## 3 Results and Discussion
### Flexural Behavior  
The measured flexural behaviors for each mixture were presented by load-deflection curves, as shown in Figure 8. All mixtures clearly showed deflection hardening behavior until the peak load, which could be obtained only when a proper amount of fibers was added with good dispersion. Each mixture also showed a clear difference in the peak load and corresponding CMOD, and the deviations between specimens with identical mixture proportions were not significant compared to those between mixtures with different mixture proportions. This proves that the placing method adopted in this study provided a consistent fiber distribution and thus eliminates the influence of the placing method on the fiber distribution and the consequent mechanical performance. Therefore, it is possible to compare the pure effect of the rheological properties related to the amount of WRA.  
The flexural test results are summarized in Table 2. The test results were obtained from three specimens for each mixture. The flexural tensile strength was calculated from the following equation.  
\[f_{r}=\frac{3P_{max}L}{2b\mu_{e}^{2}}, \tag{3}\]  
where \(P_{max}\) is the peak load measured in the test, \(L\) and \(b\) are the span length and the width of the beam specimen respectively, and \(h_{e}\) corresponds to the total height minus the notch depth.  
Comparing the flexural strengths and behaviors of Mix 1 to 4, it can be found that the flexural strength and the CMOD at peak load decreased as the amount of WRA increased.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Mixture** & **Peak Load (kN)** & \begin{tabular}{c} **Flexural Strength** \\ **(MPa)** \\ \end{tabular} & \
\begin{tabular}{c} **Deflection at Peak** \\ **Load (mm)** \\ \end{tabular} &
\begin{tabular}{c} **CMOD at Peak** \\ **Load (mm)** \\ \end{tabular} \\ \hline Mix 1 & 81.97 \(\pm\) 2.31 & 45.54 \(\pm\) 1.29 & 0.81 \(\pm\) 0.05 & 0.94 \(\pm\) 0.11 \\ Mix 2 & 71.42 \(\pm\) 0.86 & 39.68 \(\pm\) 0.48 & 0.87 \(\pm\) 0.26 & 0.85 \(\pm\) 0.12 \\ Mix 3 & 67.83 \(\pm\) 2.77 & 37.68 \(\pm\) 1.54 & 0.84 \(\pm\) 0.34 & 0.73 \(\pm\) 0.14 \\ Mix 4 & 57.28 \(\pm\) 1.17 & 31.82 \(\pm\) 0.65 & 0.66 \(\pm\) 0.09 & 0.48 \(\pm\) 0.09 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Flexural test results.  
Figure 7: Comparison of compressive strengths with different mixes.  
When both the flexural strengths and the compressive strengths with different mixtures are compared, Mixes 2-4 present a close relationship between the flexural strength and compressive strength; however, the comparison between Mix 1 and Mix 2 shows discordance in the strength according to the amount of WRA. The flexural strength of Mix 1 was approximately 10% higher than that of Mix 2, whereas the compressive strengths obtained from Mixes 1 and 2 presented little difference with each other. Previous studies reported that the compressive strength of UHPFRC is noticeably not influenced by the fiber distribution characteristics [38; 49; 50; 51]. Its compressive strength is mainly governed by the strength of the matrix. It can be thought that the flexural strength due to the amount of WRA might influence on the fiber distribution, resulting in the difference in the flexural strength, even though there was little difference in the compressive strength.