On Variants of the Frequency Power Law for the Electromagnetic Characterization of Hydraulic Concrete

Abstract

The objective of this paper is threefold: First, dielectric permittivity measurements on concrete specimens are compared among the different variants of Jonscher's model. Each of these variants considers just a limited number of parameters (two or three), based on certain material-dependent and/or bandwidth-related simplifying assumptions. According to this setup, these variants affect the inherent “universality” of the model by imposing a tradeoff between representativeness and practicality. Such an effect becomes more pronounced for concrete mixtures with high moisture content. Next, we propose a computationally efficient two-step procedure for estimating the four model parameters; this procedure filters the linear parameters that contribute to model deviation from the frequency power law by applying the Kramers-Krönig relations. Only two parameters therefore need to be estimated numerically, whereas the filtered parameters can be estimated in closed form as the solution to a simple linear least-squares problem. All of these variants are applied to an array of concrete mixtures and then evaluated by their goodness of fit. The results obtained demonstrate that accounting for all model parameters via the proposed procedure yields the smallest fitting error, thus enhancing the data interpretation stage. Moreover, a parametric study has been carried out in order to correlate the dispersion parameter <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> present in each variant of Jonscher's model with the physical and hydric characteristics of the concrete mixtures. This procedure has made it possible to derive trends providing information on the conditioning state of the studied media.