## 4 Discussion
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]. 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 (Figures 1c,d and 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 (Figures 1c,d and 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 \({}^{\circ}\)C, the early isothermal hydration heat measurement under a 20 \({}^{\circ}\)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 \({}^{\circ}\)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.