Dielectric properties of saturated frozen silty clay: Experimental characterization and temperature-void coupled mixing model

The hydrothermal evolution of frozen ground is a unique engineering geological phenomenon in cold regions, whereby the dielectric constant (ε) serves as a pivotal parameter for evaluating this state and improving the reliability of geophysical remote sensing monitoring. In this study, saturated silty clay specimens with nine distinct void ratios were prepared using a custom three-layer slurry consolidation apparatus. Nuclear magnetic resonance (NMR) and time-domain reflectometry (TDR) were combined to measure unfrozen water content (w_u) and ε at temperatures ranging from −5 °C to −0.5 °C. Results reveal a two-stage variation pattern of w_u and ε: the temperature-void ratio coupling effect dominates at temperatures above −1 °C, while temperature alone exerts a controlling influence at temperatures from −1 °C to −5 °C. The mean permutation importance quantifies that the influence weights of void ratio on w_u and ε are 1/12 and 1/5 of that of temperature, respectively. A modified Looyenga model considering temperature and void ratio (LMTE) was developed by incorporating a phase transition volume correction term to account for water expansion during freezing. The LMTE model achieves a high coefficient of determination (R2 = 0.96), outperforming the Brown Modification model (BM), CRIM Modification model (CM), and l-v Modification model (LVM). This study physically couples the soil freezing characteristic curve of frozen silty clay with dielectric mixing laws at the laboratory scale, providing critical technical support for the accurate remote sensing monitoring and hydrothermal state evaluation of frozen silty clay in cold-region engineering.