# Spatiotemporal Mechanical Effects of Framework-Slope Systems Under Frost Heave Conditions
## 5 Freeze-Thaw Effects on Frames and Slopes
### Coupling Mechanism of Freezing and Expansion on Slopes  
To examine the deformation mechanisms of the slope induced by moisture migration during freezing, a monitoring system was established along the slope surface to record freezing depth and displacement evolution from the toe to the crest. The moisture migration rate and pathway were considered key factors in the frost-heave-induced deformation. The spatial layout of the monitoring points and the displacement field during the frost heave period are shown in Figure 8.  
As illustrated in Figure 9, the frame-anchor support system does not impose vertical rigidity on the slope surface soil. During the frost heave period, the deformation is characterized predominantly by vertical displacement. In contrast, horizontal displacement is significantly restrained by the rigid beam-column frame structure, resulting in much lower horizontal movement compared to vertical displacement. Due to the combined constraint from the frame beam and surrounding soil, the displacements at monitoring points c, d, and e near the slope surface were limited to approximately 3 mm. However, points a and b located at the slope crest, which lack vertical constraint, showed greater  
Figure 8: Cloud map of displacement change during freezing period. vertical displacement. In frost heave Stages I and II, monitoring point b--influenced by both crest-side and surface-side freezing--exhibited vertical displacement 17.1 to 33.8% higher than point a, which is farther from the slope surface. To further explore the relationship between the temperature field, ice content, and slope deformation, Figure 10 presents the spatiotemporal evolution of these variables. The frost heave process is found to consist of the three following distinct stages:  
In Stage I (initial phase transition), surface frost heave deformation is triggered by the phase change in pore water at the slope crest. Due to thermal conduction lag, the freezing front gradually propagates downslope. During this phase, ice content remains relatively uniform across monitoring points. In Stage II, the freezing depth continues to increase, leading to the formation of dual-direction transitional zone D and dominant freezing zone E. Driven by coupled hydraulic and gravitational potential gradients, unfrozen water from deeper layers migrates upward through the soil pore network and accumulates near the slope toe. As a result, the ice content at the toe increases significantly. In Stage III, the freezing front reaches the critical freezing depth, and pore water migrates along the thermal gradient toward the front. As the slope toe acts as the terminal accumulation zone, it becomes the area with the highest volumetric ice content--substantially greater than in other regions. As shown in Figure 11, the evolution of the horizontal frost heave force field exhibits significant spatial variability characteristics. Influenced by the bidirectional freezing coupling effect, monitoring point b recorded higher horizontal frost heave forces than other monitoring points from Stage I to Stage II of frost heave. With changes in thermodynamic conditions, moisture migrated to the slope toe area, forming an ice-rich accumulation zone, resulting in notably pronounced frost heave forces at the slope toe. During the monitoring period of the frost heave stage, the horizontal frost heave force at monitoring point e on the slope toe displayed a distinct exponential growth pattern, peaking at 92 kPa in February and exceeding that of monitoring point b at the slope top. For the design of frame anchor bolt supporting systems in seasonally frozen slopes, it is crucial to significantly enhance the strength indicators of anchor bolt materials at the slope toe. This approach effectively  
Figure 9: Displacement variation at monitoring points. mitigates the risk of structural instability caused by excessive frost heave forces and ensures the overall stability of the slope. In summary, the slope toe acts as the terminal convergence zone for the advancing freezing front.