## 6 Heat-Insulating Layer Design Considerations
### Mechanical Ventilation Velocities (Using FLOLIC Material)  
The heat-insulating material employed in the following analysis is the FLOLIC material and its thermal physical parameters can be found in Table 1. The temperature of the secondary lining surface at the tunnel vault is employed to represent the temperature of the secondary lining surface. Figure 15 shows the average temperatures in December of the secondary lining in the longitudinal direction with different thicknesses (0 cm, 2 cm, 4 cm and 6 cm) of the heat-insulating layer. In the analysis, natural ventilation is considered with a constant velocity of 2.5 m/s, while mechanical ventilation is considered with two different velocities (5 m/s and 6 m/s) to check the influence of mechanical ventilation velocity. The heat-insulating layer is considered with a length of 500 m in the entrance section and the exit section, respectively. It should be noted a 0 cm thick heat-insulating layer means that no heat-insulating layer is applied on the tunnel lining. As shown in the figure, when the mechanical ventilation velocity increases from 5 m/s to 6 m/s, the temperature of the secondary lining surface at the same position decreases. It is also found that the change of the temperature is regardless of the thickness of the heat-insulating layer. Besides, the mechanical ventilation results in asymmetrical temperature distributions in the entrance section and the exit section. Regardless of the mechanical ventilation velocity, the temperature of the secondary lining surface increases rapidly in the entrance section, and drops rapidly in the exit section, while the change of the temperature is relatively slower in the middle of the tunnel without the heat-insulating layer. Moreover, it is found that the temperature of the secondary lining surface in the entrance section and the exit section that is covered by the heat-insulating layer is significantly higher than the temperature in the same section without the heat-insulating layer. The temperature of the secondary lining surface in the entrance section and the exit section that is covered by the heat-insulating layer rises by increasing the thickness of the heat-insulating layer. On the contrary, the temperature of the secondary lining surface in the middle section that is not covered by the heat-insulating layer is slightly lower than the temperature without the heat-insulating layer, and the temperature of the secondary lining surface in the middle section that is not covered by the heat-insulating layer decreases by increasing the thickness of the heat-insulating layer. In the cases with applying 2 cm, 4 cm and 6 cm heat-insulating layer, sudden drops of the temperatures are observed at 500 m length and 2443 m length, respectively. The reduction of the temperature increases by increasing the thickness of the heat-insulating layer. As a result, the length of the negative temperature region expands by increasing the thickness of the heat-insulating layer. Thus, having a thicker heat-insulating layer is not necessarily better. However, the length of the negative temperature region at the tunnel entrance and the exit will be relatively long if the heat-insulating layer is too thin. For example, the length of the negative temperature region is 55 m and 31 m in the entrance section and exit section, respectively, after applying a 2 cm thick heat-insulating layer. When the mechanical ventilation velocity is 5 m/s, 4 cm is the reasonable design thickness for the heat-insulating layer (see Figure 5a) for the example tunnel. In Figure 15b, the reasonable designthickness of the heat-insulating layer is still 4 cm after increasing the mechanical ventilation velocity to 6 m/s. This indicates that the influence of the mechanical ventilation velocity on the design thickness of the heat-insulating layer is not significant.