## 3 Results and Discussion
### Pore Structures  
Figure 4 shows the results of the porosity analysis. MIP does not accurately represent the overall pore characteristics of a specimen but provides sufficient data for relative comparison [46; 47]. As the substitution ratio of CSAe increased, the number of pores decreased. This tendency was confirmed by the gradual decrease in the peak height of the graphs of G90F0C10 (Figure 4a), G80F0C20 (Figure 4b), and G60F0C30 (Figure 4c). In addition, in the samples with SF substitution, the graph is shifted to the left as a whole, and it can be seen that pores of smaller diameter are formed. In Figure 4, the samples with SF substitution showed a similar tendency; the peak of the graph decreased as the substitution ratio of CSAe increased. The increase in the amount of CSAe increased the production of C\({}_{6}\)A\(\overline{\text{S}}_{3}\)H\({}_{32}\), which changed the pore structure by filling the pore interior. Thus, as more C\({}_{6}\)A\(\overline{\text{S}}_{3}\)H\({}_{32}\) was produced, the number and size of the internal pores decreased. As stated in previous studies, CSA reduces the size and number of pores by the production of C\({}_{6}\)A\(\overline{5}\)\({}_{3}\)H\({}_{32}\)[6; 41; 42; 45; 48]. This is consistent with the pore structure analysis results of the present study. In many studies on SF, the substitution of SF affected pore reduction due to filler effects [49] and pozzolanic reactions [39; 40; 50]. In addition, the use of SF makes the overall shape of the graph smaller and moves to the left, confirming that there is an effect of reducing pores. In Figure 4a, the graph of 10% SF sample (G80F10C10) is shifted to the left more than 5% (G85F5C10) and without-SF (G90F0C10). Similarly, in  
Figure 4: MIP results at 28 d, (**a**) 10% CSAe, (**b**) 20% CSAe, and (**c**) 30% CSAe. Figure 4b,c, 10% SF samples (G70F10C20 and G60F10C30) showed that the graph shifted to the left. This shows the effect of matrix densification according to the substitution of SF. This densification effect can be seen to contribute to the improvement of compressive strength analyzed in Figure 2. In this study, however, no pozzolanic reaction occurred. Therefore, the pore diameter reduction shown in Figure 4 may have been due to the filler effect. Figure 5 shows the total porosity for each sample. CSAe effectively reduces the size of pores by the production of ettringite in the pores. SF also has the effect of filling pores due to the size of the fine particles. Therefore, CSAe and SF can reduce the pore size as a whole. In Figure 5, the total porosity of the 20% CSAe samples was the smallest, followed by those of the 10% CSAe and 30% CSAe samples. When the substitution rate of CSAe was the same, the total porosity decreased, and the volume of pores smaller than 50 nm increased with the substitution rate of SF. This trend was seen in the 10% and 20% CSAe samples. However, the 30% CSAe samples had a significantly higher total porosity than the 20% CSAe samples. This is because the 30% CSAe substitution rate caused cracks on the surface and in the interior due to excessive expansion, thereby reducing the accuracy of the pore analysis results. The results of [PERSON] and [PERSON] [51] revealed that OPC and 30% CSAe cement increase porosity by excessive cracking. The total porosity results in Figure 5 showed similar trends in increasing the total porosity due to cracking at high CSAe substitution rates, as reported by [PERSON] and [PERSON] [51]. Therefore, in the range of the conditions considered in this study, 20% CSAe is the optimum mixing ratio for the improvement of compressive strength and the formation of a dense matrix. A CSAe content of 30% may lead to excessive expansion, which inhibits the densification of the reaction products inside and outside a specimen. C4A3S also reduces workability due to early hydration reactions [33; 52]. The increase in C4A3S accelerates the initial condensation [32], thereby reducing workability, lowering homogeneity, and causing many bubbles to form in the mixture.