## 3 Results and Analysis
### Thermal Creaks Evolution in Tunnels under Cold Ventilation
#### 3.4.2 Influences of TIL and Airflow Parameters on Crack Propagation  
TIL and airflow parameters play different roles in the variation of the temperature and stress field discussed in Section 3.3. In this section, we discussed their influence on the crack evolution in tunnel rock. Figure 13 exhibits the crack variation when the tunnel is ventilated by 100 h under different TIL thicknesses, TIL thermal conductivities, inlet airflow temperatures, and heat convection coefficients, respectively.  
The thermal cracks grow with the increased TIL thermal conductivity and reduce with the thickened TIL. The crack is unnoticeable (Figure 13a) with a few AE events (Figure 14a) and a small AE energy (Figure 15a) when TIL thermal conductivity \(\lambda_{i}\) is 0.05 W/(m\(\cdot\)K). It becomes obvious with increasing thermal conductivity \(\lambda_{i}\) to 0.1 W/(m\(\cdot\)K) and more significant with the larger thermal conductivity, followed by more AE events and larger AE energy. However, those cracks reduce as TIL thickness increases and become invisible when TIL thickness grows to 20 cm (Figure 13b), during which both the AE event and energy decrease (Figures 14b and 15b). Figure 16 illustrates the length and number of visible cracks within every 30\({}^{\circ}\) from 0\({}^{\circ}\) to 360\({}^{\circ}\). The total length of visible cracks grows from 351.42 cm to 2492.13 cm as the TIL thermal conductivity \(\lambda_{i}\) increases from 0.05 W/(m\(\cdot\)K) to 0.2 W/(m\(\cdot\)K), whereas it reduces from 2854.81 cm to 423.53 cm as the TIL thickens \(th_{i}\) grows from 5 cm to 20 cm.  
Figure 13: Crack evolution with various TIL and airflow parameters (the blue diagram is minimal stress distribution, and the red one is temperature distribution).  
Figure 14: Damage elements with various TIL and airflow parameters (the red circle denotes the damaging elements in the current step, and the black circles denotes the damaged ones in the previous steps).  
Figure 15: Variations of accumulated AE events and AE energy under different TIL and airflow parameters.  
In constant, changing the inlet airflow temperature and heat convective coefficient have little effect on the crack propagation. The crack remains nearly unchanged as the heat convective coefficient \(h\) increases from 50 W/(m\({}^{2}\cdot\)K) to 200 W/(m\({}^{2}\cdot\)K) (Figure 13c), as well as the AE event and accumulated AE energy (Figures 14c and 15c). The total crack length is 1504.60 cm, 1505.11 cm, and 1493.72 cm when the heat convective coefficient \(h\) is 50 W/(m\({}^{2}\cdot\)K), 100 W/(m\({}^{2}\cdot\)K), and 200 W/(m\({}^{2}\cdot\)K), respectively (Figure 16c). Similarly, the thermal crack increases slightly (Figure 13d) when the airflow temperature \(T_{in}\) decreases from 20 \({}^{\circ}\)C to \(-\)20 \({}^{\circ}\)C, during which the AE event and accumulated AE energy increase insignificantly (Figures 14d and 15d), and the total crack length increases from 1505.11 cm to 1654.39 cm (Figure 16d).  
As a result, increasing TIL thickness and decreasing TIL thermal conductivity efficiently weakens the crack initiation and propagation, reducing the thermal shock damage of tunnels in the HDR and similar high-temperature conditions. On the contrary, the influence of varying inlet temperature and heat convective coefficient (such as varying the airflow velocity) is unnoticeable. Therefore, the critical key for weakening thermal damage in high-temperature tunnels is how to optimize TIL parameters.  
Figure 16: Total crack lengths under different TIL and airflow parameters.