Prediction of the heat of hydration of fly ash concrete by adiabatic temperature rise test and regression analysis

A huge amount of cement is used all over the world, and cement consumption will continue to increase, driven by a growing global population and a steady demand for infrastructures. However, the contribution of carbon dioxide from the cement manufacturing process to total global emissions is reported to be about 5–7% (Huntzinger and Eatmon, 2009; Malhotra, 2000). In order to reduce carbon dioxide emissions, industrial byproducts such as silica fume, fly ash and blast furnace slag have been extensively investigated and used as supplemental cementitious materials (SCMs) for cement-based materials (Binici et al., 2005; Çelik et al., 2008; Vargas and Lopez, 2018). The known benefits of fly ash, a byproduct of coal combustion (Dirgantara et al., 2017; Malhotra and Mehta, 2002), are improved workability, reduced heat of hydration and thermal cracking of concrete at early ages, and improved mechanical and durability properties of concrete at later ages (Sahmaran and Li, 2009). In order to reduce tensile stresses that can lead to cracking, the maximum temperature of concrete is often limited to 160°F (70°C). ACI PRC-207.1.-21 (ACI, 2002) suggests that temperatures above this limit can be justified when the cementitious materials consist of a certain minimum amount of SCMs.

The heat of hydration of cement has been investigated since the 1960s, and a number of studies have been conducted on the effects of various variables. Mills (1966) derived empirical equations, often referred to as Mills’ equation, which allow prediction of the endpoint of hydration. Tanaka et al. (1995) proposed a method for estimating the adiabatic temperature rise of concrete using blast furnace slag-blended cement based on an experimental study. Schindler and Folliard (2005) proposed a hydration model incorporating the effects of variable properties of cementitious materials, mixture proportions and mechanical and thermal properties of concrete. Ng et al. (2009) developed design charts and formulas for predicting the adiabatic temperature rise, heat generation and degree of hydration of concrete mixtures, based on experimental data of the adiabatic temperature rise of concrete measured using a newly developed semi-adiabatic test method using heat loss compensation. Subasi et al. (2009) proposed a model for predicting the initial hydration heat of cement using the adaptive neuro-fuzzy inference system (ANFIS). Ballim and Graham (2009) proposed a simplified mathematical form of the heat rate curves for cement binders mixed in concrete for use in the design phase of the early age time–temperature profile. Wang et al. (2011) developed a model for simulating hydration of concrete containing fly ash or slag, which considered the reaction of calcium hydroxide produced in cement hydration and the mineral admixture consumed. Riding et al. (2012) developed a model with variables such as material properties, mixture proportions, chemical admixture type and dosage to predict the adiabatic temperature rise characteristics of concrete. For temperature prediction of mass concrete structural elements, Bobko et al. (2015) developed an improved method that combines an empirical method for predicting temperature rise associated with heat of hydration and the Schmidt method, a simplified numerical tool for solving heat transfer problems. Lim et al. (2016) combined a semi-adiabatic temperature rise test with finite element method (FEM) analysis to predict adiabatic temperature rise characteristics. Yu et al. (2023) established a new hydration kinetics model, which is based on a nucleation and growth model, and predicted the temperature development of concrete with a set-controlling admixture based on this model.

Accurate temperature change prediction is required to minimise the temperature gradient, which can cause cracks during curing of mass concrete. The basic data for estimating the temperature distribution inside mass concrete are the adiabatic temperature rise characteristics. Therefore, in this study, adiabatic temperature rise tests for concrete were performed with varying percentages of fly ash replacement and varying ratios of water–cementitious materials (w/cm). In order to propose a predictive model for the heat of hydration of concrete, a regression analysis was performed based on the adiabatic temperature rise test data. This paper aims to propose a model that can predict the heat of hydration of concrete containing fly ash by considering various variables related to concrete mixing.

The ultimate heat of hydration for cementitious materials when completely hydrated can be defined as shown in Equation 1.

where C_c is content of cementitious materials; H_T is ultimate heat of hydration; H_u is total heat of hydration of cementitious materials; h_cem is total heat of hydration of cement; h_FA is total heat of hydration of fly ash; h_slag is total heat of hydration of slag; p_cem is mass of cement to total cementitious content ratio; p_FA is mass of fly ash to total cementitious content ratio; p_slag is mass of slag to total cementitious materials content ratio.

