Analysis of Hydration Strength and CO2 Emissions of Cement–Quartz Powder Binary Blends Considering the Effects of Water/Binder Ratios and Quartz Contents

Abstract

Low-carbon design has become increasingly important in the cement and concrete industry. Previous studies have primarily focused on the impact of different types of admixtures on the carbon emissions of concrete while overlooking the influence of the water-to-cementitious materials ratio on concrete carbon emissions. To address this gap, this study aims to investigate the synergistic effects of the water-to-binder ratio and quartz powder dosage on concrete hydration, strength, and carbon emissions and to propose a comprehensive performance prediction model. Our proposed performance prediction model highlights the critical role of the water-to-cementitious materials ratio in low-carbon concrete design. It distinguishes between the dilution and nucleation effects of the quartz filler and evaluates the impact of quartz content (10% and 20%) and water-to-binder ratios (0.5 and 0.2) on the cement hydration rate; consequently, it is able to predict the concrete’s thermal, chemical, mechanical, and environmental properties. The model specifics are as follows: the parameters were determined using hydration heat data from a paste with a water-to-binder ratio of 0.5 over the first 3 days, and the chemically combined water and portlandite production was calculated up to 28 days. The water availability coefficient, derived from hydration product measurements with a ratio of 0.2, shows that lower water-to-binder ratios slow hydration as the coefficient exceeds 1. A linear equation predicts strength development based on the mix ratio and reaction degree. The CO₂ emission analysis shows that when the water/binder ratio is 0.50, with a compressive strength of 1 MPa, the carbon emissions change little with an increase in the quartz powder replacement rate. However, when the water/binder ratio is 0.2, the percentage reductions in CO₂ emissions per unit strength are 11% and 20% for the 10% and 20% quartz powder replacement rates, respectively, compared with the specimen without quartz powder. The model’s regression method is simple, versatile across mix ratios, and capable of predicting hydration heat, product composition, strength, and CO₂ emissions.

1. Introduction

Chemically inert quartz filler, a byproduct of the stone industry, has been increasingly utilized in the production of high-performance and ultra-high-performance concrete in recent years. Replacing a portion of cement with chemically inert quartz filler offers several advantages, such as reduced hydration heat and lower autogenous shrinkage. Additionally, it provides environmental benefits by decreasing the amount of cement needed for production.

Recently, numerous experimental studies have explored the properties of concrete mixed with chemically inert quartz filler. Xiong et al. found that the fluidity of ultra-high-performance concrete could be improved by replacing silica fume with quartz powder [1]. Kathirvel and Murali reported that increasing the quartz content from 20% to 30% resulted in minimal toughness improvement [2]. Yang et al. found that the mechanical strength of ultra-high-performance concrete first increased and then decreased as the dosage of ultrafine quartz powder increased [3]. Tavares et al. observed that quartz filler could lower the hydration heat in cement and concrete [4]. Lin et al. discovered that partially substituting cement with quartz filler caused only a slight reduction in strength in concrete with a low water-to-binder ratio [5].

Compared to the numerous experimental studies described in the above paragraph, the theoretical research on hydration models is relatively limited. A hydration model is a fundamental tool for evaluating the properties of cement and concrete. Many hydration models have been developed for Portland cement [6]; these models calculate the reaction level and predict properties such as strength development, hydration heat, and hydration product formation. However, research on hydration models for blended cement is less common. Some models have been developed for other additives, such as fly ash [7], slag [8], epoxy latex blended cement [9], concrete affected by high temperatures [10], and silica fume [11].

However, these models have limitations. Firstly, although experiments have demonstrated that adding chemically inert quartz filler primarily affects cement hydration through nucleation and dilution, no quantitative methods currently exist to model these effects. Additionally, existing models fail to separate the nucleation and dilution effects of quartz filler [12]. Secondly, most models focus on high-strength or ordinary-strength concrete, where the water-to-binder ratio typically exceeds 0.30. However, newer concrete technologies are developing materials with much lower water-to-binder ratios of around 20%, which are not adequately covered by most of the previous models. Finally, with the growing emphasis on reducing carbon emissions in the cement and concrete industry [13], most studies on low-carbon concrete have concentrated on how the cement substitution rate affects CO₂ reduction. Other factors, such as the impact of the water-to-binder ratio on CO₂ reduction, have been less studied [14].

To address these gaps, this study presents a new model to predict the hydration heat, combined water, portlandite, and strength development in cement and concrete blended with chemically inert quartz filler. This new hydration model applies to a wide range of water-to-binder ratios and varying quartz contents; it separates the nucleation and dilution effects of the quartz filler and emphasizes the influence of the water-to-binder ratio on the design of low-carbon concrete. The author believes that this comprehensive study will support the use of chemically inert quartz filler in the concrete industry, thereby enhancing sustainable development and waste management in society.

2. Hydration Model of Cement–Chemically Inert Quartz Filler Mixture

In the cement–quartz powder binary system, the hydration reaction of cement plays a leading role, and the presence of quartz powder mainly serves to accelerate the hydration reaction of cement.

