FREQUENCY DISPERSION DEPENDENCE OF DIELECTRIC PERMITTIVITY OF CRYOGENIC ROCKS AT THE MACRO LEVEL

Purpose. The purpose of this article is to establish the analytical expression of the frequency dispersion dependence of the real part of the dielectric permittivity of cryogenic rocks according to experimental studies. Methodology. Analytical and experimental investigations of the dependence of dielectric permittivity of cryogenic rocks on the field frequency of applied loads at the macro level have been carried out. An empirical analysis of the obtained results was carried out and a comparison of these data with experimental data was performed to prove the adequacy of the proposed mathematical models. Findings. The dielectric permittivity decreases exponentially with increasing frequency at all temperature values. The dependence parameter that corresponds to the frequency at the moment of electrical relaxation (anomalous dispersion zone) shifts toward low frequencies as the temperature decreases. The maximum and minimum values of the dielectric permittivity of cryogenic rocks are constant and independent of temperature change for a particular cryogenic rock and are dependent on humidity, mineralization and morphological structure. Originality. In this article, mathematical expressions are developed to describe the frequency dependence of dielectric permittivity under low frequency and high frequency loading, which is described by a single analytical dependence. Practical implications. The practical significance of the results obtained is the ability to establish seismic-acoustic, elastic-deformation and strength properties of rocks through the study of the characteristics of the electromagnetic properties of cryogenic rocks. Conclusions. The obtained analytical dependence of the dielectric permittivity of mountain cryogenic rocks in the form of a double exponent allows to adequately describe the influence of an external electric field, taking into account the humidity and temperature of the rocks.