## 3 Experimental Program
### Compressive and Bending Tests  
The effects of hooked-end fiber geometry and volume fraction on the compressive strength of concrete were evaluated based on compressive tests. For this, three cylindrical specimens for each variable were fabricated with a diameter of 100 mm and a height of 200 mm, as per ASTM C39 [20]. Before testing, the casting surface was polished using a diamond blade to make it flat and minimize the eccentric effect on the compressive strength measured. A uniaxial load was monotonically applied to the specimens using a universal testing machine (UTM), and the maximum load measured from a load cell attached to the machine was used to calculate the compressive strength.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**W/B**} & \multirow{2}{*}{**s/a**} & \multirow{2}{*}{\(G_{\text{max}}\)} & \multicolumn{5}{c}{**Unite Weight [kg/m\({}^{3}\)]**} & \multicolumn{5}{c}{**AE Agent \({}^{\dagger}\)**} & **Steel Fiber \({}^{*}\)** \\
**[\%]** & **[\%]** & **[mm]** & **Water** & **Cement** & **Sand** & **Gravel** & **GGBFS** & **FA** & **[B \(\times\) \%]** & **[\%]** \\ \hline \multirow{2}{*}{35} & \multirow{2}{*}{48} & \multirow{2}{*}{25} & \multirow{2}{*}{165} & \multirow{2}{*}{282} & \multirow{2}{*}{796} & \multirow{2}{*}{859} & \multirow{2}{*}{141} & \multirow{2}{*}{47} & \multirow{2}{*}{1.0} & 0.37 \\  & & & & & & & & & & & 0.60 \\ \hline \multicolumn{10}{|l|}{Note] W/B = water-to-binder ratio, s/a = ratio of amount of fine aggregate and total amount of aggregate, \(G_{\text{max}}\) = maximum gravel size, GGBF5 = ground granulated blast furnace slag, FA = fly ash, and AE agent = air-entraining agent. \({}^{*}\) Steel fiber contents are determined by volume fraction. \({}^{\dagger}\) AE agent is included by weight percentage of total binder.} \\ \end{tabular}
\end{table}
Table 1: Mixture proportions.  
Figure 2: Slump flow test results (3D hooked fiber case): (**a**) \(v_{f}\) of 0.37%, (**b**) \(v_{f}\) of 0.6%, and (**c**) \(v_{f}\) of 1.0%.  
To evaluate the effectiveness of adding hooked-end steel fibers on the flexural behavior of concrete and determining the appropriate fiber volume fractions producing deflection-softening and deflection-hardening SFRCs, three-point bending tests were conducted according to the EN 14651 standard [19]. To achieve this, 150 \(\times\) 150 \(\times\) 550 mm\({}^{3}\) prismatic beams were fabricated and tested with a clear span length of 500 mm. In accordance with the standard, a notch with a depth of 25 mm was provided at the center of the beams before testing, and the crack mouth opening displacement (CMOD) was measured using a clip gauge. The midspan deflection for determining the residual flexural strengths was calculated from Equation (3) [19] as follows:  
\[\delta=0.85\times CMOD+0.4 \tag{3}\]  
where \(\delta\) is the midspan deflection.  
Since the casting surface was relatively rough, we rotated the beams 90\({}^{\circ}\) from the casting surface before testing to minimize the eccentric effect, and a uniaxial load was applied to the beams using the UTM through a displacement control. The applied load was measured from the attached load cell, and the flexural strength was calculated based on the maximum load value using the following equation [21]:  
\[f=\frac{3P_{\text{max}}L}{2b(h-a_{0})^{2}} \tag{4}\]  
where \(P_{\text{max}}\) is the maximum load, \(L\) is the clear span length, \(b\) is the beam width, \(h\) is the beam height, and \(a_{0}\) is the notch depth.