## 4 Results and Discussions  
### Rheology Test  
Viscosity and shear stress under different shear rates were obtained and are shown in Figures 2 and 3. Viscosities of all cementitious pastes showed the general decreasing trend with the increase of shear rate from 0 to 100 s\({}^{-1}\). However, it can be observed that the viscosity increased in shear rate between 10 and 40 s\({}^{-1}\) for 10% FA-20% BFS, 15% FA-15% BFS and 20% FA-10% BFS. There are two main causes of the humps. First, the initial inadequate mixing in the paste preparation caused the increase of the apparent viscosity. As the shear rate increased, cementitious paste became relatively homogeneous. Second, particle migration may occur in the rheology tests because of the difference in shear gradient [29], which may cause the abnormal change of viscosity in certain range of shear rate. After the shear rate was larger than 80 s\({}^{-1}\), viscosities reached stable values. It can be clearly observed  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **C (kg/m\({}^{3}\))** & **FA (kg/m\({}^{3}\))** & **BFS (kg/m\({}^{3}\))** \\ \hline C & 280 & 0 & 0 \\ A1 & 224 & 56 (20\%) & 0 \\ A2 & 224 & 0 & 56 (20\%) \\ A3 & 196 & 84 (30\%) & 0 \\ A4 & 196 & 0 & 84 (30\%) \\ A5 & 196 & 28 (10\%) & 56 (20\%) \\ A6 & 196 & 56 (20\%) & 28 (10\%) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Mix proportions.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Cement (kg)** & **Compressive Strength (MPa)** & **Effective Porosity (\%)** & **Permeability Coefficient (Cm/s)** \\ \hline
160 & 3.3 & 35.0 & 25.0 \\
210 & 4.5 & 33.3 & 19.1 \\
240 & 5.5 & 30.8 & 11.7 \\
280 & 8.4 & 28.3 & 6.9 \\
320 & 10.6 & 26.3 & 4.5 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Performance of pervious concrete incorporating different amounts of cement.  
that the incorporation of FA significantly increased the apparent viscosity. While the sample with 30% BFS did not show viscosity increase after the shear rate was larger than 40 s\({}^{-1}\).  
Non-Newtonian curves between the shear stress and shear rate as shown in Figure 3 was used to interpret the relationship between shear rate and the shear stress. The curves were fitted using a least square function corresponding to the Bingham model as shown in Equation (2) [30].  
\[\tau=\tau_{0}+\mu_{p}\dot{\gamma} \tag{2}\]  
where \(\tau\) is the shear stress, \(\tau_{0}\) is the yield stress, \(\mu_{p}\) is the plastic viscosity and \(\dot{\gamma}\) is the shear rate. All the pastes showed an essentially linear proportionality between the shear stress and shear rate for the range of shear rates selected. Replicated measurements on three separately prepared samples of cementitious paste indicated coefficients of variation of 16% and 9% for yield stress and plastic viscosity, respectively.  
From Figure 2, it can be observed that the high shear rate reduced the viscosity of all mixtures. At low shear rates (\(<\)40 s\({}^{-1}\)), viscosities of pastes with binary and ternary blends of FA and BFS were larger than the control paste. At large shear rates (\(\geq\)40 s\({}^{-1}\)), paste containing 30% BFS presented the same viscosity as the control mix, while the incorporation of FA significantly increased both the apparent viscosity and shear stress. Research [31] showed that particle size and content of FA significantly affects the rheology behavior of cementitious pastes. It is the particle morphological difference between FA and BFS that led to the different rheology behavior of the six mixtures. A reconciling effect could be found by combining the effects of FA and BFS at all shear rates when the cementitious pastes were made with ternary blends of FA and BFS. In Figure 3, shear rates were plotted along with shear stresses. Linear regression was conducted, and the fitted curves showed all the mixtures belonged to the Bingham model. It can be observed that there was no obvious difference between the control mix and the mix with 30% BFS.  
Figure 3: Shear stress.  
Figure 2: Viscosity.