2.1. Hydration Model of Cement

In our previous study, we developed a hydration model for Portland cement [15]. This model is based on phenomenological principles and simulates the fundamental processes associated with the release of hydration heat, including the initial rapid heat release during the early contact phase, the dormant phase, the boundary reaction phase, and the diffusion-controlled deceleration phase. The equation governing the hydration reaction is as follows:

(1)$\begin{array}{ll}{\displaystyle \frac{d\alpha }{dt}}& ={\displaystyle \frac{3{\rho }_w}{(v+w_g)r_0{\rho }_c}}{\displaystyle \frac{S_w}{S_0}}{\left[{\displaystyle \frac{W0-0.4C0\alpha }{W0}}\right]}^{\mathrm{wr}}\\ & {\displaystyle \frac{1}{(\frac{1}{\raisebox{1ex}{$B$}\!\left/ \!\raisebox{-1ex}{${\alpha }^{1.5}$}\right.+C{\alpha }^3}-\frac{r_0}{D\mathrm{e}0\ln (\frac{1}{\alpha })})+\frac{r_0}{D\mathrm{e}0\ln (\frac{1}{\alpha })}{(1-\alpha )}^{\frac{-1}{3}}+\frac{1}{k_r}{(1-\alpha )}^{\frac{-2}{3}}}}\end{array}$

Here, α represents the degree of reaction, ranging from 0 (indicating no chemical reaction between the water and cement) to 1 (indicating complete chemical reaction between the water and cement). The variable t denotes time, and ρ_w represents the density of water. The term (ν + w_g) stands for the total amount of water consumed during cement hydration, including both chemically combined water, ν (0.25 g/g), and physically bound water, w_g (0.15 g/g); their combined value is 0.4 g/g. The variable r₀ denotes the average particle size of the cement, while ρ_c represents the density of the cement. S_W/S₀ accounts for the reduction in the contact area between the hydration products and capillary water [15]. W0 and C0 denote the mass of water and cement in the mixture, respectively, while (W0 − 0.4C0α) represents the capillary water present during hydration. W0 is the initial amount of capillary water, and the ratio (W0 − 0.4C0α)/W0 indicates the proportion remaining. In concrete with a low water-to-(cement + quartz) ratio, there is a significant reduction in capillary water during the later stages of hydration, making the capillary water content a critical factor in controlling the hydration reaction [15]. In this study, the dilution effect of the chemically inert quartz filler was determined by analyzing its impact on the capillary water content. The index variable wr serves as the water availability coefficient. For concrete with a relatively high water-to-(cement + quartz) ratio, the value of wr is 1, meaning that all the capillary water is available for cement hydration. However, in concrete with a low water-to-(cement + quartz) ratio, the value of wr is greater than 1, indicating that only a portion of the capillary water is available for hydration. The larger the value of wr, the faster the reduction in the hydration rate, leading to a much slower overall hydration process [15].

B, C, De0, and kr are parameters associated with the cement–particle hydration reaction. B corresponds to the initial rapid exothermic phase of the hydration reaction. Parameter C is related to the dormant phase. De0 represents the diffusion phase, where De0ln (1/α) describes the later stage of the hydration reaction. When the degree of reaction α approaches 1, the diffusion rate becomes nearly 0, and the rate of heat release from hydration also approaches 0. This aligns with the experimental values observed for the heat release during cement hydration [10]. The parameter kr is associated with the boundary reaction phase of hydration.

The invariant parameters of the hydration model are the hydration rate parameters B, C, De0, and kr. In our previous study [16], we calculated the chemically bound water for different water/cement ratios (from 0.19 to 0.50) and different curing ages (7 days, 28 days, and 90 days), and the experimental results were in good agreement with the calculated results (as shown in Figure S1). This is because the proposed hydration model considers the effect of capillary water concentration and the contact between hydration products on the hydration rate.

Effect of cement fineness: In Portland cement, as the fineness increases, the reactivity becomes stronger. The increase in fineness means a decrease in the average particle size r0. Equation (1) takes the effect of cement fineness into account through the use of r0.

Effect of cement mineralogical composition: In the different types of Portland cement, the mineral compositions are similar; they are all C₃S, C₂S, C₃A, and C₄AF, but the corresponding mass percentages of these minerals are different. Early-strength cement contains more C₃S and C₃A, and low-heat cement contains more C₂S. In a multi-component hydration model, it is assumed that the individual mineral components of the cement, C₃S, C₂S, C₃A, and C₄AF, hydrate independently. Based on the experimental results of the degree of hydration of each mineral, the reaction rate parameters B, C, De0, and Kr corresponding to each mineral component, C₃S, C₂S, C₃A, and C₄AF, can be calibrated separately. In our previous work [17], the multi-component hydration model was used to consider the effect of cement mineralogical composition.

2.2. Effect of Chemically Inert Quartz Filler on Cement Hydration

According to the tested values of hydration heat [5], after adding chemically inert quartz filler, the hydration heat release rate in the boundary reaction period and the diffusion period of the cement increased significantly. This was mainly due to the nucleation effect of chemically inert quartz filler [18]. By using the tested values of hydration heat, we propose the following formulas (Equations (2) and (3)) to describe the nucleation effect of chemically inert quartz filler:

(2)$k_r’=k_r\left(1+\mathrm{nu}1\ast {\displaystyle \frac{\mathrm{Q}0}{\mathrm{Q}0+\mathrm{C}0}}\right)$

(3)$De0’=De0\left(1+\mathrm{nu}2\ast {\displaystyle \frac{\mathrm{Q}0}{\mathrm{Q}0+\mathrm{C}0}}\right)$

kr′ and De0′ are the reaction parameters for the boundary reaction period and diffusion period, respectively; they take into account the nucleation effect of the chemically inert quartz filler. Q0 represents the initial mass of the chemically inert quartz filler, while Q0/(Q0 + C0) denotes its substitution rate. nu1 and nu2 are the parameters that describe the nucleation effect of the quartz filler during the boundary reaction period and diffusion period, respectively. When the substitution rate of the chemically inert quartz filler is 0 and Q0 = 0, Equations (2) and (3) revert to those for pure Portland cement.

