## 3 Field Test of the Dege Tunnel
### Model Validation  
In order to verify the accuracy of the proposed numerical model, test-numerical comparisons are carried out in this section. As shown in Figure 8, the field test results and the numerical results of three different test points (S1-S3) at the tunnel vault and the tunnel spandrel in four different cross-sections (C1-C4) are compared. Section C1 and section C2 represent the cross-sections at 15 m and 715 m from the tunnel entrance (near Chengdu), while section C3 and section C4 represent the cross-sections at 15 m and 715 m from the tunnel exit (near Lasa). It should be noted that only C1 and C3 sections are covered by FLOLIC heat-insulating layer. S1 represents the point at the surface of the secondary lining, S2 represents the point at the back of lining (0.6 m from the surface of the secondary lining), and S3 represents the point in the soil domain with a buried depth of 2 m. It should be noted that the numerical results obtained at the test points are the average temperatures for each month, while the test results are the average temperatures for each half month. As shown in Figure 8, the average temperatures of the secondary lining surface are always above 0 \({}^{\circ}\)C during the whole year at section C1 and section C3. It indicates that the heat-insulating layer applied on the tunnel entrance and the exit is able to protect the secondary lining from frozen damage. It is also found that the average temperatures measured near the exit are higher than the average temperatures measured near the entrance at the same distance. In general, the test measurements are in reasonable agreement with the numerical predictions in terms of the curve trend and the magnitude of the temperature. It is also found that there are relatively larger differences between the test measurements and the numerical results in cold months (from January to March and from October to December), compared to hot months (from April to September). The deviations between the numerical model and test data are probably due to instrumental/measuring errors. The deviations may be also because the simplifications used in the proposed numerical model, such as ignoring the heat dissipation provided by the transportation  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Material**} & **Density** & **Heat Capacity** & **Heat Capacity** & **Thermal Conductivity** & **Thermal Conductivity** \\  & **(\(\mathbf{dz/m^{3}}\))** & **(Unfrozen Zone)** & **(\(\mathbf{f/kg.^{\circ}}\)C)** & **(\(\mathbf{f/kg.^{\circ}}\)C)** & **(\(\mathbf{w/m.^{\circ}}\)C)** \\ \hline Surrounding rock & 2450 & 1178 & 896 & 1.91 & 2.77 \\ Concrete material & 2385 & 970 & 970 & 1 & 1 \\ FLOLIC & 60 & 230 & 230 & 0.024 & 0.024 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Thermal physical parameters.  
vehicles in the tunnel, and the drainage of the tunnel through pipes behind the tunnel lining. As the Dege tunnel is still in trail operation and the traffic flow in the tunnel changes significantly during the service time, it is very difficult to measure the actual heat dissipation from the transportation vehicles in the tunnel. The investigation on the influence of the heat dissipation from the vehicles would be carried out in the future study. There are smaller differences between the test data and the numerical results in the deep surrounding rock compared to those on the surface of the secondary lining.  
To further investigate the influence of the heat-insulating layer on temperature fields of cold region tunnels, a parametric study is presented in the following section.  
Figure 8: Test-numerical comparisons for: (**a**) tunnel vault at section C1, (**b**) spandrel of tunnel at section C1, (**c**) vault of tunnel at section C2, (**d**) spandrel of tunnel at section C2, (**e**) vault of tunnel at section C3, (**f**) spandrel of tunnel at section C3, (**g**) vault of tunnel at section C4 and (**h**) spandrel of tunnel at section C4.