Full-wave modeling of the time domain reflectometry signal in wetted sandy soils using a random microstructure discretization: Comparison with experiments

Time domain reflectometry (TDR) is a proven, nondestructive method for the measurement of the permittivity and electrical conductivity of soils, using electromagnetic (EM) waves. Standard interpretation of TDR data leads to the estimation of the soil's equivalent electromagnetic properties since the wavelengths associated with the source signal are considerably greater than the microstructure of the soil. The aforementioned approximation tends to hide an important issue: the influence of the microstructure and phase configuration in the generation of a polarized electric field, which is complicated because of the presence of numerous length scales. In this paper, the influence of the microstructural distribution of each phase on the TDR signal has been studied. We propose a two-step EM modeling technique at a microscale range (200 mu m): first, we define an equivalent grain including a thin shell of free water, and second, we solve Maxwell's equations over the discretized, statistically distributed triphasic porous medium. Modeling of the TDR probe with the soil sample was performed using a three-dimensional finite difference time domain scheme. The effectiveness of this hybrid homogenization approach is tested on unsaturated Nemours sand with narrow granulometric fractions. The comparisons made between numerical and experimental results are promising, despite significant assumptions concerning (1) the TDR probe head and the coaxial cable and (2) the assumed effective medium theory homogenization associated with the electromagnetic processes arising locally between the liquid and solid phases at the grain scale.