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.
Highlights
The main characteristic of internal erosion is the transient dislodgement and transport of fine particles in the soil matrix or at interfaces of different soil layers causing changes in porosity and density
The local differences in the porosity of water saturated glass beads cause a local change in the dielectric permittivity, which affects the propagation of the electromagnetic waves along the coaxial dielectric permittivity, which affects the propagation of the electromagnetic waves along the coaxial cell cell and alters the reflection coefficient measured at the cell input
Apart from these minor issues, the proposed electromagnetic measurement technique, which combines the use of a coaxial cell and a forward transmission line model combined with an appropriate inversion approach, has shown its ability to determine porosity profiles for stationary states and for relatively fast changing porosity changes in erosion tests
Summary
The main characteristic of internal erosion is the transient dislodgement and transport of fine particles in the soil matrix or at interfaces of different soil layers causing changes in porosity and density. One possibility is the determination of the rate of the washed out fine fraction [4,5] The weight of this fraction collected downstream of the soil sample was recorded for a given time period and hydraulic boundary condition. Another possibility consists in measurement techniques based on the interaction of electromagnetic fields with the surrounding material Such approaches take advantage of the dipolar character of water molecules resulting in high electric permittivity in comparison to other phases such as solid and gas. The term STDR (Spatial TDR) was created for his method The latter approach has been successfully applied for the measurement of water content distributions in river dikes [22] as well as the determination of porosity profiles of samples with a rod probe [23].
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