## 3 Results and Discussion
### Resistivity Variation Characteristics of Frozen Clayey Sand
#### 3.2.2 Influence of Initial Volumetric Water Content on the Resistivity of Frozen Clayey Sand  
The variation curves of electrical resistivity with initial volumetric water content under different temperatures are shown in Figure 8. Overall, the electrical resistivity decreases first and then slightly increases with the increase in initial volumetric water content, exhibiting a typical \"U\"-shaped trend, indicating that initial water content plays a significant role in regulating the electrical conductivity of frozen soil. In the low initial water content range (3-6%), the ice content after freezing is limited, resulting in restricted conductive paths and insufficient contact among soil particles, leading to lower overall conductivity and higher resistivity. As the initial volumetric water content increases (6-9%), the ice crystals formed by frozen water partially fill the pores, enhancing the compactness of the ice-soil interface and improving the continuity of conductive paths, thus significantly reducing resistivity [51]. However, when the initial water content further increases (>9%), the dominant presence of ice crystals may lead to the isolation of soil particles, disrupting the original conductive network. Moreover, the poor conductivity of ice at low temperatures leads to a rebound in resistivity. Therefore, for each given dry density, there exists a specific initial water content at which the frozen soil exhibits the lowest resistivity, referred to as the \"optimum volumetric water content\" [52].  
Further examination of the curves under different dry densities shows that overall resistivity decreases with increasing dry density, especially in the mid-to-low water content range (6-10%). Soils with higher dry density have a denser skeleton structure and closer particle contacts, allowing ice to bond more effectively with soil particles during freezing. This facilitates the formation of a more stable composite conductive network, thereby significantly reducing resistivity [53; 54]. Additionally, a comparison between Figure 8a (\(-\)15 \({}^{\circ}\)C) and Figure 8b (\(-\)5 \({}^{\circ}\)C) reveals that under identical initial water content and dry density conditions, resistivity is generally higher at lower temperatures. This is attributed to the reduced conductivity of ice at lower temperatures and enhanced freezing intensity, which hinders charge migration and increases the insulating nature of the medium [55].  
In summary, the electrical resistivity of frozen clayey sand is jointly influenced by initial volumetric water content, dry density, and freezing temperature. The lowest resistivity point corresponding to the optimum initial volumetric water content reflects the most continuous conductive channels and the best ice-soil interfacial bonding. Identifying this optimum point and understanding its underlying mechanisms are of great theoretical and practical significance for the accurate electrical testing of frozen soil, the identification of subsurface freezing characteristics, and the analysis of anomalous resistivity distribution zones.  
Figure 8: Variation curves of resistivity of frozen clayy sand with initial volumetric water content under different temperatures: (**a**) \(-\)15 \({}^{\circ}\)C, (**b**) \(-\)5 \({}^{\circ}\)C.