A NUMERICAL-ANALYSIS OF THE EFFECTS OF COATINGS AND GAPS UPON RELATIVE DIELECTRIC PERMITTIVITY MEASUREMENT WITH TIME-DOMAIN REFLECTOMETRY

Fluid-filled gaps or dielectric coatings around parallel-wire transmis sion lines affect the ability of time domain reflectometry (TDR) to me asure the water content of soils and other porous materials. We use a steady state, two-dimensional, finite element numerical solution of La place's equation to analyze these effects. We prove that the numerical ly determined electrostatic potential distribution and boundary fluxes can be used to calculate the equivalent relative dielectric permittiv ity measured by TDR by comparing the results of the numerical model wi th those obtained using existing analytical solutions for special case s. We then analyze the effects of fluid-filled concentric gaps that co mpletely or partially surround TDR rods. The results show that an anal ytical solution due to Annan [1977b] for nonconcentric gaps can be use d as a good approximation to predict the effect of concentric gaps or coatings that completely surround the rods. Coatings or gaps filled wi th low relative dielectric permittivity materials have a greater impac t on the measured relative dielectric permittivity than those filled w ith high dielectric media. An increase in the thickness of the gap or coating for given rod diameters and separations increases the impact o f the coating. To a lesser degree, the impact of a coating of a given thickness decreases with an increase in the ratio of the rod diameter to the rod separation. A gap or coating of a given thickness and relat ive dielectric permittivity will have a greater impact on the response of a three-rod probe than on that of a two-rod probe with the same ro d diameter and separation of the outermost rods. Partial air gaps surr ounding less than 30 degrees of the rod circumference are not likely t o affect the probe response significantly.