2.3. Summary of the Proposed Hydration Model

In summary, this study takes into account the nucleation and dilution effects of chemically inert quartz filler to calculate the hydration heat release rate and the reaction level. The nucleation effect is addressed using Equations (2) and (3), while the dilution effect is accounted for with the term ${\left[{\displaystyle \frac{W0-0.4C0\alpha }{W0}}\right]}^{\mathrm{wr}}$ in Equation (1). The original cement hydration reaction model was first introduced by Tomosawa [19], with subsequent modifications made by Park [20], Maruyama [21], Wang [15], and others to incorporate additional influencing factors. However, the previous models did not consider the effect of chemically inert quartz filler. This study incorporates the impact of quartz filler, thereby enhancing the applicability of the traditional model. Furthermore, the earlier research primarily focused on cement and concrete with water-to-binder ratios above 0.3. This study extends the application of the hydration model to concrete materials with a water-to-binder ratio of 0.2; this is a ratio commonly used in producing ultra-high-performance concrete. To date, most studies on ultra-high-performance concrete have been experimental [1], with limited theoretical research into hydration. This study aims to fill this gap in the existing literature.

3. Performance Prediction of a Cement–Chemically Inert Quartz Filler Binary Mixture

Using the hydration model of the cement–quartz powder binary system presented in Section 2, various properties of hardening cement-based materials can be predicted, such as hydration heat, hydration products, and compressive strength. Furthermore, by comparing the strength and CO₂ emissions, the carbon emissions per unit strength of different mix ratios can be evaluated.

3.1. Experimental Overview

In our previous research, we performed an experimental study on binary mixtures of chemically inert quartz filler and cement [5]. The substitution rates for the quartz filler were 10% and 20%, and the water-to-(cement + quartz) ratios were 0.5 and 0.2. The average particle size of the cement was 18.73 microns, while the average particle size of the quartz filler was 4.56 microns. The mixture compositions for the specimens are presented in Table 1. For mixtures M1, M2, and M3, the water-to-(cement + quartz) ratio was 0.50, with quartz replacement levels of 0%, 10%, and 20%, respectively. For mixtures M4, M5, and M6, the water-to-(cement + quartz) ratio was 0.20, with quartz replacement levels of 0%, 10%, and 20%, respectively. In M4, M5, and M6, the mass of the superplasticizer was 1% of the total mass of cement and quartz.

The experimental items primarily included isothermal hydration heat at 20 °C, chemically combined water content, portlandite content, and compressive strength [5]. The hydration heat test was conducted from the time of mixing up to 3 days, while the tests for chemically combined water, portlandite content, and compressive strength were performed at 1 day, 3 days, 7 days, and 28 days after mixing [5]. All the specimens were cured under sealed conditions at a temperature of 20 °C. Our previous research mainly focused on the description and analysis of the experimental results [5], whereas this study is primarily concerned with the development of theoretical hydration models.

The isothermal hydration heat experiment shows that in the mixture of cement and chemically inert quartz filler, the cement hydration reaction remains dominant. The presence of the chemically inert quartz filler does not alter the fundamental process of the hydration reaction; however, it does cause the reaction to accelerate. Specifically, the reaction rate increases during the boundary reaction and diffusion periods [5].

3.2. Prediction of the Performance of Chemically Inert Quartz Filler Concrete with a Water/(Cement + Quartz) Ratio of 0.5

The hydration model introduced in the previous section includes a set of parameters. These parameters can be determined from various experimental data, such as accumulated hydration heat or the formation of hydration products. The reaction level can be calculated by taking the ratio of the experimentally measured cumulative hydration heat to the maximum possible hydration heat release, as shown in Equation (4).

α = H(t)/H_max(4)

H(t) represents the change in accumulated hydration heat over time, while H_max denotes the maximum amount of hydration heat that can be released by the cement. This maximum value can be estimated based on the cement’s compound composition or derived from regression using the measured hydration heat data [10]. In this study, we calculated the compound composition of the cement from its chemical composition and determined Hmax to be 480 J/g.

In this model, it is assumed that the production of chemically combined water is directly proportional to the cement’s reaction level, as indicated in Equation (5):

Combined water = C0 ∗ α ∗ w_max/(Q0 + C0)(5)

Here, w_max represents the maximum amount of chemically combined water in 1 g of cement, which can be calculated based on the cement’s compound composition. According to the measured values of chemically combined water [5], the maximum value of wmax for chemically combined water in 1 g of cement is set at 0.21 g/g, which is slightly lower than the typical value of 0.23 g/g. This difference is due to the measurement range of chemically combined water. In our previous work, we assumed that the temperature range for measuring chemically combined water was between 105 °C and 900 °C [5], while the hydration product AFt decomposed at around 65 °C. Therefore, the chemically combined water in AFt is not included in the measurement results.

In this model, it is also assumed that the formation of portlandite content is directly proportional to the cement’s reaction level, as indicated in Equation (6):

CH = C0 ∗ α ∗ CHmax/(Q0 + C0)(6)

Here, CH_max represents the maximum amount of portlandite produced by the hydration of 1 g of cement, which can be determined based on the cement’s compound composition.

Based on the measured values of portlandite, the maximum amount generated by the hydration of 1 g of cement is set to 0.23 g/g [5]. This aligns with the common assumption that when 1 g of cement is fully hydrated, approximately 0.2 to 0.3 g of portlandite is formed [5].

