## 3 Numerical Analysis and Verification
### Numerical Results and Validation  
Figure 10 shows the temperature field contour nephogram after the 78-h calculation. It can be clearly seen from the figure that the isolines are diffused outward from the high-temperature region, and the convective boundary has a significant influence on the distribution of the temperature field. From the bottom of the model along the Y-axis to the top, the temperature gradient increases first and then decreases. In the direction of the X-axis, the disturbance of the external environment temperature to the soil temperature is \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Physical** & **Density** & **Thermal Conductivity** & **Isobaric Specific Heat** \\
**Parameters** & **(kg/m\({}^{3}\))** & **(W/(m\({}^{\circ}\)C))** & **Capacity J/(kg\(\cdot\)C)** \\ \hline Values & 2412 & 1.78 & 1046 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The thermal physical parameters of the filled soil. Figure 8: Finite element meshes. Figure 9: Test equipment: **(a)** SW6086 thermal anemometer and **(b)** HFM 446 Lambda. obvious within 0.6 m from the boundary of both ends. This range of influence depends on many factors, mainly the geographical location, climatic conditions, topographic relief, thermal and physical properties of the rock and soil, etc. The calculated results were compared and analyzed with the corresponding temperature values of 13 measuring points in the X direction, and the temperature values at 12 h, 24 h, 48 h, and 78 h were selected, as shown in Figure 11. It can be seen from the figure that the variation trend of the calculated value is basically the same as that of the monitored value, but there is a certain difference between them. The maximum difference occurs at measuring point \(Z_{2}\) buried in the tunnel, which is caused by vibration and incompaction when the tunnel is filled and sealed. As time progressed, the difference between the calculated value and the monitored value gradually narrowed, from 12 h to 78 h, and the maximum difference decreased from 1.9 \({}^{\circ}\)C to 0.6 \({}^{\circ}\)C. In addition, it can be seen that the calculated value is generally greater than the test value, mainly because the monitored value has a certain lag compared with the calculated value. The monitoring values of measuring points \(Z_{1}\)-\(Z_{9}\) were compared with the calculated values, and the temperature values over the whole time period at measuring point \(Z_{5}\) were also compared, as shown in Figure 12. Figure 12a shows that the temperature distribution  
Figure 11: Comparison of the filled soil temperature in the X direction. Figure 10: Contour cloud map of the numerical simulation temperature field (at 78 h). is high in the middle and low at both ends. At measurement points \(Z_{1}\), \(Z_{2}\), \(Z_{8}\), and \(Z_{9}\) at both ends, the difference between the calculated values and the monitored values is obvious, and the difference gradually decreases after 48 h. Figure 12b shows the variation rule of the calculated and monitored temperatures at measuring point \(Z_{5}\) during the whole test process. In the first 12 h, the difference between the calculated value and the monitored value is obvious. This is because the initial temperature of the filled soil is inconsistent along the depth direction, which increases with depth. However, in the numerical calculations, the average value is selected at time 0. In general, the final maximum difference between the calculated value and the monitored value is only 0.7-0.9 \({}^{\circ}\)C with a 2.1% error, and the variation of the two values is consistent.