Since the calcium oxide (CaO) content differs depending on the fly ash source, the difference in the heat of hydration of the fly ash can be explained based on the CaO content (Schindler and Folliard, 2005). In general, most Class F fly ash contains less than 15% CaO, whereas Class C fly ash typically contains more than 20% CaO (ACI, 1996). Kishi and Maekawa (1995) recommended a heat of hydration of 209 J/g for fly ash (CaO = 8.8% and SiO₂ = 48.1%). In this study, the total heat of hydration of the fly ash h_FA is determined by Equation 3 (Schindler and Folliard, 2005).

where p_{FA -CaO} is the fly ash CaO weight ratio to total fly ash content.

The total heat of hydration of cement can be determined by Equation 4 (Schindler and Folliard, 2005).

where $pC2S$⁠, $pC3S$⁠, $pC3A$⁠, $pC4AF$⁠, p_MgO, $pSO4$ and p_FreeCaO are the weight ratio of C₂S, C₃S, C₃A, C₄AF, MgO, SO₄ and free CaO to total cement content, respectively.

To estimate the concrete heat of hydration, an empirical model was developed by Schindler and Folliard (2005). The model mathematically expresses that degree of hydration of cement is proportional to the heat released, as shown in Equation 5.

where α(t) is degree of hydration at time t and H(t) is cumulative heat of hydration released at time t.

Data determined from experiments on the degree of hydration development can be represented by a mathematical model, as shown in Equation 6.

where α_u is ultimate degree of hydration; β is a hydration slope parameter; τ is a hydration time parameter.

For α_u, Mills (1966) reported that hydration of most cement pastes stops before the cement is totally consumed. From the research by Mills (1966), an empirical equation that can predict the endpoint of hydration depending on the w/cm ratio was derived, as shown in Equation 7.

Mills’ equation has been used by some researchers to predict the heat generation of concrete.

Based on the experimental results, Ng et al. (2009) developed a new equation by regression analysis, as shown in Equation 8.

Schindler and Folliard (2005) developed the best-fit model delineated in Equations 9–11 by conducting a nonlinear regression analysis based on 352 response variables.

where Blaine is Blaine value, specific surface area of cement (m²/kg); $pSO3$is the weight ratio of SO₃ to total cement content.

As shown in Equations 12–14, Ge (2005) developed a heat of hydration model based on laboratory and literature data. The nonlinear regression method was applied to perform a statistical analysis.

where HI is hydraulic index (proposed by Mantel, 1994).

Riding et al. (2012) developed two models for calculating the heat of hydration of concrete based on a large data set of 204 concrete mixtures tested using semi-adiabatic calorimetry. To develop the heat of hydration model, they performed a nonlinear regression analysis on the calibration data set for each of the cement phase composition analysis methods, either calculated using Rietveld refinement (Rietveld, 1969) of the cement X-ray diffraction pattern or using the Bogue method ASTM C150 (ASTM, 2002). Regardless of Rietveld analysis (Scrivener et al., 2004) or Bogue calculations ASTM C150 (ASTM, 2002), the fit of the regression model to the data used to generate the model showed little difference, such as a coefficient of determination (R²) of 0.994. The models developed based on oxide analysis and Bogue calculations ASTM C150 (ASTM, 2002) are shown in Equations 15–17.

where $pNa2O$ is the weight ratio of Na₂O in cement; $pNa2O+0.658∗K2O$ is the weight ratio of alkalis as sodium oxide equivalent; ACCL is ASTM Type C accelerator; LRWR is ASTM Type A water reducer; MRWR is midrange water reducer; NHRWR is ASTM Type F naphthalene or melamine-based high-range water reducer; PCHRWR is ASTM Type F polycarboxylate-based high-range water reducer; WRRET is ASTM Type B and D water reducer/retarder.

