# A New Method to Determine the Steel Fibre Content of Existing Structures--Evaluation and Validation
## 3 Results and Discussion
### Testing of Drilling Core Samples
#### 3.2.3 Estimation of the Fibre Content  
Based on the electrical resistivity, the fibre content of the concrete specimens was calculated with Equation (2). While for the cubic specimens (Section 3.1.2) for a frequency of the alternating current of 1 kHz, the fibre content was tendentially overestimated. For the drilling cores, a massive underestimation can be observed (Figure 14). For the specimens drilled of a plate with a fibre content of 40 kg/m\({}^{3}\), a fibre content of 20.4 kg/m\({}^{3}\) was calculated, which corresponds to 51% of the actual mixed in fibres. Furthermore, for the specimens, with a mixed fibre content of 80 kg/m\({}^{3}\), the difference between the result and expectation is even higher with a calculated fibre content of 28.1 kg/m\({}^{3}\), representing 35% of the expected content. Both values are much too low, which is a result of the too high electrical resistivities of the specimens that were already described in Section 3.2.2 and could not be explained. In comparison to the results of earlier studies of the authors (see [2]) on casted cylindrical specimens, where the fibre content has been overestimated by trend, it seems that the open fibre ends and the cutting process of single fibres through the drilling process is the reason for this behaviour. The presumably best explanation could be the number of truncated fibres that lead to changes in the effective aspect ratio, which is used for the calculations. Truncated fibres thus could be calculated with a different aspect ratio, and so the estimation of the fibre content would be possible again. In this case, for the specimens with a fibre content of 40 kg/m\({}^{3}\), a resulting aspect ratio of 39.9 can be calculated by use of Equation (3), when it is assumed that the fibre content inside the specimens is really 40 kg/m\({}^{3}\). Concerning the fibre diameter of 1 mm, this can be interpreted as an average fibre length of 39.9 mm, which means a huge number of the fibres were cut by the drilling process. For the specimens with a fibre content of 80 kg/m\({}^{3}\), the resulting fibre length to have a correct estimation of the fibre content is even smaller, with approximately 31.4 mm. Therefore, it can be concluded that the fibre length used for Equation (3) has to be adjusted  
Figure 14: Calculated fibre content of the drilling cores as a function of the actually added fibre content. and is a function of the fibre content itself with a decrease of the value by increasing fibre content or decreasing specimen size. As an asymptotic behaviour of this correlation can be assumed, an exponential curve was used to adjust Equation (3) based on the fibre content and the smallest dimension of the specimen. In this case, a factor could be derived from the results of the measurements that can be calculated by Equation (4) and has to be used to calculate the adjusted aspect ratio for Equation (3). \[AR_{ad}=AR*\left(\left(1-\frac{l_{f}}{d_{min}}\right)+\left(\frac{l_{f}}{d_{min} }\right)*V_{f}^{-\Phi*\left(d_{min}-l_{f}\right)}\right) \tag{4}\]  
with: \(AR_{ad}\): adjusted aspect ratio of the fibres  
\(l_{f}\): fibre length in mm  
\(d_{min}\): smallest specimen dimension  
\(V_{f}\): fibre volume, calculated by \(l_{f}\) and \(d_{min}\) in mm\({}^{3}\)  
\(\Phi\): expected fibre volume fraction  
For the use of Equation (4), several parameters of the fibres, such as the fibre reinforced concrete, must be known or alternatively estimated. If there is no documentation of the fibre type and planned fibre content available, a small sample of concrete has to be crushed, and fibres have to be extracted to measure the actual fibre diameter and length. Additionally, the equation has to be used iteratively in combination with Equation (3) and adapted to determine the fibre content. The calculation with the adjusted aspect ratio leads to significantly improved results for the fibre content (see Figure 15).