Numerical modeling for investigating the physical meaning of the relationship between relative dielectric permittivity and water content of soils

The relative permittivity of soils is related to the volumetric liquid water content by a monotonous and general relationship. Among others, Topp et al. [1980] have proposed a simple empirical function to allow a direct determination of the water content. The moment method is applied here to calculate the apparent permittivity of a given volume of soil resulting from the electrical coupling between its different constituents and to attempt to reproduce the empirical function. This is not possible when considering randomly isotropically distributed elementary volumes of water, solid, and air. To reproduce the empirical function, it is necessary to consider that as the water content increases, the elementary volumes of water become more elongated since the liquid phase is continuous.