As shown in Table 1, only the model by Riding et al. (2012) considered p_cem for predicting all three parameters α_u, τ and β. Ge (2005), Riding et al. (2012) and Schindler and Folliard (2005) all considered p_FA also for estimating α_u and τ, but only Ge (2005) considered p_FA also for estimating β. Ge (2005), Riding et al. (2012) and Schindler and Folliard (2005) considered p_{FA − CaO} for estimating τ, but Riding et al. (2012) considered p_{FA − CaO} also for estimating α_u. Ge (2005), Riding et al. (2012) and Schindler and Folliard (2005) all used w/cm to predict α_u. Ge (2005) and Schindler and Folliard (2005) used Blaine in their model to estimate τ and β, but Riding et al. (2012) did not use Blaine in their model.

From Equation 5, the cumulative heat of hydration released at time t, H(t) (J/m³), is derived as

Substituting Equation 1 into the previous equation, an equation for predicting H(t) is derived as

The heat capacity of concrete can be calculated using the specific heat capacity and unit weight of each constituent (de Larrard, 1999). The heat capacity of curing concrete can be calculated as shown in Equation 20. For the specific heat capacity of each constituent, values given in studies by de Schutter and Taerwe (1995), Holman (2002) and Bentz et al. (2011) were used.

where A is the unit weight of aggregate in concrete; c is the unit weight of cement in concrete; FA is the unit weight of fly ash in concrete; w is the unit weight of water in concrete; ψ is the heat capacity of curing concrete.

Dividing H(t) in Equation 19 by ψ, the equation for predicting adiabatic temperature rise at time t is derived as follows.

where T(t) is adiabatic temperature rise at time t.

Adiabatic temperature rise tests were performed on 12 different concrete mixtures. Table 2 provides a summary of the concrete mixtures that were tested. A standard ASTM Type I cement was chosen and Class F fly ash was used in this study. The chemical composition and physical properties of the cementitious materials are presented in Table 3.

The adiabatic temperature rise was monitored using a specially designed computer-controlled test set-up, as shown in Figure 1. The fresh concrete sample was placed in a thin-walled cylindrical steel container (150 mm diameter by 150 mm height) and a thermocouple junction was inserted for temperature measurement at the centre of the container. The initial temperatures of the batch materials were measured, and the temperature of the water was varied to achieve the target initial concrete temperature of 20°C. During the test, the activation of the heaters was controlled depending on the temperature difference between the centre and the surroundings of the concrete sample inside the machine. The temperatures were recorded every 10 min, and the test was ended after seven days.

The effect of the percentage of fly ash replacement on the adiabatic temperature rise of concrete was studied at the initial placing temperature of 20°C. The adiabatic temperature rise for different percentages of fly ash and w/cm are shown in Figure 2 and are summarised in Table 4.

The results in Table 4 show that fly ash replacement resulted in a significant reduction of the adiabatic temperature rise. However, as the percentage of fly ash replacement was increased, the reduction in adiabatic temperature rise tended to slow down. As shown in Figure 2, fly ash replacement delays the initial hydration of concrete. The time delay effect is described elsewhere (Fajun et al., 1985) and the replacement of fly ash p_FA is considered for estimating the parameter τ, as shown in Table 1. The initial hydration rate of concrete decreased as the percentage of fly ash replacement increased.

The adiabatic test results show that there was a decrease in the adiabatic temperature rise and the initial hydration rate as w/cm increased. The effect of w/cm on the adiabatic temperature rise has already been identified, and Equation 7 by Mills (1966) applies this effect. Hu et al. (2014) reported that the lower the water-to-cement ratio, the higher the rate of initial heat of hydration after cement–water contact. This effect of w/cm on the initial hydration rate can also be observed in the results of the adiabatic test by Maekawa et al. (1998). However, the effect of w/cm on the initial hydration rate was not considered in the hydration models proposed by other researchers (Ge, 2005; Riding et al., 2012; Schindler and Folliard, 2005), as shown in Table 1. Therefore, the contribution of w/cm to the hydration slope parameter β will be considered in this study.

