## 2 Materials and Methods
### Rheological Tests  
The flowability and the rheological properties of four types of UHPFRC mixtures were evaluated. The flowability, the mini-slump flow, was measured using a mini-slump cone specified in ASTM C 1437 [43], and the rheological properties were obtained by using a rotational rheometer with a vane-type spindle, which was adopted to prevent segregation of the fibers from the cementitious matrix during measurement. Figure 1 shows the rheometer and the protocol of the rheology test. After a 20 second pause, the rotational speed was increased from 0 to 19 rpm (rotation per minute) with an increment of 1.9 rpm every 20 seconds. After reaching the highest rotational speed, it was decreased to zero with the same step and interval. From the rheology test, flow curves, which are expressed as a relation between shear stress (\(\tau\)) and shear rate (\(\dot{\gamma}\)), were obtained. The viscosity (\(\mu\)) and yield stress (\(\tau_{0}\)) were then calculated by a linear regression analysis using the Bingham model (\(\tau=\tau_{0}+\mu\dot{\gamma}\)), which is chosen because it is generally appropriate to characterize the flow behavior of cement-based material [44].  
To estimate the effect of the amount of water reducing admixture on the mechanical performance of UHPFRC, compressive strength and flexural tests were performed. The compressive strength was measured with cylindrical specimens with a diameter of 100 mm and a height of 200 mm according to ASTM C 39 [45]. The flexural test was carried out with \(100\times 100\times 500\) mm\({}^{3}\) beam specimens. When the beam specimens were fabricated, fresh UHPFRC was placed at one end of the form and flowed itself toward the other end, inducing shear flow of the matrix as shown in Figure 2. This consistency in placing is important to avoid variation of the flexural performance according to differences in the  
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline \multirow{2}{*}{**Mixture**} & \multirow{2}{*}{**Cement**} & \multirow{2}{*}{**Silica Fume**} & \multicolumn{6}{c}{**Unit Weight (kg/m\({}^{3}\))**} \\ \cline{4-10}  & & & & & \multicolumn{4}{c}{**Admixtures**} & \multirow{2}{*}{**Anti-Foamer**} & \multirow{2}{*}{**Steel Fiber**} \\ \cline{4-10}  & & & & & & \multicolumn{2}{c}{**WRA\({}^{*}\)**} & & \multicolumn{2}{c}{**EA ***} & \multicolumn{2}{c}{**SRA ***} \\ \hline Mix 1 & & & & & 165 & 30.8 & & & & \\ Mix 2 & 771 & 193 & 231 & 848 & 160 & 46.3 & & & & \\ Mix 3 & 771 & 156 & 61.7 & 57.8 & 7.70 & 1.40 & 156 \\ Mix 4 & & & & 151 & 77.1 & & & & \\ \hline \multicolumn{10}{l}{* WRA: Water reducing admixture; ** EA: Expanding admixture; *** SRA: Shrinkage reducing admixture} \\ \end{tabular}
\end{table}
Table 1: Mix proportion of ultra-high-performance fiber-reinforced concrete (UHPFRC).  
Figure 1: (**a**) Rheometer (Brookfield DV-III ULTRA) and (**b**) rotational speed protocol applied for rheometer test.  
placing method, and consequently to precisely investigate the effect of rheological properties on the flexural performance. All the prepared specimens were cured in air at room temperature for 48 h and demolded. They were then cured in hot water with a temperature of (90 \(\pm\) 3) \({}^{\circ}\)C for 72 h. The specimens were subsequently stored in water with a temperature of (20 \(\pm\) 3) \({}^{\circ}\)C until testing.  
To evaluate the flexural performance, a three-point bending test was conducted with a notch at the midspan of the specimen. The span length for the test was 300 mm. The depth of the notch was 10 mm and the width was 3 mm. A loading rate of 0.3 mm/min was applied for the test. During the test, the crack mouth opening displacement (CMOD) at the notch was measured by a clip gauge and the central deflection was measured using a linear variable differential transducer. Figure 3 shows the three-point bending test set-up with the notched beam.