# Pullout Response of Ultra-High-Performance Concrete with Twisted Steel Fibers
## 3 Experimental and Verification
### Comparison between Test and Analytical Solution  
As the experimental data has a certain degree of discreteness, the mean value of each embedment length is compared with the analytical results. To obtain the analytical results of untwisting pullout force \(P_{f}\), the dimension of twisted fiber (i.e., \(a\)=0.265 mm, \(b\)=0.185 mm, \(l_{0}\)=10 mm), the uniaxial tensile yield strength of twisted fiber \(\sigma_{p}\)=2500 MPa, the effective untwisting length \(\Delta l\) from Table 1 are inputted into the Equations (15), (16) and (19).  
Figure 9 shows the comparison between the testing values of the pullout force and the analytical solution. The results are in good agreement. The mean values of the three groups of different embedment lengths are 4.2%, 6.1% and 1.3% higher than the analytical solution. This might because the analytical model neglected the tangential frictional resistance after the debonding between the UHPC matrix and the twisted steel fiber; only the friction on the fiber-fiber interface at the effective untwisting length is considered. The pullout force can reach 200 N, which is generally larger than  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**le/mm**} & \multirow{2}{*}{**ID**} & **Ep** & **Average Pullout** & \multirow{2}{*}{**s1 (mm)**} & \multirow{2}{*}{**s2 (mm)**} & **Untwisting** \\  & & **(N.mm)** & & & & & **Pullout Force (N)** \\ \hline \multirow{6}{*}{15} & Average line & 2873 & 191.5 & 1.26 & 13.24 & 1.76 & 199.1 \\  & T15-1 & 3295 & 219.7 & 1.11 & 13.94 & 1.06 & 229.5 \\  & T15-2 & 2980 & 198.7 & 1.75 & 13.04 & 1.96 & 210.2 \\  & T15-3 & 2461 & 164.1 & 1.41 & 13.63 & 1.37 & 179.7 \\  & T15-4 & 2895 & 193.0 & 1.21 & 13.31 & 1.69 & 201.3 \\  & T15-5 & 2810 & 187.3 & 1.21 & 13.75 & 1.25 & 195.8 \\  & T15-6 & 2539 & 169.3 & 1.37 & 13.51 & 1.49 & 182.1 \\ \hline \multirow{6}{*}{20} & Average line & 3905 & 193.3 & 1.27 & 18.28 & 1.72 & 203.3 \\  & T20-1 & 3476 & 173.8 & 1.54 & 18.65 & 1.35 & 180.1 \\  & T20-2 & 4355 & 217.8 & 1.51 & 18.68 & 1.32 & 223.9 \\  & T20-3 & 3993 & 199.7 & 2.17 & 18.32 & 1.68 & 207.5 \\  & T20-4 & 3763 & 188.2 & 1.21 & 18.25 & 1.75 & 197.7 \\  & T20-5 & 3873 & 193.7 & 1.01 & 18.13 & 1.87 & 201 \\  & T20-6 & 3965 & 198.3 & 1.12 & 18.2 & 1.8 & 207.8 \\ \hline \multirow{6}{*}{25} & Average line & 4582 & 184.4 & 1.22 & 23.35 & 1.65 & 193.0 \\  & T25-1 & 4720 & 188.8 & 1.28 & 23.44 & 1.56 & 198.3 \\ \cline{1-1}  & T25-2 & 4678 & 187.1 & 1.31 & 23.12 & 1.88 & 194.8 \\ \cline{1-1}  & T25-3 & 4494 & 179.8 & 1.33 & 22.61 & 2.39 & 192.1 \\ \cline{1-1}  & T25-4 & 4427 & 177.1 & 1.29 & 23.61 & 1.39 & 184.0 \\ \cline{1-1}  & T25-5 & 4445 & 177.8 & 1.23 & 23.70 & 1.30 & 184.3 \\ \cline{1-1}  & T25-6 & 4738 & 189.1 & 1.25 & 22.47 & 2.53 & 196.6 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Results of single fiber pullout tests his is a table.  
Figure 8: Sketch of calculation method for pullout force.  
the existing studies [13; 14; 17]. This increase may be due to the higher mechanical properties of pure concrete without fibers and the better matrix-fiber interface produced in this study.