# A New Method to Determine the Steel Fibre Content of Existing Structures--Evaluation and Validation
## 2 Materials and Methods
### Modelling of the Current Flow  
To analyse different electrode configurations and different specimens, the LCR measurements, which give the electrical resistance, as a result, have to be further converted into electrical resistivities, which are independent of geometry. As for trivial electrode configurations (two parallel plates of basic setup, see Section 2.2.1) the geometry factors for the conversion of resistance into resistivity can be easily calculated; for the advanced test setup with a more complex structure, FEM modelling of the test setup and the current flow is needed. The software Comsol Multiphysics (version 5.3a, build version 229) enables the generation of a network model and thus the simulation of the current flow between several electrodes in various configurations. For the analysis of the specimens in this study, the model of [2] was used, but because effects of surface pressure of the electrodes and electrical conductivity of the sponge cloths contacts cannot directly be considered, different electrical material parameters for the electrodes have been analysed to find the optimum accordance of the model and the real experiment. The drilling core inside the model was represented by a cylinder with a diameter of 100 mm and a height of 200 mm. The electrical resistance was set to 100 f\(\mathrm{m}\), which fits the experimental data. Similar to the cylindrical frame of the test setup, also in the model, twelve electrodes were added as stainless steel elements with an area of 40 \(\times\) 10 mm\({}^{2}\) and a thickness of 1 mm. The electrodes were placed on three height levels with 20 mm in between each level and angular distances of 90\({}^{\circ}\) as segments of a circle. This  
Figure 3: Cylindrical frame with 12 stainless steel electrodes on three height levels with angular distances of 90\({}^{\circ}\) (**a**) and electrodes with covering and isolation (**b**). way, a good connection of the specimen's surface and the electrode was guaranteed. The grid size of the single elements in the simulation was set to extremely fine because a high accuracy was needed for the simulation of the current flow. For the modelling, the following assumptions have been made: The behaviour of all materials, such as concrete and steel, is presumed as homogeneous and isotropic. Polarization effects on the electrodes have been disregarded because of the use of alternating current. The simplification of homogeneity of the materials, especially the concrete, was conducted to keep the numerical model as easy as possible to reduce computing time and not predictable results based on a presumed inhomogeneity which is not well known. It was decided that the inaccuracy of the model based on this simplification is better to accept than the assumption of any parameters to describe an inhomogeneity of the concrete, especially in the context of unknown fibre distribution and orientation that lead to another inhomogeneity and will not be constant for different specimens with varying fibre content. This FEM model makes it possible to simulate the current flow and the resulting electric current of several configurations and thus calculate the geometry factors of those electrode configurations. For the simulations, the electric potential of the contacted electrodes was set to 0 V respectively 600 mV. Thus, the current flow between a pair of electrodes or a group of electrodes was simulated. The chosen values of 0 V and 600 V at this juncture represented the real experimental setup with the LCR meter, which uses a voltage amplitude of 600 mV rms. The simulations were carried out with two different electrical parameters for the electrodes. First, the electrical conductivity of the electrodes was set to the one of stainless steel with 1.4 \(\times\) 10\({}^{6}\) S/m to represent a perfect connection between concrete and electrodes. In this case, the not contacted electrodes show conduction effects and thus have a great influence on the current flow.