## 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 Tables 2 and 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,  
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.  
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 [PERSON] and [PERSON] [23] simulated the cumulative hydration heat and hydration heat release rate at different temperatures. [PERSON] et al. [18] and [PERSON] 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 ([PERSON] 2014) [25].