## 4 Discussion  
The temperature variation between the tunnel rock and airflow induces thermal stress, which is unnoticeable in most tunnel projects with small temperature differences [29; 37]. Previous studies paid attention to the temperature evolution around the tunnel rock, preventing tunnels in the cold region from freezing-thawing damage [2; 16] and reducing the airflow temperatures in high-temperature tunnels to improve production efficiency and equipment safety [3; 4]. However, thermal stress gradually becomes significant as the tunnel rock temperature increases, resulting in rock damage and crack initiation [29] that threatens tunnel construction safety. Unfortunately, the existence of only few studies in this field results in a knowledge gap. Our research successfully fills this gap and lays the foundation for subsequent research. The tunnel rock temperature sharply decreases after tunnel excavation due to the heat transfer between the tunnel rock and airflow [22], inducing thermal stress and possible thermal damage in the rock mass [37]. That thermal stress is significantly weakened after paving a TIL on the tunnel wall that reduces the heat transfer flux and the temperature gradient between the tunnel rock and airflow. As a result, it postpones crack initiation and decreases the ultimate crack density, providing efficient time to adopt engineering measures for tunnel supporting. The insulation capacity is significantly enhanced via increasing the TIL thickness and decreasing the TIL thermal conductivity, which agrees with previous studies in cold region tunnels [10; 45; 46]. However, with thickening TIL and decreasing TIL thermal conductivity, the enhancement of the thermal insulation capacity remarkably decreases [25; 47], but the TIL cost rapidly increases [43; 44]. Therefore, how to balance the TIL insulation capacity and economy is necessary to be considered in the design of high-temperature tunnels. Airflow parameters, such as inlet temperature and airflow speed, play vital roles in preventing the cold tunnels from freeze-thaw damage in tunnels [20; 42; 48], but their impact on thermal damage is unnoticeable. This disagrees with the stimulation results of [PERSON] et al. [29], who suggested that a more significant heat conductive coefficient leads to earlier and more cracks in the rock mass. The reason for this difference includes two aspects. Firstly, the heat convective coefficient adopted in our study is from 20 W/(m\({}^{2}\)-K) to 300 W/(m\({}^{2}\)-K), which is small compared to [PERSON] et al. [29], from 300 W/(m\({}^{2}\)-K) to 30,000 W/(m\({}^{2}\)-K). Secondly, we discussed the long-term effect of cold shock in this paper, not the short-term effect studied by [PERSON] et al. [29]. The tunnel rock temperature rapidly decreases in a short time when ventilated by the cold airflow, during which increasing the heat conductive coefficient can enhance the temperature reduction [29; 49]. However, the tunnel wall temperature rapidly decreases as the ventilation time grows and immediately equals the inlet temperature. Then, the Robin condition between the tunnel rock and the airflow swifts to the Dirichlet condition with a constant boundary temperature, where changing the convection heat transfer coefficient is meaningless for heat exchange. Thus, varying the heat convection coefficient has an unobvious effect on thermal stress and rock damage in long-term ventilation. Meanwhile, the inlet temperature reduces the average temperature in high-temperature tunnels, extending the valid ventilation distance where the temperature is acceptable for workers [3]. However, the temperature difference via varying inlet temperature is very small in our study, which is not enough to change the thermal stress and crack evolutions significantly. In actual tunnels, in situ stress plays a crucial role in tunnel rock damage and associated cracks' evolution [29], and rocks experience plastic deformations in tension [40], which should be considered in the further simulation.