In this study, the experimental results in Section 3.2.1, which are shown in Figure 1a (isothermal hydration heat), are used for the calibration of the model parameters; the rest of the results in Section 3 are used for the validation of the model. After calibration, the parameters of the hydration model based on early-age hydration heat and the hardening properties of the cement-based materials can be evaluated using the hydration degree and the mixtures.

3.2.1. Calibration of Input Parameters of Quartz Powder–Portland Cement Binary Blends

Using the 72 h isothermal hydration heat data of Portland cement (with a water-to-binder ratio of 0.5 and no quartz), we determined the hydration kinetic reaction parameters for Portland cement, as presented in Table 2.

Additionally, using the parameters B, C, De0, and kr from the cement hydration model and the 72 h isothermal hydration heat data of the cement–quartz blends (with a water-to-binder ratio of 0.5 and 20% quartz), we determined the parameters for the nucleation effect of the chemically inert quartz filler during the boundary reaction period (nu1) and the diffusion period (nu2), as shown in Table 3.

Figure 1a presents the calculated and experimental results for the hydration heat at a water-to-(cement + quartz) ratio of 0.5. Within the first 72 h, increasing the amount of chemically inert quartz filler from 10% to 20% does not result in a significant change in the hydration heat. This is primarily because the nucleation effect of the chemically inert quartz filler accelerates the cement hydration reaction and raises the hydration heat, offsetting the reduction caused by dilution. Furthermore, it is observed that in the later stages of the hydration reaction, the cumulative hydration heat decreases as the amount of chemically inert quartz filler increases. This reduction is mainly due to the dilution effect of the quartz filler. In other words, the nucleation effect of the quartz filler is more pronounced in the early stage of hydration, while the dilution effect becomes more significant in the later stage.

3.2.2. Evaluation Properties of Quartz Powder–Portland Cement Binary Blends with a Water/Binder Ratio of 0.5 (Water Availability Coefficient wr = 1.0)

Figure 1b shows the calculated results for the cement reaction level. As the amount of chemically inert quartz filler increases, the reaction level of the cement also increases due to the acceleration of the hydration reaction caused by the nucleation and dilution effects. In Figure 1c,d, these two effects are separated: the solid line represents both the nucleation and the dilution effects, while the dashed line only accounts for the dilution effect. The difference between the two lines illustrates the nucleation effect. It is observed that for cement and concrete with a water-to-(cement + quartz) ratio of 0.5, the difference in the reaction level becomes more pronounced as the amount of chemically inert quartz filler increases from 10% to 20%. This indicates that the nucleation effect of the chemically inert quartz filler becomes more significant as its substitution rate increases.

Figure 1e presents the calculated results for chemically combined water. As the amount of chemically inert quartz filler increases, the quantity of chemically combined water decreases, particularly in the later stages of curing (28 days). This is because the dilution effect of the quartz filler becomes the dominant factor in the later stages of hydration. Figure 1f shows the calculated results for portlandite, which follows a trend similar to that of chemically combined water.

3.3. Performance Prediction of Chemically Inert Quartz Filler Concrete with a Water/(Cement + Quartz) Ratio of 0.2 (Water Availability Coefficient wr = 1.0)

According to the performance prediction model for chemically inert quartz filler concrete with a water-to-(cement + quartz) ratio of 0.5, as discussed in the previous section, the water availability coefficient is set to 1. This assumes that all capillary water is available for the cement hydration reaction. In this section, we maintain the assumption that the water availability coefficient is equal to 1 and examine whether this assumption holds true for chemically inert quartz filler concrete with a water-to-(cement + quartz) ratio of 0.2. The calculated results are shown in Figure 2. As illustrated in Figure 2a, the reaction level increases as the amount of chemically inert quartz filler rises due to the nucleation and dilution effects of the quartz filler. However, when comparing the calculated results with the experimental values for the hydration heat (Figure 2b), chemically combined water (Figure 2c), and portlandite content (Figure 2d), a common pattern emerges: the calculated results are generally higher than the tested values. We believe this discrepancy arises because the assumption that the water availability coefficient is 1.0 is not realistic. In ultra-high-strength concrete with a very low water-to-(cement + quartz) ratio, the consumption of capillary water during hydration reduces the size of the saturated capillary pores [15], which can lower the reaction level. As the proposed model does not account for this factor, the calculated results tend to be overestimated.

3.4. Performance Prediction of Chemically Inert Quartz Filler Concrete with a Water/(Cement + Quartz) Ratio of 0.2 (Water Availability Coefficient wr > 1)

In our previous study, we analyzed the calculated results for chemically combined water in concrete mixed with fly ash and assumed that the water availability coefficient decreased as the water-to-(cement + fly ash) ratio decreased [15]. This specific relationship is expressed in Equation (7):

wr = 2.6 − 4 ∗ W0/(C0 + FA0)          (W0/(C0 + FA0) < 0.4)wr = 1               (W0/(C0 + FA0) ≥ 0.4)(7)

Here, FA0 represents the mass of fly ash. It should be noted that in reference [15], Equation (7) is used to model the hydration of concrete blended with fly ash. However, it is uncertain whether Equation (7) is applicable to the concrete blended with quartz used in this study. To test this assumption, we substitute the mass of quartz filler (Q0) for the mass of fly ash (FA0) in Equation (7).

