## 3 Results and Analysis
### Thermal Creaks Evolution in Tunnels under Cold Ventilation  
#### 3.4.1 Creaks Propagation in Tunnels with and without TIL  
The tunnel wall is quickly cooled once the tunnel is ventilated under the cold airflow, resulting in a sharp temperature drop and associated thermal stress. The stress induced by the temperature variation possibly leads to rock damage and crack initiation when it exceeds the tensile strength of the tunnel rock [29], weakening the tunnel stability. Figure 11 presents the crack evolution in tunnels with and without TIL through the heterogeneous model (\(m=6\)) as the ventilation time increases. The thermal stress immediately exceeds the tensile strength of the tunnel rock once the airflow enters the high-temperature tunnel without TIL, causing damage elements observed around the tunnel wall (Figure 11a). Then, the thermal stress weakens, and the number of new damage element decreases (Figure 11b). However, the total number of damage element gradually increases as the ventilation time goes on, which coalesces and nucleates to visible cracks in the rock mass around the tunnel wall (Figure 11c). Those cracks become more pronounced when the ventilation time \(t\) reaches 10 h and 100 h (Figure 11d,e), during which some cracks gradually stop growing and others unstoppably propagate into the rock interior. This induces the long crack to alternate with short cracks around the tunnel wall with the same spacings. Such hierarchical cracks have been found by [PERSON] et al. [29]. Note that the initial crack propagates in the direction perpendicular to the tunnel wall, slightly deflected at its tip with the increased ventilation time. The failure elements disturb the heat conduction of  
Figure 10: Temperature and stress variations with varying heat conductive coefficients and inlet airflow temperatures.  
adjacent elements, which changes the temperature gradient and associated tensile stress, thus deflecting the following crack propagation.  
After paving a TIL with 0.1 m of thickness and 0.1 W/(m-K) of thermal conductivity, the crack initiation time is remarkedly postponed. Few unnoticeable cracks are discovered around the tunnel rock surface until the ventilation time \(t\) grows to 10 h (Figure 11f-i). Although hierarchical cracks appear around the tunnel rock after 100 h of ventilation (Figure 11j), the number and length of cracks are remarkably less than those without TIL. Figure 12 shows the visual crack evolution in the tunnel rock with ventilation time. The total length of visible cracks in the tunnel without TIL is 791.93 cm at \(t=1\) h, which extends to 1721.48 cm and 3214.02 cm as the ventilation time \(t\) grows to 10 h and 100 h, respectively. However, the visible cracks in the tunnel with TIL are firstly found at \(t=10\) h, with a total length of 309.52 cm, then the total length increases to 1505.11 cm as the ventilation time grows to 100 h, which is only 47% of that in the tunnel without TIL.  
In summary, the cold airflow decreases the tunnel temperature, forming a noticeable temperature variation and associated tensile stress-dominated area. The crack initiates and  
Figure 11: Crack evolution with increasing ventilation time in tunnels: (**a**)–(**e**) without TIL, (**f**)–(**j**) with TIL.  
Figure 12: Cracks evolution with various ventilation time \(t\): (**a**) without TIL and (**b**) with TIL.  
propagates in this area, damaging tunnel rock and endangering tunnel safety. Paving a TIL is of help to decrease the heat exchange between the cold airflow and the tunnel rock, which reduces the decreasing velocity of the tunnel temperature. It weakens the thermal damage in tunnel rock, postponing the crack initiation and decreasing the crack density.