# Spatiotemporal Mechanical Effects of Framework-Slope Systems Under Frost Heave Conditions
## 5 Freeze-Thaw Effects on Frames and Slopes
### Anchor Axial Force Analysis  
The variation pattern of anchor bolt axial forces in supported slopes under frost heave effects is illustrated in Figure 14. A comparative analysis between natural conditions and the frost heave period reveals that the axial force during the frost heave period is approximately 1.3 times that under natural conditions. The significant increase in anchor bolt axial forces during the frost heave period can be primarily attributed to two factors. First, unfrozen water migration during soil freezing induces phase change volume expansion, generating frost heave forces that act on the anchor bolt structure through shear displacement constraints. Due to the rigid connection constraint between the anchor bolt and the frame structure, axial deformation is restricted, leading to the accumulation of internal tensile stress and manifesting as abnormal axial force elevation. Second, as shown in the deformation characteristics of the slope during the frost heave period in Figure 11, soil freezing-induced expansion generates displacements in the free face direction. This tensile action on the anchor bolts results in a notable increase in axial forces. The monitoring data along the slope profile direction show that the axial force response of the anchors shows a significant elevation effect, and the axial load of the support structure shows gradient-increasing characteristics from the foot of the slope to the top of the slope during the freezing and expansion process. According to Figure 14, it can be seen that the anchorage system in the top area (the first row) produces significant load jump in the freezing and expansion stage, and the axial load of its anchorage section increases by about 215 kN compared with the baseline value in the natural stage; the axial load increment of (the second and the third rows) is about 145 kN and 155 kN, respectively, which confirms that freezing and expansion have significant spatial heterogeneity; according to the change rule of its displacement field, temperature field, and stress field, it is shown that, under the action of freezing and expansion, the support structure axial load response shows a significant elevation effect from the foot to the slope. According to its displacement field, temperature field, and stress field, the region at the top of the slope under the action of freezing and expansion shows that the displacement change is obvious, the depth of freezing and expansion is large, and the axial force of the anchor rod changes greatly. Figure 14: Variation in anchor axial force under natural and frost heave conditions. Combined with Figure 11, it is evident that during the frost heave period, both the axial force of the anchor rods and the horizontal frost heave forces exerted on the slope body exhibit an increasing trend, with the axial force ranging from 145 to 215 kN and the frost heave forces ranging from 20 to 52 kPa, indicating a significantly greater increase in axial force compared to frost heave forces. By the end of the frost heave period, as temperatures rise, the axial force of the anchor rods retracts slightly but remains higher than that under natural conditions. This residual stress arises from two coupled mechanisms, namely the continued alteration of the soil's internal friction angle and cohesion due to moisture migration during thawing and the irreversible nature of slope displacement induced by the freezing process. Since frost heave deformation cannot be fully recovered, the axial force at the end of the frost heave period consistently exceeds that in the natural state. This indicates that the portion of axial force added to the anchor rods during the frost heave period becomes locked into the anchor system through the permanent deformation of the soil structure.