In this section, a heat of hydration model is developed based on a regression analysis. The model, as shown in Equations 15–17, developed by Riding et al. (2012) based on oxide analysis and Bogue ASTM C150 (ASTM, 2002) calculations, was used as a basis for developing a heat of hydration model in this study.

In this study, the following three steps of analysis were conducted to develop a heat of hydration model. The independent variables were selected by developing linear regression models to predict each of the three degrees of hydration parameters (Equation 6) for all 12 mixtures in this study.

As the first step, a regression analysis was performed on the ultimate degree of hydration α_u using the adiabatic temperature rise test data of concrete mixtures with no fly ash. The ultimate degree of hydration α_u in the adiabatic temperature rise test was obtained from the test data using the following equation.

Next, for concrete mixtures with fly ash, a regression analysis was performed on the hydration time parameter τ using the initial hydration time delay characteristics in the adiabatic temperature rise test data according to the increase in percentage of fly ash replacement.

Finally, a regression analysis was performed on the hydration slope parameter β and, at this time, the effect of w/cm discussed in the ‘Adiabatic temperature rise’ section was additionally considered in predicting the hydration slope parameter.

Prior to developing a heat of hydration model, this study compared the predictions made by models developed by other researchers (Riding et al., 2012; Schindler and Folliard, 2005) with the adiabatic temperature rise test results obtained in this study.

Figure 3 presents a comparison between the degree of hydration measured by the tests conducted in this study and the predicted values from models developed by other researchers. As depicted in the figure, the model developed by Riding et al. (2012) underestimated the test results at the initial degree of hydration (<0.2) and subsequently overestimated the degree of hydration (>0.3) by up to 25%. A similar trend was observed in the model developed by Schindler and Folliard (2005), which overestimated the test results by up to 22%. The graphs include equations for trend lines that depict the correlation between the degree of hydration measured in this study and the predictions made by the models, indicating x and y relationships. The slopes of the trend lines for the models developed by Riding et al. (2012) and Schindler and Folliard (2005) were 1.26 and 1.18, respectively, suggesting that these models may not adequately predict the experimental values obtained in this study.

Therefore, to adequately predict the test results of this study, a regression analysis was conducted using the variables employed in the test and the degree of hydration observed in the test outcomes. This analysis resulted in the derivation of the following Equations 23–25.

Figure 4 shows a comparison between the degree of hydration predicted by the regression analysis conducted in this study and the degree of hydration observed in test results. As indicated in the figure, the slope of the trend line for the model developed from the regression analysis is 1.04, suggesting that the model adequately predicts the experimental values obtained in this research. Although the discrepancy between the values predicted by this model and the experimental data shows a lower error of 15% compared with models proposed by other researchers, it still exhibits a tendency to underestimate the experimental results at the initial degree of hydration (<0.2) and to overestimate them by up to 15% at higher degrees of hydration (>0.3).

Therefore, as indicated by the test results, a regression analysis was performed to include the contribution of the water-to-cementitious materials ratio (w/cm) to the hydration slope parameter β in the heat of hydration model. This analysis led to the derivation of the following equation for β.

Table 5 compares the hydration parameters obtained from the adiabatic test data in this study with those obtained by other researchers. In the model developed by Schindler and Folliard (2005), the effect of the percentage of fly ash replacement on the hydration slope parameter was not considered (Table 1) for predicting the parameter β, and constant β values were obtained for all mixtures. However, in the model developed by Riding et al. (2012) and in this study, the values of three parameters, α_u, τ and β, are different for each mix, and thus it appears that the variables for each mix are properly considered.

Table 6 compares the test and predicted values for the adiabatic temperature rise. As a result of comparing the average values for all concrete mixtures, the model developed in this study as well as the previously proposed models showed high prediction accuracy for the ultimate temperature of the adiabatic temperature rise test.

However, while the model proposed by Schindler and Folliard (2005) and the model proposed by Riding et al. (2012) showed 9% and 6% covariance, respectively, the model developed in this study showed 3.1% covariance. Therefore, it is found that the model developed in this study has high applicability for predicting the heat of hydration of concrete within the experimental variable range of the study.

