## 4 Results
### Simulation Results of Slopes with Different Freeze-Thaw Cycles
As the number of subsequent freeze-thaw cycles increases, the damage will gradually decrease to approximately zero. Freezing and thawing cycles produce two types of cracks in geotechnical mixtures: one caused by stretching and one caused by shearing [44]. Among them, the most important damage is caused by volume expansion and stretching; volume expansion occurs in geotechnical materials during the freezing process when the internal water in the low-temperature environment freezes into ice. This transition significantly increases volume and produces greater stress on the surrounding geotechnical soil. This leads to further expansion of geotechnical fissures; the geotechnical structure of the damaging effects of the freezing and thawing cycle will continue to accumulate, resulting in the gradual deterioration of the geotechnical structure. Although the volume expansion theory can explain part of the freeze-thaw damage phenomenon, not all freeze-thaw damage can be attributed to volume expansion. Freeze-thaw damage is a complex process that involves the interaction of several factors, including water migration, chemical action, and the formation and growth of ice crystals. During freezing, water migrates from areas of high potential energy to areas of low-potential energy, especially when the soil freezes, and unfrozen water is transferred to the frozen surface, a phenomenon known as positive permafrost \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Measuring Point** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** \\ \hline Stress in the X-direction/kPa & 20 & 14 & 27 & 71 & 32 & 140 & 160 & 100 \\ Stress in the Y-direction/kPa & 49 & 25 & 49 & 62 & 27 & 64 & 420 & 320 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Measurement point stress data. Figure 16: Crack distribution of the slope model (1–8) are the monitoring point codes). water migration. In the freeze-thaw cycle, moisture is continuously transformed and migrated between solid, liquid, and gaseous states as the temperature rises and falls. This moisture migration has an important effect on freeze-thaw damage. Migrated moisture forms ice crystals during freezing, which produces volume expansion and pressure on the geotechnical structure, leading to cracking and fragmentation within the geotechnical structure. In turn, the melting of ice crystals during thawing may lead to destabilization and the settlement of the geotechnical structure. The volume expansion and migration of water particles during the freeze-thaw process is one of the main causes of freeze-thaw damage, as shown in Figure 18.  
Figure 17: Changes in the number of contacts and cracks during the freeze–thaw cycle. Figure 18: Freeze–thaw damage process. Figure 19a shows the relationship between the maximum particle displacement and the reduction coefficient obtained by reducing the strength of the dump site slope under different freeze-thaw cycle conditions to induce landslides. At 0, 1, 3, 5, 10, and 20 freeze-thaw cycles, the reduction coefficients when particle displacement suddenly occurs are 1.92, 1.58, 1.47, 1.43, 1.27, and 1.18, respectively. According to each freeze-thaw cycle, the slope safety factor under cyclic conditions can be obtained by obtaining the relationship between the slope stability coefficient of the dump site and the freeze-thaw cycle period, as shown in Figure 19b. Analysis of Figure 19b shows that the stability coefficient of the dump site slope decreases with the increase in the number of freezing and thawing cycles. According to the fitting results, the two have a power function relationship:  
\[F_{\text{s}}=(-175.06+180.32\times T^{-0.0065})^{-\frac{1}{3.99}} \tag{7}\]  
Among them is the stability coefficient; T is the number of freeze-thaw cycles, and the correlation coefficient is 0.93. Under the influence of freeze-thaw cycle deterioration, the macroscopic strength, cohesion, and internal friction angle of the SRM will be damaged, thus affecting the stability coefficient of the dump site slope.