## 4 Discussion
### Relationship between Capillary Water Absorption and the Pore Structure  
#### 4.2.1 Porosities and Capillary Water Absorption Coefficients  
The capillary water absorption capacity of cement-based materials is related to their internal microstructure. By analyzing the literature [4; 37; 38; 42; 46; 66; 67] and test results, the capillary water absorption coefficient, \(S_{1}\), of cement-based materials with different porosities was obtained. Figure 9 analyses the relationship between the porosity of the cement-based material and the capillary water absorption coefficient. As the porosity of the cement-based material increased, its capillary water absorption coefficient showed an increasing trend. The specific trend between the capillary absorption coefficient and the porosity of cement-based materials is shown in Equation (7) (correlation coefficient R\({}^{2}\) = 0.766). Here, the porosity is defined as the percentage of the pore volume inside the cement-based material relative to the total volume of the material, which largely characterizes the compactness of the cement-based material. When the porosity of the cement-based material was less than the critical value of 12.87%, its capillary water absorption coefficient increased slowly as the porosity increased. When the internal porosity of the cement-based material exceeded the critical value, the capillary water absorption coefficient increased rapidly as the porosity continued to increase. Figure 9: Relationship between porosity and \(S_{1}\). The capillary water absorption coefficient of cement-based materials exhibited two stages with the change in its internal porosity, indicating that the internal microstructure of cement-based materials fundamentally changed when the porosity exceeded a certain characteristic value. The most probable pore size corresponds to the peak value in the pore size differential curve obtained from MIP measurements, i.e., the most likely pore size according to the pore size distribution. Therefore, the most probable pore size may accurately characterize the change in the internal microstructure of cement-based materials with changes in porosity. \[\left\{ \begin{array}{l}S_{\text{P}}=3.045\lambda_{\text{P}}+25.937,\lambda_{ \text{P}}\leq 12.87\%\\ S_{\text{P}}=51.0(\lambda_{\text{P}}-12.87)+65.13,\lambda_{\text{P}}>12.87\% \end{array} \right., \tag{7}\]  
where \(S_{\text{P}}\) is the first-stage capillary water absorption coefficient of materials with different porosities \(S_{1}\) (\(10^{-4}\) mm\(\cdot\)s\({}^{-1/2}\)), and \(\lambda_{\text{P}}\) is the porosity. Many scholars have studied the classification of pore sizes in cement-based materials. At present, three common cement stone pore classification methods are mainly used, as shown in Table 7. [PERSON] classified pore sizes according to their effects on the performance of cement-based materials, while the two other methods classified pores according to their type. The classification method reported by [PERSON] et al. is the most common method used in current research. Therefore, this paper applies the method reported by [PERSON] et al. to analyze the relationship between the porosity of cement-based materials and the most probable pore size. The results are shown in Figure 10.  
With the continuous increase in the porosity of the cement-based material, the most probable pore size of the cement-based material showed an increasing trend. When the porosity of the cement-based material was less than 11.43%, the most probable pore size was in the range of the gel pores. When the porosity exceeded 11.43%, the most probable pore size of the cement-based material transitioned from gel pores to capillary pores; thus, as the porosity of the cement-based material decreased, its internal pore structure was continuously refined. This result also explains why the capillary water absorption coefficient of the cement-based material exhibited a two-stage property with increasing porosity.