## 3 Performance Predictions of Cement-Eggshell Powder Binary System
### Prediction of the Amount of Hydration Products  
Based on the hydration degree of cement, we can predict the amount of chemically bound water and calcium hydroxide produced. Assuming that the chemically bound water is proportional to the hydration degree of cement, the calculation equation of chemically bound water W(t) is as follows [1; 2; 3]:  
\[\text{W(t)}=\text{C}_{0}\,\times\,\alpha\times 0.23 \tag{4}\]  
The coefficient 0.23 in Equation (4) means that when 1 g of cement reacts completely, the mass of chemically bound water produced is 0.23 g. We need to note that the chemically bound water calculated by Equation (4) is based on the unit mass of cement, and the chemically bound water measured experimentally is based on the unit mass of binder. It needs to be transformed to compare with the experimental results. Assuming that the content of calcium hydroxide and cement is proportional, the mass of calcium hydroxide CH(t) is calculated as follows [1; 2]:  
\[\text{CH(t)}=\text{C}_{0}\,\times\,\alpha\times 0.22 \tag{5}\]  
The coefficient 0.22 in Equation (5) means that when 1 g of cement reacts completely, the mass of calcium hydroxide produced is 0.22 g [24]. This 0.22 is specific to the cement we used [24]. For other types of cement, the mass of calcium hydroxide produced per unit mass of cement will be different [25]. Figure 3a shows the calculated results of chemically bound water. Similar to the heat of hydration, chemically bound water is also one of the indicators for measuring the degree of cement hydration. In the early stage, the chemically bound water increases rapidly, and in the later stage, the increase rate of chemically bound water is not obvious. Overall, the calculated results are in good agreement with the experimental results. At the early age of 1 day, the calculated chemically bound water is slightly lower than the experimentally measured chemically bound water. This is because in our simulation, it is assumed that the hydration rates of all cement mineral components C\({}_{3}\)S, C\({}_{2}\)S, C\({}_{3}\)A, and C\({}_{4}\)AF are the same. In fact, compared with other components, the hydration rate of C\({}_{2}\)S is slower. Correspondingly, the chemically bound water generated by C\({}_{2}\)S appears later than the chemically bound water of other components. Therefore, the measured value of chemically bound water is slightly higher than the predicted value of chemically bound water in one day. Figure 3b shows the calculated results of calcium hydroxide. Calcium hydroxide is also a hydration product of cement. Both C\({}_{3}\)S and C\({}_{2}\)S will produce calcium hydroxide when they are hydrated. In one day, the calculated results of calcium hydroxide are also slightly lower than the experimental results. This is also because the calcium hydroxide generated by C\({}_{2}\)S appears later than the calcium hydroxide generated by C\({}_{3}\)S, resulting in  
Figure 2: Long term hydration heat and hydration degree. (**a**) Long term hydration heat for 1 g cement. (**b**) Long term hydration degree. (**c**) Long term hydration heat for 1 g binder. the measured value of calcium hydroxide being slightly higher than the predicted value of calcium hydroxide in one day. Figure 4a,b show the predicted results of chemically bound water and calcium hydroxide for the 7.5% eggshell powder specimen, and Figure 5a,b show the predicted results of chemically bound water and calcium hydroxide for the 15% eggshell powder specimen. From Figure 3a, Figure 4a, and Figure 5a, we can see that at 28 days, for the samples with eggshell powder content of 0%, 7.5%, and 15%, the chemically bound water at 28 days is 0.191, 0.188, and 0.180 g/g binder, respectively. As the eggshell powder content increases from 0 to 15%, the mass of chemically bound water per gram of binder decreases. This is because in the later stage of curing, as the eggshell powder content increases, the dilution effect of the eggshell powder plays a dominant role, reducing the amount of chemically bound water generated.