## 5 Fibre Groups Embedded in UHPC
### Monotonic Tensile Loading  
As part of the evaluation, the general relationship \(\sigma=F/(n\cdot A)\) coverts the measured loads \(F\) into tensile stresses \(\sigma_{\text{st}}^{t}\), with \(n\) being the number of fibres (here nine). The calculation of the cross-sectional area \(A\) considers a fibre diameter of \(\varnothing_{t}=0.19\) mm (see Section 4.2). Each test series comprises at least three individual tests to gather possible scatter. Figure 8 shows the pullout curves of fibre groups with an orientation of 30\({}^{\circ}\), 60\({}^{\circ}\), and 90\({}^{\circ}\) under monotonic loading (mean values = mv). The highest pullout resistance for an embedded length of 6.50 mm (\(l_{t}/2\)) is approximately 1175 N/mm\({}^{2}\), which equals to nearly one-third of the tensile strength. All other pullout resistances show lower values. Additionally, the pullout resistance for an embedded length of 3.25 mm (\(l_{t}/4\)) does not correspond proportionally to 50% of the pullout resistance for an embedded length of 6.50 mm; the relation is approximately 40%. Due to the low utilization of the tensile strength of the fibre, there was always a systematic fibre pullout, i.e., no steel fibre broke. The pullout tests of the steel fibres orientated at 60\({}^{\circ}\) and 90\({}^{\circ}\) with an embedded length of 6.50 mm showed the typical course of a standardized bond test of conventional reinforcement, i.e., they reached the maximum pullout resistance relatively quickly and then dropped almost linearly. Many contributions ([11, 16, 20, 21]) observed similar phenomena but only for 90\({}^{\circ}\)-orientated fibres. The pullout curve of steel fibres with an orientation of 30\({}^{\circ}\) shows a different course of the curve than the standardized bond tests. The maximum pullout resistance occurs at a higher relative displacement between the fibre and the UHPC (black dashed lines in Figure 8). The fibre bending effects might control the relation of the highest pullout resistance and relative displacement. These bending effects occur at the exit point of the concrete canal and need some relative displacement for activation. Low fibre orientation angles (e.g., 30\({}^{\circ}\)) result in higher bending effects than high angles of orientation (dashed line in Figure 8). Figure 9 visualizes the context of the bending effects at the exit point of the inclined fibres. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Name** & **Number** & **Orientation \(\alpha\)** & **Length \(l_{e}\)** & **Max. Pullout** & **Displacement \(\delta\) at** & **Load Changes** & **Failure Mode** \\  & & & & **Resistance \(\sigma_{\text{st,max}}^{t}\)** & **Max. \(\sigma_{\text{st,max}}^{t}\)** & **\(N_{\text{um}}\)** & \\ \hline VMZ60-1 & 3 & 60\({}^{\circ}\) & 3.25 & - & - & 88\({}^{\pm 19}\) & Pullout \\ \hline VMZ60-2 & 3 & & 6.50 & - & - & 848\({}^{\pm 422}\) & Pullout/Rupture \\ \hline VMZ90-1 & 3 & & 3.25 & - & - & 455\({}^{\pm 399}\) & Pullout \\ \hline VMZ90-2 & 3 & & 6.50 & - & - & 373\({}^{\pm 12}\) & Pullout \\ \hline \hline \end{tabular}
\end{table} 
Table 6: \(Cont.\)  
Figure 8: Pullout behaviour (tensile stress displacement curves) of steel fibre from UHPC under monotonic loading for an embedded length of \(l_{t}/4\) (**a**) and \(l_{t}/2\) (**b**). Besides the bending effects of the fibre, a concrete breakout occurred at the exit of the UHPC canal. A visual investigation showed that the concrete breakout area got bigger with lower fibre orientation angles. The combination of the fibre inclination and uniaxial load caused a constriction of the fibre into the concrete canal. Compression stresses emerged between the fibre and the concrete, and caused concrete spalling at the exit point. This phenomenon refers to \"snubbing\" [22] and has been observed on the fractured surfaces of uniaxial UHPFRC tensile tests [12; 23]. The snubbing effect was visualised by digital microscopy images, as shown in Figure 10, and the concrete breakout areas were measured with MountainsMap.