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.

Physical observations of the transient evolution of the porosity distribution during internal erosion using spatial time domain reflectometry

“…A schematic of the experimental setup is provided in Figure 1. A detailed description of the experimental apparatus (including calibration and validation) has been presented in Bittner et al (2019). A brief summary of the apparatus is presented below, as this paper focusses on the application of the coaxial erosion cell to investigate the mixing process in filtration experiments.…”

“…The third step is the conversion of the dielectric permittivity profile to a porosity profile, n(x), using theoretical mixing equations. Prior studies indicated the applicability of the Lichtenecker-Rother model (Bittner et al, 2017(Bittner et al, , 2019 for saturated glass beads, where the dielectric permittivity of the mixture is computed as the weighted sum of the dielectric permittivity of the water and glass beads by their respective volume fraction:…”

“…Experimental investigations suggested that the shape factor is dependent on the soil structure (Brovelli and Cassiani, 2008) and that it should remain as a fitting parameter. Bittner et al (2019) compared various mixing models and shape factors, and results indicated that a shape factor of a = 2/3 is appropriate. Further details on the inversion technique is provided in Bittner et al (2019).…”

“…Bittner et al (2019) compared various mixing models and shape factors, and results indicated that a shape factor of a = 2/3 is appropriate. Further details on the inversion technique is provided in Bittner et al (2019).…”

“…In addition, spatial TDR has been applied to laboratory experiments to investigate pressure profile measurements (Scheuermann and Huebner, 2008) and moisture content in unsaturated soils (Yan et al, 2021). This paper investigates the application of spatial TDR to determine the onset and progression of the mixing process in filtration experiments based on the measured local porosity distribution using a purposebuilt coaxial cell permeameter (Bittner et al, 2019). Different size ratio of base and filter materials are considered, with a focus on base-filter combinations that meet the continuing erosion criteria by Foster and Fell (2001).…”