Determination of the Porosity Distribution during an Erosion Test Using a Coaxial Line Cell

Abstract

The detection of porosity changes within a soil matrix caused by internal erosion is beneficial for a better understanding of the mechanisms that induce and maintain the erosion process. In this paper, an electromagnetic approach using Spatial Time Domain Reflectometry (STDR) and a transmission line model is proposed for this purpose. An original experimental setup consisting of a coaxial cell which acts as an electromagnetic waveguide was developed. It is connected to a transmitter/receiver device both measuring the transmitted and corresponding reflected electromagnetic pulses at the cell entrance. A gradient optimization method based on a computational model for simulating the wave propagation in a transmission line is applied in order to reconstruct the spatial distribution of the soil dielectric permittivity along the cell based on the measured signals and an inversion algorithm. The spatial distribution of the soil porosity is deduced from the dielectric permittivity profile by physically based mixing rules. Experiments were carried out with glass bead mixtures of known dielectric permittivity profiles and subsequently known spatial porosity distributions to validate and to optimize both, the proposed computational model and the inversion algorithm. Erosion experiments were carried out and porosity profiles determined with satisfying spatial resolution were obtained. The RMSE between measured and physically determined porosities varied among less than 3% to 6%. The measurement rate is sufficient to be able to capture the transient process of erosion in the experiments presented here.