## 4 Experimental Investigation
### Investigation Results
#### 4.2.2 Cyclic Loading  
The test results of the cyclic loaded pullout tests (fibre group pullout tests) were evaluated in an S/N-diagram with related load amplitude and number of cycles to failure. The load amplitude is related to the maximum pullout resistance in Table 2, and no distinction is made with respect to the embedded length. Figure 4 shows the respective S/N-diagram of the pull-out tests. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Series** & **Amount** & \begin{tabular}{c} **Aimed Embedded** \\ **Length** \(l_{\epsilon}\) \\ \end{tabular} & \begin{tabular}{c} **Orientation** \\ **Angle** \(\alpha\) \\ \end{tabular} & \begin{tabular}{c} **Measured Embedded** \\ **Length** \(l_{\epsilon,\epsilon}\) \\ \end{tabular} & \
\begin{tabular}{c} **Tensile Stress/** \\ **Fibre** \(\sigma_{\rm st}^{\rm f}\) \\ \end{tabular} &
\begin{tabular}{c} **Utilisation Rate** \\ \(\eta=\sigma_{\rm st}^{\rm f}\)/\(l_{\rm st}^{\rm f}\) \\ \end{tabular} \\ \hline
[-] & [-] & [mm] & [\({}^{\circ}\)] & [mm] & [\({\rm N/mm^{2}}\)] & [-] \\ VES30-1 & 3 & 3.25 & 30 & 3.11 \(\pm\) 0.61 & 940.1 \(\pm\) 528.1 & 0.26 \\ VES30-2 & 3 & 6.50 & 30 & 6.87 \(\pm\) 0.79 & 1329.5 \(\pm\) 459.1 & 0.37 \\ VES60-1 & 4 & 3.25 & 60 & 2.88 \(\pm\) 0.11 & 958.8 \(\pm\) 65.02 & 0.27 \\ VES60-2 & 3 & 6.50 & 60 & 5.55 \(\pm\) 1.02 & 1226.6 \(\pm\) 176.9 & 0.34 \\ VES90-1 & 6 & 3.25 & 90 & 3.51 \(\pm\) 0.45 & 710.0 \(\pm\) 151.0 & 0.20 \\ VES90-2 & 6 & 6.50 & 90 & 6.60 \(\pm\) 0.17 & 1374.1 \(\pm\) 285.7 & 0.38 \\ VMS30-1 & 3 & 3.25 & 30 & 4.20 \(\pm\) 0.43 & 375.7 \(\pm\) 19.68 & 0.11 \\ VMS30-2 & 3 & 6.50 & 30 & 6.71 \(\pm\) 0.50 & 1046.5 \(\pm\) 48.4 & 0.29 \\ VMS45-1 & 3 & 3.25 & 45 & 3.33 \(\pm\) 0.35 & 998.0 \(\pm\) 135.8 & 0.28 \\ VMS45-2 & 3 & 6.50 & 45 & 6.81 \(\pm\) 0.63 & 953.6 \(\pm\) 151.9 & 0.27 \\ VMS60-1 & 3 & 3.25 & 60 & 3.14 \(\pm\) 0.33 & 501.9 \(\pm\) 87.0 & 0.14 \\ VMS60-2 & 3 & 6.50 & 60 & 8.15 \(\pm\) 0.36 & 1184.3 \(\pm\) 33.4 & 0.33 \\ VMS75-1 & 3 & 3.25 & 75 & 3.36 \(\pm\) 0.12 & 798.9 \(\pm\) 52.0 & 0.22 \\ VMS75-2 & 3 & 6.50 & 75 & 6.72 \(\pm\) 0.41 & 890.1 \(\pm\) 68.4 & 0.25 \\ VMS90-1 & 3 & 3.25 & 90 & 3.65 \(\pm\) 0.38 & 575.8 \(\pm\) 51.9 & 0.16 \\ VMS90-2 & 3 & 6.50 & 90 & 6.72 \(\pm\) 0.41 & 1197.9 \(\pm\) 65.2 & 0.33 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Test results, calculated tensile stresses and utilisation rate in relation to the fibre strength. Figure 3: Calculated utilisation rate of pulled out fibres in UHPC under quasi-static loading and mean value. Figure 4 shows that the fatigue resistance of fibres embedded in UHPC depends significantly on the orientation angle. For each orientation studied, an S/N-line was established using a regression formula given in Equation (2). Detailed background information can be found in [19]. \[\Delta\sigma_{\text{st}}^{\text{f}}=(0.07\cdot\ln[\alpha]-0.34)\cdot\ln N-(0.28 \cdot\ln[\alpha]-2.05) \tag{2}\]  
It can be recorded that the higher the inclination angle of the fibre with respect to the loading direction, the lower the fatigue resistance. The inclination of the fibre also determines the failure mechanism under cyclic loading. Hence, 30\({}^{\circ}\) and 45\({}^{\circ}\) inclined fibres predominantly exhibit a fibre rupture failure, while 75\({}^{\circ}\) and 90\({}^{\circ}\) inclined fibres tend to exhibit the bond zone failure. For 60\({}^{\circ}\) inclined fibres, both failure mechanisms occur with approximately equal frequency. Fibre rupture also occurs more frequently at a high embedded depth of approximately 6.50 mm (\(=l_{\text{f}}/2\)). The reasons for this can be seen in the intensity of the damage to the fibre material, which is caused on the one hand by the orientation and on the other hand by the movement of the fibre as a result of the cyclic loading. As shown in Figure 5, on the left side of the fibre, the load-induced \"straightening\" is pressing the fibre to the wall of the fibre channel. Due to the cyclic loading, friction occurs between the concrete channel and the fibre material.