Figure 3 illustrates the impact of different water availability coefficients on the reaction level. As the water availability coefficient increases from 1.0 to 1.8, the calculated results for the cement reaction level decrease significantly (Figure 3a). The reaction level of the cement also increases as the chemically inert quartz filler substitution amount rises (Figure 3b). Figure 3c,d show the separation of the dilution and nucleation effects: the solid line represents both effects, the dotted line shows only the dilution effect, and the difference between the two lines indicates the nucleation effect. For concrete with a water-to-(cement + quartz) ratio of 0.2, the solid and dashed lines are relatively close, suggesting that the nucleation effect is minimal. In this case, the chemically inert quartz filler primarily acts as a diluting agent. When the water availability coefficient is set to 1.8, the calculated results for the hydration heat more closely match the tested values (Figure 3e). The calculated values for the chemically combined water and portlandite are also more consistent with the experimental data (Figure 3f,g). For concrete with a low water-to-(cement + quartz) ratio of 0.2, the changes in the amounts of chemically combined water and portlandite are minimal when the substitution rate of the chemically inert quartz filler varies from 10% to 20%. Our simulation results successfully reproduce this experimental observation. Additionally, on day one, the tested values are slightly higher than the calculated results. This discrepancy may be because our simulation did not consider the delaying effect of the superplasticizer on the cement hydration reaction [5].

3.5. Prediction of the Compressive Strength

After determining the reaction level, we can use it to estimate the strength development of the cement and concrete. The compressive strength can be represented as a linear function of the cement’s reaction level, as described in Equation (8) [15]:

(8)$f_c(t)=A_1{\displaystyle \frac{C0\alpha }{W0}}-A_2$

Here, f_c represents the compressive strength, and A₁ and A₂ are strength coefficients. Figure 4a illustrates the relationship between strength and ${\displaystyle \frac{C0\alpha }{W0}}$. For different mix ratios and ages, the overall compressive strength is a linear function of ${\displaystyle \frac{C0\alpha }{W0}}$, with a coefficient of determination for the linear regression of 0.77. However, for the specimen with a water-to-(cement + quartz) ratio of 0.2, the one-day strength deviates from the regression curve. When we excluded the one-day strength data for the specimen with a water-to-(cement + quartz) ratio of 0.2 and performed the linear regression again, the coefficient of determination increased to 0.91, which is significantly higher than that shown in Figure 4a.

Figure 5 illustrates the impact of the chemically inert quartz filler content and the water-to-(cement + quartz) ratio on the 28-day strength. In Figure 5a, where the water-to-(cement + quartz) ratio is 0.5, the compressive strength decreases as the substitution amount of chemically inert quartz filler increases from 0 to 20%. In Figure 5b, where the water-to-(cement + quartz) ratio is 0.2, the change in compressive strength is minimal as the substitution amount of chemically inert quartz filler increases from 0 to 20%. This indicates that at a low water-to-(cement + quartz) ratio, replacing cement with chemically inert quartz filler is beneficial. It reduces cement consumption and carbon dioxide emissions without significantly affecting the strength.

3.6. Analysis of CO₂ Emissions for Unit Volume and Unit Strength

CO₂ emissions are a crucial indicator for assessing the environmental performance of cement-based materials. The CO₂ emissions for 1 kg of paste components are presented in Table 4 [5].

Using the mixtures listed in Table 1 and the CO₂ emissions provided in Table 4, we can calculate the CO₂ emissions for 1 m³ of paste. The calculation formula is as follows:

(9)$C{O}_{2V}={\displaystyle \sum _{i=1}^{i=4}(C{O}_{2i}\ast m_i})$

Here, CO_2V represents the CO₂ emissions for 1 m³ of paste, while CO_2i and M_i are the CO₂ emissions and mass of each paste component, respectively. The index i = 1, 2, 3, 4 corresponds to the four components of the paste: cement, quartz powder, water, and superplasticizer. Figure 6a,b show that the CO₂ emissions per unit volume of concrete decrease as the amount of quartz powder replacement increases. This is because the CO₂ emissions per unit mass of quartz powder are significantly lower than those of cement. Additionally, as the water/binder ratio decreases (from Figure 6a to Figure 6b), the CO₂ emissions per unit volume of concrete increase due to the greater amount of cementitious materials used.

Furthermore, using the CO₂ emissions for 1 m³ of paste and the 28-day compressive strength of the paste (as shown in Figure 5), we can calculate the CO₂ emissions per 1 MPa of concrete as follows:

(10)$C{O}_{2F}={\displaystyle \frac{C{O}_{2V}}{F_{C28}}}$

Here, CO_2F represents the CO₂ emissions per unit strength, and F_C28 denotes the compressive strength after 28 days.

Figure 7a shows that for concrete with a water/binder ratio of 0.50, the CO₂ emissions per unit strength do not change significantly with the increase in the quartz powder replacement. In contrast, Figure 7b demonstrates that for concrete with a water/binder ratio of 0.20, the CO₂ emissions per unit strength decrease significantly as the amount of quartz powder replacement increases. When the water/binder ratio is 0.2, the reductions in CO₂ emissions per unit strength are 11% and 20% with the 10% and 20% quartz powder replacement rates, respectively, compared with the specimen without quartz powder. This is primarily because the dilution effect of quartz powder enhances the degree of hydration (as shown in Figure 3b) and strength (Figure 5b), thereby lowering the CO₂ emissions per unit strength.

