## 5 Fibre Groups Embedded in UHPC  
### Test Specim and Test Programme  
The test specimens VM (fibre-group-pullout-tests, Figure 7) consisted of two plain UHPC cubes with nine oriented fibres located in between [15; 16; 17]. The concrete age of all tests was at least 28 days and the cylinder compressive strength reached more than 150 N/mm\({}^{2}\). The components of the used UHPC are listed in Table 5. \begin{table}
\begin{tabular}{c c} \hline
**Components** & **UHPC-1017** \\ \hline
[-] & [kg/m\({}^{3}\)] \\ Cement CEM I & 795.0 \\ Silica fume & 168.6 \\ Superplasticiser & 24.1 \\ Quartz powder & 198.4 \\ Quartz sand 0.125/0.5 mm & 971.0 \\ Water & 189.9 \\ \hline \end{tabular}
\end{table} 
Table 5: Mix proportions of the used plain UHPC-1017. The production of the test specimens needed two casting steps. First, nine steel fibres with a diameter of \(\varnothing_{\text{f}}=0.19\) mm and a length of \(l_{\text{f}}=13.0\) mm were put with a 1 cm \(\times\) 1 cm grid in a polystyrene cube, so that half (or 3/4) of the fibre was in the cube and the other half (resp. 1/4) was \"on the air\". A template ensured the desired orientation \(\alpha\) and embedded length \(l_{\text{e}}\) of the fibres. Afterwards, the polystyrene cube with the aligned steel fibres was placed in a formwork. Then, the concreting of the first half of the test specimen followed. After one day of hardening, the polystyrene cube was removed. Subsequently, the second concreting was carried out. A foil between the UHPC cubes prevented transmission of tensile forces between the concrete. Bonded steel plates with threaded holes ensured load transmission between the testing machine and the specimen. The experimental programme of the pullout tests contained a variation of the fibre orientation between \(\alpha\approx 30^{\circ}\), \(60^{\circ}\), and \(90^{\circ}\) as well as different embedded lengths of \(l_{\text{e}}\approx 6.50\) mm (\(l_{\text{f}}/2\)) and \(l_{\text{e}}\approx 3.25\) mm (\(l_{\text{f}}/4\)). The displacement transducer of the testing machine measured the displacement of the two UHPC cubes and the so-called \"crack mouth opening displacement\". A comparative measurement between the transducer and an optical laser in preliminary tests confirmed its accuracy. The loading velocity was 0.01 mm/s (cf. Section 4.2) for the monotonic tests. The load amplitude of the cyclic tests oscillated between 10% and 70% of the maximum pullout resistance of the monotonic tests. The test frequency of the cyclic tests varied between 0.5 and 1 Hz. Table 6 shows the test programme including typical results. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Name**} & \multicolumn{1}{c}{**Number**} & \multicolumn{1}{c}{**Orientation \(\alpha\)**} & \multicolumn{1}{c}{**Length \(l_{\text{e}}\)**} & \multicolumn{1}{c}{**Max. Pullout**} & \multicolumn{1}{c}{**Displacement \(\delta\) at**} & \multicolumn{1}{c}{**Load Changes**} & \multicolumn{1}{c}{**Failure Mode**} \\ \hline \multicolumn{1}{c}{[-]} & \multicolumn{1}{c}{[No.]} & \multicolumn{1}{c}{[\({}^{\circ}\)]} & \multicolumn{1}{c}{[mm]} & \multicolumn{1}{c}{[N/mm\({}^{2}\)]} & \multicolumn{1}{c}{[mm]} & \multicolumn{1}{c}{[No.]} & \multicolumn{1}{c}{[-]} \\ \hline VMS30-1 & 3 & \multirow{3}{*}{30\({}^{\circ}\)} & 3.25 & 376.9\({}^{\pm 41.2}\) & 1.46 & - & Pullout \\ \cline{3-6} VMS30-2 & 3 & & 6.50 & 993.6\({}^{\pm 66.6}\) & 2.28 & - & Pullout \\ \cline{3-6} VMS60-1 & 3 & & 3.25 & 480.7\({}^{\pm 71.0}\) & 0,63 & - & Pullout \\ \cline{3-6} VMS60-2 & 3 & & 6.50 & 1176.3\({}^{\pm 26.7}\) & 0.60 & - & Pullout \\ \cline{3-6} VMS90-1 & 3 & & 3.25 & 568.7\({}^{\pm 42.4}\) & 0.45 & - & Pullout \\ \cline{3-6} VMS90-2 & 3 & & 6.50 & 1159.1\({}^{\pm 53.3}\) & 0.50 & - & Pullout \\ \cline{3-6} VML230-1 & 3 & & 30\({}^{\circ}\) & 3.25 & - & - & 158\({}^{\pm 116}\) & Pullout \\ \cline{3-6} VML230-2 & 3 & & 6.50 & - & - & 250\({}^{\pm 42}\) & Pullout \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Experimental programme and test results of the monotonic and cyclic loaded pullout tests.