## 6 Numerical Simulation of the Temperature Field of a Block-Stone Subgrade
### Analysis of Simulation Results of Cooling Effectiveness of Block-Stone Subgrade  
The distribution of the temperature field in the 5 th year, 10 th year, and 15 th year in October is analyzed based on the simulation results. The 0 \({}^{\circ}\)C isotherm is marked with a red line in the contour plot, as shown in Figures 12 and 13. As the simulation time increased, the permafrost table decreased to varying degrees at all locations in the lower part of the straight-filled 1 m block-stone subgrade. The permafrost table in the lower part of the medial divider decreased by 4.99 m, with an average rate of decline of 0.33 m/a, and the rate of decline per 5 years was 0.42 m/a, 0.34 m/a, and 0.24 m/a in that order. The permafrost table in the lower part of the left toe of the slope decreased by 3.62 m, with an average rate of decline of 0.24 m/a, and the rate of decline per 5 years was 0.43 m/a, 0.21 m/a, and 0.10 m/a. The permafrost table in the lower part of the right toe of the slope declined by 4.49 m, with a descending average rate of 0.30 m/a and a descending rate of 0.48 m/a, 0.25 m/a, and 0.17 m/a every 5 years in the order of 0.48 m/a, 0.25 m/a, and 0.17 m/a. The permafrost table in the lower part of the natural ground surface declined by 1.83 m, with a descending average rate of 0.17 m/a and a descending rate of 0.16 m/a every 5 years in the order of 0.16 m/a, 0.12 m/a, and 0.08 m/a. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Particle Size** & **k** & **C\({}_{\rm v}\)** & \(\lambda_{\rm s}\) & **n** & **\(\rho\)** \\
**(cm)** & **(m\({}^{2}\))** & **(kJ/(m\({}^{3}\cdot\)K))** & **(W/(m\(\cdot\)K))** & **(\%)** & **(kg/m\({}^{3}\))** \\ \hline
4–6 & 7.6e-7 & 1270 & 0.407 & 45.1 & 2100 \\
6–8 & 4.3e-6 & 1250 & 0.396 & 45.7 & 2040 \\
10–15 & 8.3e-6 & 1180 & 0.385 & 46.2 & 1950 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Physical parameters of the block-stone layer with different particle sizes. As the simulation time increased, the permafrost table decreased to varying degrees at all locations in the lower part of the replacement 1 m block-stone subgrade. The permafrost table in the lower part of the medial divider decreased by 4.71 m, with an average rate of decline of 0.31 m/a, and the rate of decline per 5 years was 0.40 m/a, 0.33 m/a, and 0.22 m/a. The permafrost table in the lower part of the left toe of the slope decreased by 3.29 m, with an average rate of decline of 0.22 m/a, and the rate of decline per 5 years was 0.35 m/a, 0.21 m/a, and 0.09 m/a. The permafrost table in the lower part of the right toe of the slope declined by 4.10 m, with an average rate of decline of 0.27 m/a, and the rates of decline per 5 years were 0.45 m/a, 0.22 m/a, and 0.15 m/a. The permafrost toe in the lower part of the natural ground surface declined by 1.70 m, with an average rate of decline of 0.17 m/a, and the rates of decline per 5 years were 0.14 m/a, 0.11 m/a, and 0.09 m/a. In order to illustrate more clearly the change in the permafrost table under ordinary and block-stone subgrades, the trend of change in the permafrost table under different locations of the subgrades over a period of 15 years was analyzed, as shown in Figure 14.  
Figure 12: Contour plots of temperature field distribution at various time points for the straight-filled 1 m block-stone subgrade. Figure 13: Contour plots of the temperature field distribution at each time point of the replacement 1 m block-stone subgrade. As can be seen from Figure 14, the permafrost table of block-stone subgrade in different locations is higher than that of ordinary subgrade in the same year, and block-stone subgrade can effectively lift the permafrost table and play a certain role in heat preservation. The rate of decline in the permafrost table at different locations of both types of block-stone subgrades is decreasing from year to year, with a stabilizing trend.