In this study, the curing temperature of the sample is 20 °C. In the hydration model, the effect of temperature on the hydration rate can be considered using the Arrhenius law [17]. In the strength model, the increase in temperature accelerates the early strength development but reduces the later strength development, which can be investigated by adjusting the gel/space ratio and by taking into account the hydration reaction rate at different curing temperatures, the increase in the solid/volume ratio of the cement during the hydration reaction, and the uniformity of the distribution of hydration products [17]. Our previous work [17] considered the effect of curing temperature on hydration and strength development.

4. Discussion

Section 3 shows the validation of the cement–quartz powder binary hydration model proposed in this study. In this section, the advantages and disadvantages of the proposed hydration model are explained based on a comparison with previous studies.

The strengths and limitations of the proposed model are summarized as follows:

1. Short-Term Data Extrapolation: One significant advantage of the newly proposed hydration model is that its coefficients are derived from the hydration heat observed within the first 72 h (as shown in Figure 1a). The measured values of the 72 h hydration heat are used to predict property development from the start of mixing up to 28 days, such as that of the reaction level (Figure 1b), hydration products (Figure 1e,f), and strength (Figure 4a,b). In other words, the model’s parameters can be obtained from short-term hydration heat experiments (such as those conducted over 3 days), and the results can be extrapolated to longer terms (such as 28 days). This approach is highly beneficial for reducing the number of long-term experiments and the associated costs, especially when scientific research funding is limited. In such cases, reliable theoretical models provide a valuable complement to experimental work [6].

2. Versatility and Applicability: Another notable advantage of the hydration model is its versatility. The model parameters remain unchanged across different mix ratios (as shown in Table 2 and Table 3). This means the model can be used to calculate the results for different mix ratios by using the parameters obtained from a specific mix ratio without adjusting these parameters. In practical concrete engineering, the water-to-(cement + quartz) ratio and the amount of substituted chemically inert quartz filler can vary widely. The proposed model is particularly useful for such scenarios. Moreover, while many hydration models exist, most of the previous ones only considered general-strength or high-strength concrete and rarely addressed ultra-high-performance concrete with a water-to-binder ratio of 0.2 [22]. This study fills that gap.

3. Comparison with previous cement–quartz hydration models: The binary hydration model of the cement–inert admixture proposed by Poppe and Schutter [23] simulated the cumulative hydration heat and hydration heat release rate at different temperatures. Cyr et al. [18] and Lawrence et al. [24] used the equivalent coefficient model to simulate the physical effect of inert fillers and to predict early strength before 2 days. Compared with these published models, this study has a wider range of applications; it is not only applicable to general-strength cement-based materials (water/binder ratio 0.5) but also to ultra-high-strength cement-based materials (water/binder ratio 0.2). This study also covers more research objects and considers all aspects of thermal, mechanical, chemical, and sustainable development.

4. Comparison with the Powers and CEMHYD3D (version 2.0) models: The Powers hydration model is a classic model. Based on the degree of hydration, it calculates the various compositions and property developments of hydration products, including porosity (capillary pores and gel pores), chemically bound water, solid products, gel/space ratio, and compressive strength. The CEMHYD3D model connects the relationship between the microstructure and macroscopic properties of hydration, and it can calculate the composition of the pore solution, the chloride ion diffusion coefficient, and the solid composition of hydration products. The CEMHYD3D model also considers the influence of various mineral admixtures. Compared with CEMHYD3D, the main advantages of the hydration model proposed in this study are as follows: first, the proposed model is applicable to different water/binder ratios, including those of ultra-high-performance concrete (Wang 2014) [25]. At present, the CEMHYD3D model lacks sufficient verification in the field of ultra-high-performance concrete. Secondly, the model proposed in this study is very simple, and it consists of only a few equations; thus, it is suitable for individual researchers to use as each detail of the calculations can be checked. The CEMHYD3D model is a little complex; it is a huge engineering software package that is similar to a black box to some extent. In the absence of specialized training, it is difficult for individual researchers to master all of the calculation details of the CEMHYD3D model. Finally, the model proposed in this study has good portability, and other researchers from various countries have used the equations proposed in this study to simulate various properties of different types of concrete [26].

5. Low-Carbon Concrete Design: Designing low-carbon concrete materials has become an increasingly important research topic. Most of the previous studies have focused on the substitution rate of mineral admixtures while neglecting the impact of the water-to-(cement + quartz) ratio [13]. The model analysis in this study revealed that with the same substitution rate, the strength of concrete with a low water-to-(cement + quartz) ratio does not significantly decrease. In fact, when the substitution rate is low (10%), the strength slightly increases (Figure 5b). This occurs because the dilution effect of the chemically inert quartz filler enhances both the reaction level of the cement and the strength. Thus, this study offers a new perspective on the material design of low-carbon concrete. Additionally, the model focuses on cement and concrete mixed with chemically inert quartz filler, and similar effects might be observed with other mildly reactive filler materials, such as limestone filler [18].

6. Compatibility with Thermodynamic Models: Thermodynamic equilibrium models are increasingly used for analyzing reaction products and predicting the durability of cement and concrete [7]. When using thermodynamic models, the change in the cement reaction level over time is a necessary input factor [6]. The method proposed in this study allows the calculation of the cement reaction level using different water-to-(cement + quartz) ratios and different replacement ratios of chemically inert quartz filler. These results can be used as input parameters in thermodynamic models to analyze the composition and durability of cement and concrete.

7. Decoupling Nucleation and Dilution Effects: When chemically inert quartz filler is added, nucleation and dilution effects are the primary phenomena; this is a conclusion commonly reached by many researchers through experiments [27]. However, the challenge of decoupling these two effects has not been resolved. The model proposed in this study successfully decouples the dilution effect from the nucleation effect (Figure 1c,d and Figure 3c,d), overcoming the limitations of previous models. For concrete with a lower water-to-(cement + quartz) ratio, the dilution effect is predominant (Figure 3c,d), while the nucleation effect becomes more apparent with increasing quartz content (Figure 1c,d and Figure 3c,d).

