## 3 Performance Prediction of a Cement-Chemically Inert Quartz Filler Binary Mixture
### 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 \({}^{\circ}\)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 \({}^{\circ}\)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]. 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). \[\alpha=\mathrm{H(t)/H_{max}} \tag{4}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **Water/** & **Quartz/** & **Cement** & **Quartz** & **Water** & **Superplasticizer** \\  & **(Cement + Quartz)** & **(Cement + Quartz)** & **(kg/m\({}^{3}\))** & **(kg/m\({}^{3}\))** & **(kg/m\({}^{3}\))** \\ \hline M1 & 0.5 & 0 & 1223.30 & 0.00 & 611.65 & 0.00 \\ \hline M2 & 0.5 & 10\% & 1092.96 & 121.44 & 607.20 & 0.00 \\ \hline M3 & 0.5 & 20\% & 964.51 & 241.13 & 602.82 & 0.00 \\ \hline M4 & 0.2 & 0 & 1899.15 & 0.00 & 379.83 & 18.99 \\ \hline M5 & 0.2 & 10\% & 1690.01 & 187.78 & 375.56 & 18.78 \\ \hline M6 & 0.2 & 20\% & 1485.52 & 371.38 & 371.38 & 18.57 \\ \hline \end{tabular}
\end{table} 
Table 1: Mixtures of paste specimens [5]. H(t) represents the change in accumulated hydration heat over time, while Hmax 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.