## 5 Parametric Study
### Temperature Characteristics of Tunnel Lining and Lane Plate under Ventilation Conditions  
Figure 11 shows the average temperature contours of the tunnel lining (primary support and secondary lining) and the lane plate in December at K0 + 015 cross-section with and without the FLOLIC heat-insulating layer (Case I and Case II). In Figure 11a, it can be found that the tunnel lining and lane plate stay in a negative temperature state in December and the isotherms distribute densely without the heat-insulating layer. It is also found that the temperature gradient of the tunnel lining and lane plate is relatively significant, while the temperature difference between the inner and outer surface of the tunnel lining is 4-5 \({}^{\circ}\)C in Case I. After applying the heat-insulating layer, the tunnel lining covered by the heat-insulating layer stays in a positive temperature state, with the distribution of the isotherms being sparser and more uniform. It is found that the temperature gradient becomes smaller, while the temperature difference between the inner and outer surface of the tunnel lining is 2-3 \({}^{\circ}\)C in Case II. However, the lane plate and tunnel springing are still in a negative temperature state, as the heat-insulating layer is applied only on the secondary lining above the lane plate. This may lead to damages from frost in the bottom of the tunnel. Thus, it is necessary to take some anti-freezing measures to these positions.  
In order to investigate the temperature characteristics of the tunnel lining surface under different heat-insulating conditions (Case I and Case II), monthly average temperatures are measured at four different points on the lining surface, namely A, B, C and D. Points A, B, C and D are on the tunnel vault, tunnel spandrel, tunnel springing and lane plate, respectively (see Figure 12). It should be noted that points A, B and C are on the surface of the secondary lining, wh  
Figure 11: Average temperature contours in December of the secondary lining and lane plate: (**a**) without heat-insulating layer and (**b**) with heat-insulating layer (cross-section K0 + 015).  
lane plate of the tunnel. Figure 12a shows that the monthly average temperature varies at different locations in Case I. This is due to the fact that the ground temperature increases by increasing the depth, while the airflow temperature inside the tunnel distributes non-uniformly at the cross-section of the tunnel. It is also found that the temperature differences at different locations stay within the range of 1-3 \({}^{\circ}\)C in cold months (from January to March and from October to December), while the temperature differences in hot months (from April to September) are within the range of 0-0.6 \({}^{\circ}\)C. Obviously, the temperature differences in cold months are more significant than those in hot months. It is also found that temperatures at different locations in the same tunnel cross-section from the lowest to highest points are at the center of lane plate (point D), the tunnel vault (point A), the tunnel spandrel (point B) and the tunnel springing (point C), respectively. Figure 12b shows that the monthly average temperature curves in Case II are significantly different with the curves in Case I. Firstly, it is observed that the monthly average temperatures at points A and B, which are exactly the same, are significantly higher than the temperatures at points C and D. As a result, the points A and B are on the secondary lining surface behind the heat-insulating layer. Furthermore, the monthly average temperatures at points A and B (covered by the heat-insulating layer) in Case II stay in positive range during the whole year, while the temperatures at the two points in Case I are negative in cold months and positive in hot months. This indicates that the heat-insulating layer could help to maintain the temperature on the inner surface of the tunnel lining above 0 \({}^{\circ}\)C even in cold months.