Effective Properties of Frozen Soils of Different Cryogenic Structures

The impact of the cryogenic texture of a frozen soil sample on its effective conductivity is investigated. The effective conductivity here is introduced as a second-rank diagonal tensor. It allows one to trace the anisotropic behavior in the homogenized media. To determine the components of the conductivity tensor, a series of direct problems are solved. Each direct problem is about the distribution of the scalar electric potential in a heterogeneous medium with varying directions of electromagnetic field propagation. The diagonal components of the tensor are determined on the base of Ohm's law. At the level of the frozen soil sample, a stationary scalar boundary value problem is formulated and solved by the heterogeneous multiscale finite element method. The method is chosen due to the complex internal structure of the computational domain with a significant variation in the scale of the components. The calculated effective characteristics are further used to solve the direct electromagnetic problem in the frequency domain (kHz range) when the electromagnetic field is excited by an inclined solenoidal loop. This study allows one to estimate the influence of the internal cryogenic structure of frozen soil at the macro level, which is the level of ground electromagnetic measurements. At the macro level, authors use the computational scheme based on the vector finite element method. The tetrahedral finite elements are implemented. The Webb vector basis of the first full order is used.