## 5 Comparison of Proposed Model with the Three-Parameter Hydration Model [24; 31; 32]  
The hydration model in our recent papers [24; 31; 32] belongs to the three-parameter hydration model. The advantage of the three-parameter hydration model is that the model form is simple and there are only three parameters. These three parameters can be easily regressed from the experimental results.  
Although the three-parameter model has the advantage of simple form, we need to note that the three-parameter model also has disadvantages that cannot be ignored. The most important disadvantage is that when the mix ratio of concrete changes, the values of the input parameters of the three-parameter model need to be regressed. In contrast, the model proposed in this article takes into account the influence of water-binder ratio and eggshell powder substitution. When the mix ratio of concrete changes, there is no need to regress the input parameters. Using Equations (1) and (2) of the hydration model and the relevant input parameters (Table 1), we can automatically calculate the relevant hydration degree.  
Figure 7 shows the parameter analysis of the hydration model proposed in this paper. In the parameter analysis, two water-binder ratios of 0.50 and 0.35 and two eggshell powder replacement amounts of 7.5% and 15% were considered. As shown in Figure 7a-c, the reaction level of cement decreases with the decrease in water-binder ratio. As the replacement amount of eggshell powder increases, the reaction level of cement increases.  
Figure 7d shows the effect of the replacement amount of eggshell powder (7.5% and 15%) and water-binder ratios (0.35 and 0.50) on the relative reaction level of cement. Relative reaction level is defined as follows:  
Relative reaction level = reaction level of cement in the mix containing eggshell powder/reaction level of cement in the mix without eggshell powder  
where the water-binder ratio of the numerator and denominator corresponding to the mix is the same.  
As shown in Figure 7d, the relative reaction level of cement increases with the decrease in the water-binder ratio of concrete. This is because of the dilution effect of eggshell powder. The results in Figure 7d show that compared with a higher water-binder ratio 0.50, in concrete with a lower water-binder ratio 0.35, using eggshell powder as a filler can obviously promote cement hydration, improve cement reaction level, avoid cement waste, and achieve energy-saving effects. The trend of analysis results shown in Figure 7d is consistent with [PERSON]'s experimental results [5].  
It is important to recall again that the results in Figure 7a-d cannot be obtained using the three-parameter model [24; 31; 32] and can only be obtained using the hydration kinetics model proposed in this paper.  
Figure 7: Parameters study of proposed hydration model. (**a**) No eggshell powder, water–binder ratios 0.50 and 0.35. (**b**) A proportion of 7.5% eggshell powder, water–binder ratios 0.50 and 0.35. (**c**) A proportion of 15% eggshell powder, water–binder ratios 0.50 and 0.35. (**d**) Effects of eggshell powder contents and water–binder ratio on relative reaction level of cement.