## 2 Materials and Methods
### Modelling of Current Flow  
For the comparison of the resulting values of the measurements with the LCR meter, the electrical resistance must be converted to electrical resistivity considering geometry factors, which depend on the current flow. While the electrical resistivity, measured in \(\Omega\)m, is a material-specific parameter and is free of any geometrical influences, the electrical resistance, measured in \(\Omega\), is a measurable value based on a specific configuration of the test setup and the specimen geometry. For trivial electrode configurations, such as two parallel plates, which have been used for the cubic specimens in earlier studies [33], this geometry factor is easy to calculate, but a simulation of the electrical current flow is necessary for more complex configurations. For this purpose, the software Comsol Multiphysics (version 5.3a, build version 229) was used and a grid model of the cylindrical specimens was generated. The model consists of a cylinder with a diameter of 100 mm and a height of 200 mm and represents the concrete specimen. On the surface, there are 12 electrodes at three height levels, 4 on each level, in circular distances of 90\({}^{\circ}\) and with a thickness of 1 mm. Each electrode has an area of 40 \(\times\) 10 mm\({}^{2}\) and is simulated as a segment of a circle to enable optimal connection to the cylinder. In this way, the model can be used for various electrode configurations. The FEM model of the test setup is presented in Figure 3a and the resulting grid model for a 12-electrode configuration can be seen in Figure 3b. The model presented was set up using the following assumption: the concrete and steel domain are considered to show homogeneous and isotropic behaviour and the sponge cloths as well as the polarization behaviour of the steel electrodes can be neglected. The latter is considered to be a valid assumption for the alternating current (AC) measurements using the parameters stated above. With this model, the geometry factors (k) of all applied electrode configurations were determined assuming a specific material resistance for the concrete of 100 \(\Omega\)m and an electric potential of 0 V for one electrode or set of parallel connected electrodes and 600 mV for the second electrode or set of parallel connected electrodes. Those values were chosen for the simulations as near realistic values for the test setup and materials (see Section 2.2). The simulations resulted in a calculated current by Comsol, which enabled the estimation of the geometry factor using Equation (1). The calculated k factors are mentioned in respective areas for each section of the results. \[k=\frac{I*\rho}{U} \tag{1}\]  
with \(k\): the geometry factor in m  
Figure 3: FEM model for cylindrical specimens consisting of a concrete cylinder (grey) and twelve electrodes (40 \(\times\) 10 mm\({}^{2}\)) at three height levels and with angular distances of 90 \({}^{\circ}\)C (blue) (a) and grid model to simulate current flow with an extremely fine grid (b). \(I\): the electric current in A  
\(\rho\): the electrical resistivity (set to 100 \(\Omega\)m)  
\(U\): the electric potential (set to 1 V)  
Since the connection of the MMO grids, embedded in the concrete, illustrate a near optimal connection of electrodes and concrete, the electrical conductivity of the electrodes was set to that of titanium, for MMO, of \(2.5\times 10^{6}\) S/m. The visualisation in Figure 4a shows that unconnected electrodes (at the middle height level) have an impact on the iso-surfaces of the current, which represent locations with identical electric potential, in the case of a good electrical connection between the concrete and the electrodes. The current flow can be supposed to be orthogonal to those iso-surfaces. For the setup with a lower number of embedded electrodes with angular distances of 180\({}^{\circ}\), Figure 4b shows that the iso-surfaces are more parallel in the parts of the specimen where no electrodes are embedded, but less uniformly distributed over the whole specimen.