## 4 Results and Discussions
### Hydraulic Performance  
Figure 5 shows the effective porosity of the seven concrete mixtures. At the age of 28 days, the porosities of concrete containing FA and/or BFS are lower than the control mixture. The addition, the fine particles of FA and BFS causes segmentation of large pores and increases nucleation sites for precipitation of hydration products in cement paste [35]. On the other hand, considering the binary blends, concretes with the same percentage of FA or BFS replacement showed nearly the same effective porosity. With the content increase of FA or BFS, the effective porosity decreased. However, when the replacement rate was 30% (A4, A5, A6, and A7), concretes with ternary blends presented obviously larger effective porosity. This may be caused by the interaction between FA and BFS. On the other hand, the difference of absorption capacity among cement, FA and BFS may also cause the porosity difference, since the published results already verified that the absorption capacity affects the porosity [36; 37]. In this study, the effect of absorption capacity on the effective porosity was beyond the limit of this study, and further study on this point will be conducted in the future.  
Figure 6 gives the permeability coefficients of all concrete mixtures. Similar to effective porosity, FA and BFS both decreased the permeability and as the replacement of FA and BFS increased, the reduction in permeability was larger. Compared to FA, the permeability of concrete containing BFS was lower considering the same replacement content.  
Figure 5: Effective porosity.  
Figure 6: Permeability coefficient.  
As the effective porosity increases, the permeability increases correspondingly [38; 39]. Figure 7 shows the relationship between effective porosity and permeability coefficient. It should be noted that data in Table 3 were also included in Figure 7. From these results it can be concluded that previous concrete samples with higher average porosity also had a higher permeability. [PERSON], et al. [1] set up an exponential equation to represent the relationship between porosity and the permeability coefficient. However, permeability of a pervious concrete is also affected by many other factors, such as the pore structure, et al. In this study, an exponential equation was generated to present the relationship between the permeability coefficient and effective porosity. Besides, although the addition of FA and/or BFS decreased the permeability and porosity, the permeability coefficient and effective porosity were still in the general range [10; 11].  
The presence of pores can adversely affect the material's mechanical properties such as failure strength, elasticity and creep strains [40]. Besides the request in hydraulic performance, pervious concrete also needs to be able to withstand some traffic loads. Quantitatively set up the relationship between porosity and compressive strength of pervious concrete is important in characterizing the concrete behaviors and in the mix design of pervious concrete. Figure 8 shows the relationship between the effective porosity and the compressive strength of pervious concrete in Table 4. It can be clearly observed that as the porosity increased, the compressive strength decreased.  
For simple homogeneous materials, the relationship between porosity and strength can be expressed as the following equation [17]:  
\[S=S_{0}\cdot e^{-kp} \tag{4}\]  
Figure 8: Effective porosity vs. strength.  
Figure 7: Effective porosity vs. permeability.  
where \(S\) is the strength of the material which has a given porosity \(p\); \(S_{0}\) is the intrinsic strength at zero porosity; \(k\) is a constant parameter.  
In this study, regression was conducted using the same procedure. The fitting equation was shown in Figure 8. \(R^{2}=0.976\) shows that the equation could accurately represent the relationship between the porosity and the strength.