On the variants of Jonscher´s model for the electromagnetic characterization of concrete

The objective of this paper is twofold. Firstly, we carry out a comparison on measurements of the dielectric permittivity of concrete among the different variants of Jonscher´s model found in the literature. Each of these variants considers only a limited number of parameters (two or three) based on certain material-dependent and/or bandwidth-related simplifying assumptions. Hence, they affect the inherent “universality“ of the model by imposing a tradeoff between representability and practicability. This effect becomes more pronounced for concrete mixtures with high moisture content. Secondly, we propose a computationally efficient, two-step procedure for the estimation of the four model parameters. The proposed procedure filters the linear parameters that contribute to the deviation of the model from the frequency power law by employing the Kramers-Krönig relations. Therefore, only two parameters need to be estimated numerically, whereas the filtered parameters are estimated in closed form as the solution of a simple linear least-squares problem. All the variants are applied to various concrete mixtures and evaluated by their goodness of fit. The obtained results show that accounting for the whole parameters of the model via the proposed procedure provides the lowest fitting error, and thus enhances the interpretation of data.