Figure 5 shows the difference between hydration models for 15% replacement of fly ash concrete depending on whether w/cm is considered in the equation for the parameter β. As shown in Figure 5(a), the experimental hydration rate was well predicted in the LF15 mixture (w/cm = 0.56). However, the hydration rate was underestimated in the MF15 (w/cm = 0.44) and HF15 (w/cm =  0.28) mixtures, and the difference became larger as w/cm was lowered. Considering the effect of w/cm on prediction of the parameter β, the actual hydration rate could be well simulated, as shown in Figure 5(b). Therefore, it was confirmed that it is reasonable to consider the effect of w/cm in predicting the hydration slope parameter β.

Figure 6 shows a scatter plot of degree of hydration values obtained experimentally against predicted values using Equation 23. To verify the proposed hydration model, the test data of Maekawa et al. (1998), which provided an adiabatic temperature rise curve, were additionally included along with the experimental results in this study. Based on an R² value of 0.991, it may be concluded that 99.1% of the experimental variation of the hydration parameters can be explained by the model proposed in this study. The regression analysis conducted in this study resulted in a final model with a trend line slope of 0.99, indicating that the model appropriately predicts the experimental values obtained. Additionally, the discrepancy between the predicted values from this model and the actual experimental results was significantly low, at only 7%, compared with models proposed by other researchers. Furthermore, no tendencies for significant underestimation or overestimation were observed throughout the entire range of the degree of hydration in the adiabatic temperature rise tests.

In this study, adiabatic temperature rise tests for concrete were performed with varying percentages of fly ash replacement and varying ratios of w/cm. Based on the test and regression analysis results, the following conclusions were drawn.

• (a)

  An increase in w/cm was associated with reductions in both the adiabatic temperature rise and the initial hydration rate, while the substitution of fly ash significantly lowered the adiabatic temperature rise and delayed the initial hydration of fly ash-blended cements, with the rate of initial hydration decreasing as the proportion of fly ash increased.

• (b)

  When using models proposed by other researchers, which neglected the effect of w/cm, to predict the degree of hydration observed in the experimental results of this study, a tendency to overestimate or underestimate the test results was observed. Furthermore, considering the slope of the trend line and the range of error in the correlation between values by the models and the tests, it was determined that these models could not adequately predict the test results in this study.

• (c)

  Considering the effect of w/cm in predicting the parameter β, the actual hydration rate can be well simulated. Therefore, it is reasonable to consider the effect of w/cm in predicting the hydration slope parameter β.

• (d)

  It is deemed that the model developed in this study provides a reasonable and accurate representation of the heat of hydration development under different percentages of replacement of fly ash and w/cm.

This work was supported by Chungnam National University, Republic of Korea.

A

unit weight of aggregate in concrete

C_c

content of cementitious materials

c

unit weight of cement in concrete

H_T

ultimate heat of hydration

H(t)

cumulative heat of hydration released at time t

H_u

total heat of hydration of cementitious material

h_cem

total heat of hydration of cement

h_FA

total heat of hydration of fly ash

h_slag

total heat of hydration of slag

$pC2S$

weight ratio of C₂S to total cement content

$pC3S$

weight ratio of C₃S to total cement content

$pC3A$

weight ratio of C₃A to total cement content

$pC4AF$

weight ratio of C₄AF to total cement content

p_cem

mass of cement to total cementitious content ratio

p_FA

mass of fly ash to total cementitious content ratio

p_{FA -CaO}

fly ash CaO weight ratio to total fly ash content

p_FreeCaO

weight ratio of free CaO to total cement content

p_MgO

weight ratio of MgO to total cement content

$pNa2O$

weight ratio of Na₂O in cement

$pNa2O+0.658∗K2O$

weight ratio of alkalis as Na₂O equivalent

$pSO3$

weight ratio of SO₃ to total cement content

$pSO4$

weight ratio of SO₄ to total cement content

p_slag

mass of slag to total cementitious materials content ratio

T(t)

adiabatic temperature rise at time t

w

unit weight of water in concrete

α(t)

degree of hydration at time t

α_u

ultimate degree of hydration

β

hydration slope parameter

τ

hydration time parameter

ψ

heat capacity of curing concrete