcem =available heat of hydration of the cement (J/gram).
The value Hcem can be calculated as shown in Eq. (4) .
Hcem = the total heat of hydration of portland cement (J/gram) at Î± = 1.0, and
Pi = the mass of i-th component to total cement content ratio
Despite of the simplicity of this method, it has some serious drawback which limits the use of this method. The determination of the linear acceleration phase region is subjective to some extent because the selection of the linear portion of the acceleration part of the heat evolution rate is done manually. At low temperature it is very difficult to identify the beginning of acceleration period. Moreover this method is only used for the change in the acceleration portion of the curve and neglects what occurs in the later hydration rate evolution .
126.96.36.199 Incremental calculation
I tis generally agreed upon that the activation energy of cement remains constant between to . After that, there is some debate as to whether or not the activation energy should change. At early ages () the hydration is controlled by reaction rate and in later period () in controlled by diffusion through hydrated layer [21, 24]. The incremental calculation method is used to attempt to describe how Ea changes as the reaction becomes more dominated by other mechanisms such as diffusion, water availability, or space for products to form . The following section will show the mathematical process how Ea is calculated by this method.
A number of researchers [35, 36] have suggested an exponential function to characterize cement hydration based on degree of hydration data. The most commonly used relationship is a three-parameter model defined in Eq. (5)
Î±(te) = the degree of hydration at equivalent age te,
= the hydration time parameter (hours),
= the hydration shape parameter, and
= the ultimate degree of hydration.
Equivalent age te can be calculated from the equation (6) shown below
te(Tr) = equivalent age at reference temperature,
Tr = reference temperature,
Tc = temperature of the concrete; Ea and R are as defined previously
Ea can be determined at any age if the reaction rate at different temperature k(T) can be computed at a constant . An isothermal calorimeter is needed for this method. If P(t) is the power required to maintain the isothermal condition, then the Eq. (7) represent the relation between , k(T), and P(t); and k(T) may be related to change in degree of hydration as follows 
k(T) = the reaction rate J/s,
f(Î±) = the function depending on degree of hydration 1/J,
= the degree of hydration as in Eq. (2), and
= the rate of change of degree of hydration 1/s.
If the total amount of heat available for the reaction of a mixture is Hu, then the change of can be expressed as shown in the equation  below.
Hu = the total heat available for reaction, and
H(t) = the cumulative heat evolved at time t.
If calibration of the calorimeter is perfect, then the reaction rate and power is identical and reaction and power can be related as Eq. (9) .
P(,T) = the power measured for a given , T.
Ea values over a range of can be calculated by this method. By using least square best-fit line Ea can be calculated for any number of temperature. Equation (10) can be used to compute Ea as a continuous function of ï¡ï€®ï€ ï›Error: Reference source not found, 24]
Tn = Isothermal test temperature (different for each test n).
There are several serious limitations of this method. This method is very sensitive to errors in measurement and calculation, measurement bias and precision (especially at low temperatures). The accuracy of u calculated from isothermal calorimetry, which is necessary for the purposes of curve fitting to Eq. (5) is questionable compared to other established methods. Heat evolved after the first few days is neglected in the isothermal test. The incremental method produces a variable Ea, which is not easily quantifiable .
188.8.131.52 ASTM C 1074
This method uses the mortar strength value for Ea calculation. The mortar compressive strength for three different temperatures are measured at different ages. There are three different Ea calculation procedures proposed by ASTM C 1074 to calculate Ea from the mortar strength results . These processes vary only by the technique used to determing the k-value, which is the rate constant. First, one needs to find the time of final set.. By this method a graph obtained by plotting reciprocal of age beyond the final setting in X-axis and reciprocal of strength in Y-axis. To determine the k-value for each temperature the intercept of each line is divided by the slope of each line. Determination of k by the other method suggested by ASTM C 1074 does not need to know the final setting time. Instead, the k-value can be calculated by fitting the following Eq.(11)
S = average cube compressive strengthen at the age t,
t = test age,
Su = limiting strength,
to = age when strength development is assumed to begin, and
k = the rate constant.
A computer program is used to calculate the best-fit value of Su, to, k.
There is other way of calculating k-value. Using strength value of last four test age a plot of reciprocal of strength (Y-axis) versus reciprocal of age (X-axis) has to be generated. Then interception of the Y-axis needs to be determined, where the inverse of the intercept value is the limiting strength Su. The value of Su for each of the three temperatures needs to be determined to compute the value of A, where A can be defined by the following Eq. (12)
where, S and Su are defined earlier.
A plot of A versus age is then made for each curing temperature, where the slope of a best-fit straight line for each curing temperatures is the k-value for that temperature.
After calculating the k-value using any of the methods discussed earlier a plot of natural logarithms of k (Y-axis) versus the inverse of temperature in Kelvin (X-axis) needs to be produced. Ea is calculated by multiplying the negative of the slope of the best-fit straight line by the Universal gas constant R.
184.108.40.206 Modified ASTM C 1074
Modefies ASTM C 1074 method was developed by the researchers [22, 27, 37 ] to calculate Ea from isothermal calorimetry data. This method is very similar to ASTM C 1074 method. One problem with the ASTM C 1074 method is that it does not consider the strength development before the time of set. The three-parameter hydration function does not have that problem and was used for this study .
The relationship between at the reference temperature and test temperature is comparable to the relationship between t and te, as expressed in Eq. (13) 
= chronological age,
Ï„e = the equivalent age by Eq. (5),
f(Tc) = the age conversion factor,
k(Tc) = the reaction rate at temperature of concrete Tc,
k(Tr) = the reaction rate at reference temperature Tr,
= the hydration time parameter at temperature of concrete Tc, and
= the hydration time parameter at reference temperature Tr.
The following equation can be derived from Eq. (1) and (13) to calculate Ea .
where Ea, t, Tr, Tc, and R are as defined previously.
220.127.116.11 Setting Time:
This method considers setting time as a mean of Ea calculation. Both initial and final setting time can be used for Ea calculation in this method. This calculation technique was first described by Pinto and Hover in 1998 . In this method arrhenious plot for setting time need to be drawn. Natural logarithm of the inverse of the setting time in Y-axis and inverse of temperature in Kelvin in X-axis needs to be plotted to obtain arrhenious plot. Ea can be calculated by multiplying the negative value of the slope of the best fitted straight line by the Universal gas constant R.