Seasonal Frozen Soil Electrical Resistivity Estimation Based on Capillary Fractal Model

Frozen soil resistivity exhibits high sensitivity to temperature variations and ice-water distribution. The conversion of soil water content (SWC) and resistivity based on petrophysical relationships enables the characterization of spatial distribution and changes in freezing and thawing states. Monitoring ground resistivity is essential for understanding frozen soil structure and evaluating climate change and ecosystems. The previous studies demonstrate that estimating soil resistivity below zero degrees based on the empirical model has significant errors. This work proposes a capillary bundle fractal model for frozen soil resistivity estimation based on SWC hydrologic parameters. The fractal theory describes the geoelectrical features of frozen porous media through the variable pore geometry and representative elementary volume. The sensitivity analysis discusses the potential relationships between pore parameters, conductance components, and fractal geometric parameters within frozen soil resistivity and reconstructs the hysteresis separation of freeze-thaw processes. The field test application in the seasonal freeze-thaw monitoring site demonstrates that the estimated resistivity and experimental samples are consistent with the field monitoring resistivity data. By combining unified conceptual assumptions, we established the connection between electrical permeability and thermal conductivity, offering a basis for exploring coupled hydro-thermal mechanisms in frozen soil. The proposed model accurately estimates the variations in seasonal frozen resistivity, providing a reliable reference for quantitatively analyzing the mechanisms of freeze-thaw processes.