the superscript Ј refers to the real part of ε and the superscript ″ refers to the imaginary part of ε. For a static E-field the real The electrical permittivity and conductivity of the bulk soil are a part of the permittivity, εЈ, is usually referred to as dielectric function of the permittivity and conductivity of the pore water. For soil constant. The imaginary part of the permittivity, ε″, represents water contents higher than 0.10 both functions are equal, facilitating in the total energy absorption or energy loss. The energy losses situ conductivity measurements of the pore water. A novel method include dielectric loss, ε ″ d , and loss by ionic conduction is described, based on simultaneous measurements of permittivity and conductivity of the bulk soil from which the conductivity of the pore ε″ ϭ ε″ d ϩ i ε 0 [2] water can be calculated. A prototype of a pore water conductivity sensor based on this method is presented. Validation results show that the method can be used for a broad range of soils and is valid for where i is the specific ionic conductivity of the material, and water contents between 0.10 and saturation and for the conductivity of the radian frequency (rad s Ϫ1). The frequency (Hz) of the the pore water up to 0.3 S m Ϫ1. applied E-field is f ϭ /2. The permittivity for free space is ε 0 ϭ 8.854 ϫ 10 Ϫ12 F m Ϫ1. Let us consider the water that can be extracted from the pores of the soil matrix. The permittivity and conductivity of O ne method of determining the conductivity of the the pore water will be denoted by subscript p. The imaginary pore water of soil, p , is by extracting a sample of part of the complex permittivity of the pore water is ε″ p. In water from the soil matrix. This is a labor-intensive task soil science it is not customary to use ε″ p. It is more practical and not well suited for automation. Additionally, it is to use the conductivity of the pore water, p , which can be not certain that all ions are collected in the extracted defined as sample. Another way is to translate the electrical conductivity of the bulk soil, b , to p using methods, mod

The electrical permittivity of soil is a function of the water content, which facilitates water content measurements. The permittivity of soil is also a function of the frequency of the applied electric field. This frequency dependence can be described by the relationship between the dielectric relaxation frequency and the activation enthalpy of the water, which in turn is related to the soil matric pressure. The activation enthalpy or soil matrix pressure is a measure of the binding forces acting on a water molecule in the soil matrix. Each water molecule is differently bound, varying from tightly bound to free water. The permittivity of the bulk soil results from the contribution of all the water molecules in the soil matrix. Therefore, the permittivity of soil as a function of frequency is related to the soil matrix pressure. It is realistic to consider hygroscopic water as ice like. A relatively sharp transition can be observed from free to hygroscopic water at matric pressure – 100 MPa corresponding to relaxation frequency fr ≈ 8 GHz. Therefore, for the interpretation of dielectric data using a dielectric mixture equation, the water content of soil can be split conveniently in “free” water and “hygroscopic” water.

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A change in the relative proportions of the constituents of a porous material like soil will cause a change in its electrical permittivity. The measured permittivity reflects the impact of the permittivities of the individual material constituents. Numerous dielectric mixture equations are published, but none of these equations are generally applicable. A new theoretical mixture equation is derived, using the principle of superposition of electric (E) fields. This mixture equation relates the measured permittivity to a weighted sum of the permittivities of the individual material constituents and includes depolarization factors to account for electric field refractions at the interfaces of the constituents. The depolarization factors are related to physical properties of the material. Most other mixture equations contain one or more empirical factors. The concept of the depolarization factor is comparable with that of the “shape factor” of particles as described by other authors. A special case of the new mixture equation, for which the depolarization factors equals one (no depolarizations), appeared equal to a mixture equation for fluids derived from using thermodynamics. The new mixture equation is compared with other mixture equations. Comparison of the new mixture equation with measured data for glass beads and fine sand was promising. Concluding, depolarization factors in the new mixture equation relate the microstructural and compositional material properties to the measured bulk permittivity of a material. Although not shown, depolarization factors can be calculated from physical material properties.

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