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.

Expansive soils exhibit significant swelling-shrinkage characteristic under the cyclic moisture changes. The expansive soil slopes with high designing safety factor (gentle slope and low rainfall level) will also fail, which could not happen in an analysis ignoring expansive deformations. In this paper, the basic pore surface fractal model is derived and user-defined subroutines performing swelling-shrinkage deformation are developed to simulate the deformation features of expansive soil slopes under moisture variations. First, Fractal model is verified experimentally for accuracy in describing expansive soil issues. A hydro-mechanical coupling model based on the Fractal model in ABAQUS is then established to enable the numerical analysis of expansive soil slopes. In addition, the effects of swelling deformation, desiccation and slope ratio on deformation features are investigated. The results show that the consideration of swelling-shrinkage deformation causes the slope deformation features change, promotes larger additional displacements, and enhances water sensitivity. The simulated slopes can exhibit typical gentle sliding, shallow and progressive damage after several moisture cycling. This research provides a design reference for expansive soil slopes and expansive soil associated catastrophic issues.