# Temperature Condition Analysis for Freezing on Tunnel Lining Back Side According to Tunnel Length
## 1 Introduction  
The weather has seasonal changes in Korea, and the outside minimum temperatures in the cold regions drop below \(-25\ ^{\circ}\)C in the winter. High-speed railway tunnels have been constructed in the cold regions, and freezing-related damage, such as the obstruction of drainage flow and freezing groundwater leakage, has occurred recently. Most mountainous railway tunnels are designed with waterproofing membranes since groundwater exists on the backside of the tunnels. The related tunnel standards and existing studies were analyzed to predict freezing groundwater inside a tunnel.  
Other countries located in cold regions suggest tunnel design standards for anti-freezing. The Road Design Procedure in Japan (2018) suggests installing anti-freezing materials between the concrete lining and the waterproofing membrane from the tunnel entrance to 100 m length [1]. The road tunnel standards from the Norwegian Public Roads Administration (2004) recommend installing anti-freezing materials from the tunnel entrance to 200 m-300 m. However, for long tunnels, freezing damage should be evaluated individually [2].  
Existing studies used measurement and numerical analysis to determine inside air and lining temperatures. [PERSON] et al. (2015) measured the lining surface temperature in the Hongfu tunnel and simulated it using FEM analysis with ANSYS for a 1-year temperature cycle [3]. [PERSON] et al. (2017) also investigated the back side of the tunneltemperature using the FEM program under the daily average air temperature applied constantly. The maximum frost depth changed depending on the thickness and thermal properties of the tunnel structures [4]. Since then, studies have been conducted on the inside air temperature variation with influencing factors related to airflow motion. [PERSON] et al. (2020) installed thermometers at the vault, waist, and side walls for the total tunnel length (L = 2910 m). The closer the tunnel bottom, the lower the inside air temperature measured. The air temperature in the tunnel caused by intermittent traffic winds or natural winds blowing into the tunnel was transient [5]. [PERSON] et al. (2021) also measured the air temperature and showed that it returned to the original state within 30 min after a train passed [6]. [PERSON] et al. (2020) investigated road tunnels (L = 875 m-4905 m) in North China to analyze the inside air temperature over time. The inside air temperature field fluctuated daily, which led to freeze-thaw cycles on the lining and a lesser effect on the outside air temperature as the tunnel length increased [7].  
Long tunnels should be evaluated to specify the freezing damage according to the overseas standard. However, the existing studies on air temperature variation inside a tunnel focus on its measurement and change cycle for one year. The air temperature inside tunnels changes depending on various influencing factors, such as the outside air temperature, inlet wind speed, tunnel across-area, tunnel length, etc. Korean mountainous tunnels have certain conditions, including a surrounding ground depth exceeding 20 m and a generally low inlet wind speed at the tunnel entrance during the winter season. Therefore, the air temperature inside the tunnel is mainly closely affected by the outside air temperature and the tunnel length. The minimum air temperature inside a tunnel, which affects groundwater freezing has been presented along the tunnel length after analyzing the daily air temperature variation inside the tunnel.