## 3 Performance Prediction of a Cement-Chemically Inert Quartz Filler Binary Mixture
### Analysis of CO\({}_{2}\) Emissions for Unit Volume and Unit Strength  
CO\({}_{2}\) emissions are a crucial indicator for assessing the environmental performance of cement-based materials. The CO\({}_{2}\) emissions for 1 kg of paste components are presented in Table 4 [5]. 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. Using the mixtures listed in Table 1 and the CO\({}_{2}\) emissions provided in Table 4, we can calculate the CO\({}_{2}\) emissions for 1 m\({}^{3}\) of paste. The calculation formula is as follows:  
\[CO_{2V}=\sum_{i=1}^{i=4}\left(CO_{2i}*m_{i}\right) \tag{9}\]  
Here, CO\({}_{2V}\) represents the CO\({}_{2}\) emissions for 1 m\({}^{3}\) of paste, while CO\({}_{2i}\) and M\({}_{i}\) are the CO\({}_{2}\) 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 CO\({}_{2}\) emissions per unit volume of concrete decrease as the amount of quartz powder replacement increases. This is because the CO\({}_{2}\) 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 CO\({}_{2}\) emissions per unit volume of concrete increase due to the greater amount of cementitious materials used. Furthermore, using the CO\({}_{2}\) emissions for 1 m\({}^{3}\) of paste and the 28-day compressive strength of the paste (as shown in Figure 5), we can calculate the CO\({}_{2}\) emissions per 1 MPa of concrete as follows:  
\[CO_{2F}=\frac{CO_{2V}}{F_{\rm C28}} \tag{10}\]  
Here, CO\({}_{2F}\) represents the CO\({}_{2}\) emissions per unit strength, and F\({}_{\rm C28}\) denotes the compressive strength after 28 days. Figure 7a shows that for concrete with a water/binder ratio of 0.50, the CO\({}_{2}\) 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 CO\({}_{2}\) 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 CO\({}_{2}\) 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 \begin{table}
\begin{tabular}{c c c c} \hline
**Cement** & **Quartz Powder** & **Water** & **Superplasticizer** \\ \hline
0.86 & 0.0234 & 0.000196 & 0.944 \\ \hline \end{tabular}
\end{table} 
Table 4: CO\({}_{2}\) emissions of paste components (kg/kg). Figure 6: CO\({}_{2}\) emissions of 1 m\({}^{3}\) paste. (a) CO\({}_{2}\) emissions of 1 m\({}^{3}\) paste with water/binder ratio 0.5. (b) CO\({}_{2}\) emissions of 1 m\({}^{3}\) paste with water/binder ratio 0.2.  
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 \({}^{\circ}\)C. In the hydration model, the effect of temperature on the hydration rate can be considered using the Arrhenius law [17].