## 4 Discussion
### Relationship between Capillary Water Absorption and the Pore Structure
#### 4.2.2 Pore Volumes and Capillary Water Absorption Coefficients in Different Pore Size Ranges  
The capillary water absorption performance of cement-based materials is closely related to their porosity, and the size and distribution of the pore size also exert important effects on their water absorption characteristics. When characterizing internal pore characteristics, the use of porosity alone does not fully explain the effect of pores on capillary water absorption. Therefore, the porosity and distribution of pores of each size must be considered together. In this study, the relationship between pore volume and capillary water absorption in cement-based materials with different pore size ranges was studied using the method of pore size division described by [PERSON] et al. The pore structure distributions of the samples were determined using the MIP method (effective test range \(\geq\)3 nm). Based on the classification of the pore structure described by [PERSON] et al., the pore size range was further refined, and the pore volumes in different pore size ranges were obtained. The volumes are shown in Figure 11, where the first to third groups are NC-2 specimens with different pore characteristics; the fourth and fifth groups are UHPC-3 and UHPC-4 specimens. It can be seen from Figure 11 that the most pores were in the range of 10-50 nm in diameter for NC-2 specimens and 3-10 nm for UHPC specimens. Figure 10: Relationship between porosity and the most probable pore size. Figure 12 shows the relationship between the pore volume in different pore size ranges and the first-stage capillary water absorption coefficient. The pore volume contents of pore sizes larger than 1000 nm were similar, but the capillary water absorption coefficients of the cement-based material differed, and thus, the pore volume content of the pores larger than 1000 had little effect on the capillary water absorption coefficient of the cement-based material. With the increase in the pore volume in the range of 3-10 nm, the capillary water absorption coefficient tended to decrease, because most of the pores in this range were gel pores, and water did not readily enter these pores during the capillary test. With the increase in pore volume in the range of 10-50 nm, the capillary water absorption coefficient showed an increasing trend. Based on the Menger sponge model [71] and von Koch curve theory [72], we calculated the pore fractal dimension corresponding to each of the five groups of tests by combining the results of MIP. Figure 13 analyzes the relationship between the pore fractal dimension  
Figure 11: Statistical analysis of the pore content in different pore size ranges according to the method of pore size classification described by [PERSON] et al. Figure 12: Relationship between the pore volume and capillary water absorption coefficient in different pore size ranges. and the capillary water absorption coefficient. Figure 13 shows that as the pore fractal dimension increased, the shape of the pore structure of cementitious materials became more complex, and the capillary water absorption coefficient also increased. In addition, with increases in pore volumes in the ranges of 50-100 nm and 100-1000 nm, the capillary water absorption coefficient also showed an increasing trend, indicating that the increase in pore volume in these pore size ranges also led to an increase in the capillary water absorption capacity of cement-based materials. According to the slope of the curve, the pore content of the pore size range of 100-1000 exerted the greatest effect on the capillary water absorption coefficient, indicating that this pore size range had a major effect on capillary water absorption; capillary pores were the main pores that affected capillary water absorption.