# Spatiotemporal Mechanical Effects of Framework-Slope Systems Under Frost Heave Conditions
## 5 Freeze-Thaw Effects on Frames and Slopes
### Classification of Frost Heave Types  
Based on the spatial distribution of freezing depth and deformation patterns during the frost heave process, the slope surface can be divided into three distinct frost heave types, as illustrated in Figure 7.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Density (kg/m\({}^{3}\))**} & **Latent Heat of Phase** & **Specific Heat** & **Thermal Conductivity** \\  & **Change \(L\) (Jkg)** & **Capacity (kJ/(m\({}^{3}\cdot\)C))** & **(W/(m\({}^{\circ}\)C))** \\ \hline
1800 & 360,000 & 0.84 & 1.34 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Model parameters.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Component**} & **Density (kg/m\({}^{3}\))** & **Elastic Modulus \(E\) (MPa)** & **Poisson’s Ratio \(\mu\)** \\ \hline Frame & 2400 & 30,000 & 0.25 \\ Anchor rod & 7990 & 350,000 & 0.30 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Parameters of frame and anchor rod.  
Figure 7: _Cont._  
Type I frost heave, as shown in Figure 7a, occurs during the early stage of freezing. The slope crest begins to freeze first, followed by the slope surface and toe as the ambient temperature continues to decrease. According to the constraint conditions associated with frost expansion, three sub-regions are identified, named Region A, Region B, and Region C.  
Region A is primarily influenced by unidirectional horizontal freezing, leading to dominant vertical expansion due to minimal lateral restraint. Region B experiences dual thermal influence from both the slope crest and surface. It exhibits the deepest freezing depth and is partially constrained by the horizontal frame structure, resulting in the most pronounced vertical heave. Region C is constrained by the frame along the slope surface, as well as by adjacent zones B and the slope toe. As a result, it exhibits the smallest amount of frost-induced deformation.  
Type II frost heave, illustrated in Figure 7b, corresponds to the intermediate stage of freezing. As the ambient temperature continues to drop, the freezing depth increases,  
Figure 7: Schematic classification of slope frost heave types: (**a**) Type I—initial stage; (**b**) Type II—intermediate stage; (**c**) Type III—advanced stage.  
particularly at the crest and toe. Two additional transitional regions--Region D (on the mid-slope) and Region E (near the slope toe)--begin to emerge.  
Region D develops above Region C as a result of deepening frost penetration and forms a dual-direction constrained zone. The temperature isolines in this region run parallel to the slope surface. Being surrounded by constrained soil, Region D generates a substantial horizontal frost heave force acting on the frame. Region E shows temperature isolines with a smaller slope than in Region D and is subject to toe constraints. The freezing depth here remains relatively shallow.  
Type III frost heave, as shown in Figure 7c, occurs in the late stage of the freezing process. At this point, the freezing depth reaches its maximum, and the distribution of frozen regions undergoes significant transformation.  
Region C is completely replaced by the transitional Region D, and the slope of the isotherms in Region D becomes less steep. Region B, located near the slope crest, reaches its maximum frost penetration depth, indicating intensified frost heave.