8. Application range of the proposed model: The model proposed in this study is applicable to binary mixtures of Portland cement and quartz powder and is not applicable to concrete containing reactive mineral admixtures (such as fly ash, slag, and silica fume). With fly ash, because its pozzolanic reaction is very slow at a room temperature of 20 °C, the early isothermal hydration heat measurement under a 20 °C curing temperature is not a good experimental means of observing its reaction. It is necessary to increase the curing temperature to accelerate the reaction of the fly ash. If the curing temperature cannot be changed and is kept as 20 °C, it is necessary to extend the experimental measurement time to observe the pozzolanic reaction of the fly ash, such as by reducing the calcium hydroxide content. Slag is more reactive than fly ash, and the early hydration heat measurement can reflect the slag’s chemical reaction to a certain extent. Silica fume is more reactive than slag, and the early hydration heat measurement can also reflect the silica fume’s chemical reaction to a certain extent. In our previous work, we simulated the chemical reaction of fly ash, slag, and silica fume using a hybrid hydration model [28]. In this study, we focus on the physical effect of quartz powder. In addition, delayed ettringite formation is a durability issue; it is mainly caused by early-age high-temperature curing, which affects the volume stability of late-age concrete. However, delayed ettringite formation is not within the scope of this study.

9. Limitation Regarding Superplasticizers: A notable drawback of this model is that it does not account for the influence of superplasticizers. Various types of water-reducing admixtures are available on the market, and changes in their type and dosage can significantly impact the early reaction level [5]. As with the strength prediction model, there is an error in the model’s strength prediction at the early 1-day time point for concrete with a low water-to-(cement + quartz) ratio of 0.2 (Figure 4a). This discrepancy arises because the model does not consider the effect of the superplasticizer, which is significant at this stage. As the curing age increases, the impact of the superplasticizer on the cement hydration reaction diminishes. Future research should consider the effect of superplasticizers to improve the accuracy of property predictions at the 1-day mark.

5. Conclusions

This study presents a hydration model for a binary mixture of cement and chemically inert quartz filler. The model distinguishes between the dilution and nucleation effects of quartz filler, clarifying how different quartz filler contents (10% and 20%) and water-to-(cement + quartz) ratios (0.5 and 0.2) influence the cement hydration reaction rate.

Model Development and Validation: First, the model parameters for cement hydration and the impact of quartz filler were determined through regression analysis, using the accumulated hydration heat data of a cement slurry with a water-to-(cement + quartz) ratio of 0.5 over the first 3 days. The model was then used to calculate the production of chemically combined water and portlandite from mixing for up to 28 days. The predicted results aligned well with the experimental data. Next, hydration product measurements, including chemically combined water and portlandite, were used to determine the water availability coefficient for cement slurry with a water-to-(cement + quartz) ratio of 0.2. As the water-to-(cement + quartz) ratio decreased, this coefficient exceeded 1, leading to a decline in the hydration rate. Incorporating the water availability coefficient into the model significantly improved prediction accuracy, bringing the results into close agreement with the experimental data. Without this coefficient, the predicted trends remained similar, but the values were generally higher than the measured values.

Strength Prediction: A linear equation was developed to predict strength development based on the mix ratio and reaction level. This equation applied to specimens with varying water-to-(cement + quartz) ratios (0.5 and 0.2), quartz filler contents (0%, 10%, and 20%), and curing ages (1, 3, 7, and 28 days). When the 1-day strength data for concrete with a water-to-(cement + quartz) ratio of 0.2 were excluded, the correlation coefficient between the predicted and tested values was 0.91. However, including the 1-day data reduced this coefficient to 0.77; this was likely due to the model not fully accounting for the influence of superplasticizers on early hydration rates.

CO₂ Emission Analysis: The CO₂ emission analysis revealed that for concrete with a water/binder ratio of 0.5, the CO₂ emissions per unit strength remained relatively unchanged as the quartz powder content increased. However, for concrete with a water/binder ratio of 0.2, the CO₂ emissions per unit strength decreased significantly with the higher quartz powder content. This is because the dilution effect of quartz powder enhances both hydration and strength at a lower water/binder ratio, leading to lower CO₂ emissions per unit strength.

Final remarks: In summary, the proposed hydration model is straightforward, adaptable to various mix ratios, and capable of predicting key properties, such as hydration heat, hydration product content, and strength development. These findings have important engineering implications for the optimization of the use of chemically inert quartz filler in cementitious materials.

6. Future Directions

1. Scaling up from Cement Paste to Concrete: The research in this study focuses on the cement paste level. In the next study, it will be necessary to further scale up to the mortar and concrete level by considering the influence of aggregates. The interfacial transition zone (ITZ) has a higher porosity than the paste matrix part and may become a weak zone in terms of strength and durability. In addition, differential shrinkage is also one of the important issues related to the volume stability of concrete structures, and it needs to be further studied by combining hydration models, strength models, and concrete structure design specifications.

2. Enhancing Durability Assessment: The authors focused on the hydration kinetics, strength, and CO₂ emissions of cement–quartz powder blends without specific durability tests. Future work could include capillary absorption tests to assess durability, addressing the challenges of traditional labor-intensive methods. For this purpose, leveraged automated weight measurement [29] and computer vision techniques [30] for the liquid absorption analysis of construction materials should be used.

