# A New Method to Determine the Steel Fibre Content of Existing Structures--Evaluation and Validation
## 3 Results and Discussion
### Tests on Concrete Cubes as Additional Specimens
#### 3.1.2 Estimation of the Fibre Content and Orientation  
Based on these results, it was possible to calculate both the fibre content and the fibre orientation inside of each specimen, whereby it must be said that the electrical resistivity of the PC was averaged to have an ascertained reference value for the calculations. The calculated fibre content of the series of specimens is shown in Figure 6.  
One can see that a higher concrete age results in a slightly higher value for the fibre content, as well as a higher frequency of the alternating current. These effects can be explained by the higher differences of conductivity of the concrete and the fibres in higher age, based on the hydration process and thus the refinement of the pore structure as well as changes in the pore chemistry. The differences in the results for varying frequencies are a result of the missing information for the phase angle of the current, which makes the calculation of the real part of the impedance impossible (see [1,11]). Nevertheless, it is clear to see that the graph of the fibre content versus the inverse of the square root of the frequency can be described by a logarithmic function a \(*\ln(\lambda)+\mathrm{b}\), where the constant \(\mathrm{b}\) can be used as an indicator for the fibre content of the material, where a higher concrete age gives a better coefficient of determination as well as a better fit of the calculated fibre content  
Figure 5: Electrical resistivity of the concrete cubes in different ages. to the expectations based on the composition of the concrete. Therefore, an extrapolation of the graph infinity, which would mean a frequency of 0 Hz or direct current (DC), would lead to the corresponding fibre content of 39.427 kg/m\({}^{3}\) and 86.912 kg/m\({}^{3}\), respectively, for a concrete age of 135 days. For a concrete age of 28 days and a fibre content of 80 kg/m\({}^{3}\), the calculated fibre content would be 76.350 kg/m\({}^{3}\) and significantly lower than after 135 days. For the analysis of existing structures, a positive effect can be seen because the concrete is much older, and the hydration process has been completed. Looking at the results of the single specimens for the fibre content of 80 kg/m\({}^{3}\) shows that specimen 1 must contain a much higher amount of fibres than the other two, and thus leads to an overestimation of the fibre content (see Figure 7). For the other two specimens, the calculated fibre content fits almost perfectly to the fibre content that was mixed in the PC. Even if the extrapolation of the curve to the infinite represents the use of DC, a test setup using DC cannot be recommended because of polarisation effects on the electrodes and thus time-depending results for the measurements. While the frequency of the alternating current, as well as the age of the specimens, showed an influence of the calculated fibre content, for the fibre orientation, both parameters seem to be independent, as it was already occupied in the earlier tests (see [2]). Both the age of the specimen and the frequency of the alternating current led to results for the fibre orientation inside the concrete cubes with no significant variations. For a fibre content of 40 kg/m\({}^{3}\), much more fibres are oriented in the horizontal directions with a proportional distribution of approximately 42% in each of the horizontal directions (see Figure 8). Since the concrete was compacted by a vibration table in a vertical direction, this result was expected. In addition, it can be analysed that there is a higher scatter in the horizontal directions than in the vertical one with fibre orientation coefficients of 35% to 50%. Figure 6: Calculated fibre content of the cubic specimens at varying frequencies of the alternating current depending on the age of the concrete and the actual fibre content of the samples (dotted lines represent the fitted trend lines according to the equations given in the corresponding graph).