3. Long-Term Strength Prediction: This study focused on the strength prediction of cement–quartz powder concrete before 28 days of age. The linear relationship between reaction degree and compressive strength may not hold for all concrete systems, especially for later-age strength gain driven by the continued hydration of unhydrated cement particles. In order to predict the strength at longer ages, other strength prediction models, such as the gel/space ratio model [17], need further study.

4. Comprehensive Sustainability Assessment Beyond CO₂ Emissions: The sustainability analysis focuses primarily on CO₂ emission reduction. For a comprehensive sustainability assessment, other environmental impacts, such as embodied energy, resource depletion, or waste management, require further study. These environmental impacts can be calculated based on concrete mix proportions and life cycle analysis [31].

Author Contributions

B.Y.: writing—original draft, methodology, investigation; X.-Y.W.: data curation, writing—original draft, supervision, funding acquisition. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available from the corresponding author upon reasonable request.

Conflicts of Interest

The authors declare no conflicts of interest.

Nomenclature

α	the reaction degree of cement
t	hydration time
ρw	the density of water
ν	chemically combined water when 1 g cement hydrates
wg	physically bound water when 1 g cement hydrates
ν + wg	total amount of water when 1 g cement hydrates
r0	the average particle size of the cement
ρc	the density of cement
SW	contact area between the hydration products and capillary water at time t
S0	contact area between the hydration products and capillary water at t = 0
SW/S0	the reduction in contact area between the hydration products and capillary water
wr	water availability coefficient
B	reaction rate coefficient of the initial rapid exothermic period
C	reaction rate coefficient of the dormant period
De0	initial reaction rate coefficient of the diffusion period
kr	reaction rate coefficient of the boundary reaction period
De0′	initial reaction rate coefficient considering quartz powder of the diffusion period
kr’	reaction rate coefficient considering quartz powder of the boundary reaction period
Q0	the mass of quartz powder in mixture
C0	the mass of cement in mixture
W0	the mass of water in mixture
nu1	the nucleation effect of the quartz powder during the boundary reaction period
nu2	the nucleation effect of the quartz powder during the diffusion period
Q0/(Q0 + C0)	quartz power replacement rate
H(t)	accumulated hydration heat over time
Hmax	the maximum amount of hydration heat for 1 g cement
wmax	the maximum amount of chemically combined water for 1 g cement
CHmax	the maximum amount of portlandite produced for 1 g cement
FA0	the mass of fly ash
f c	compressive strength
A1 and A2	strength coefficients
CO2V	CO2 emissions for 1 m3 of paste
CO2i	the CO2 emissions of each paste component
Mi	the mass of each paste component
CO2F	the CO2 emissions per unit strength
FC28	the compressive strength after 28 days

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1. Evaluation results of properties of cement–quartz blends (w/b = 0.5, M1, M2, and M3).

Figure 2. Evaluation results of properties of cement–quartz blends. (w/b = 0.2, M4, M5, and M6, water availability coefficient 1.0).

Figure 3. Evaluation results of properties of cement–quartz blends. (w/b = 0.2, M4, M5, and M6, water availability coefficient 1.8).

Figure 3. Evaluation results of properties of cement–quartz blends. (w/b = 0.2, M4, M5, and M6, water availability coefficient 1.8).

Figure 4. Strength evaluation of pastes with various mixes and ages. (a) Strength evaluation considering 1-day strength of water/binder ratio 0.2. (b) Strength evaluation without considering 1-day strength of water/binder ratio 0.2.

Figure 5. Twenty-eight-day strength of paste with water/binder ratios 0.5 and 0.2. (a) Twenty-eight-day strength of paste with water/(cement + quartz) ratio 0.5. (b) Twenty-eight-day strength of paste with water/(cement + quartz) ratio 0.2.

Figure 6. CO2 emissions of 1 m3 paste. (a) CO2 emissions of 1 m3 paste with water/binder ratio 0.5. (b) CO2 emissions of 1 m3 paste with water/binder ratio 0.2.

Figure 7. CO2 emissions of 1 MPa paste. (a) CO2 emissions of 1 MPa paste with water/binder ratio 0.5. (b) CO2 emissions of 1 MPa paste with water/binder ratio 0.2.

Table 1

Mixtures of paste specimens [5].

	Water/(Cement + Quartz)	Quartz/(Cement + Quartz)	Cement (kg/m3)	Quartz Powder (kg/m3)	Water(kg/m3)	Superplasticizer (kg/m3)
M1	0.5	0	1223.30	0.00	611.65	0.00
M2	0.5	10%	1092.96	121.44	607.20	0.00
M3	0.5	20%	964.51	241.13	602.82	0.00
M4	0.2	0	1899.15	0.00	379.83	18.99
M5	0.2	10%	1690.01	187.78	375.56	18.78
M6	0.2	20%	1485.52	371.38	371.38	18.57

Table 2

Reaction parameters of the Portland cement hydration model.

B(cm/h)	C(cm/h)	De0(cm2/h)	Kr(cm/h)
2 × 10−9	0.004	1.05 × 10−10	1.55 × 10−5

Table 3

Nucleation effect parameters of chemically inert quartz filler.

nu1	nu2
4	4

Table 4

CO₂ emissions of paste components (kg/kg).

Cement	Quartz Powder	Water	Superplasticizer
0.86	0.0234	0.000196	0.944

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/app15041923/s1, Figure S1: Chemically bound water contents for plain cement.

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