# Temperature Condition Analysis for Freezing on Tunnel Lining Back Side According to Tunnel Length
## 3 Air Temperature Change inside the Tunnel in Winter
### DTR Correlation between outside and inside Air Temperature by the Tunnel Length  
#### 3.2.1 Site Measurement  
The air temperature variation inside the tunnel was measured in a railway tunnel located in a cold region. The measured tunnel was designed as a double-track tunnel with a width, height, and length of 11 m, 7.8 m, and 8293 m, respectively, as shown in Figure 5a. Cold air is denser than warm air, so thermometers are installed at the lower part of the tunnel. Therefore, thermometers were installed at a height of 90 cm from the tunnel bottom, as shown in Figure 5b. The measurement distance selected was from the tunnel entrance (0 m) to the midpoint (3270 m) considering the trend in the air temperature distribution. Fifty thermometers and one repeater were installed, as shown in Figure 5c. The thermometer box consists of a thermometer sensor and a data logger. After each thermometer sensor measured the air temperature inside the tunnel over time, the data were transmitted to the repeater through a data logger. The accumulated data in the repeater were transmitted to a remote program. The inlet wind speed at the tunnel entrance was an average of 1 m/s during the measurement period (February 2019). The ventilation system was not operated during the measuring period since it was only used for emergencies.  
\begin{table}
\begin{tabular}{c c c} \hline
**Provinces** & **Cities** & **DTR (Min\(-\)Max)** \\ \hline Seoul-Gyeonggi-do & Seoul, Incheon, Ganghwa, Suwon, Yangpyeong, Icheon, Dongducheon, Paju & 7.3 \({}^{\circ}\)C\(-\)12.1 \({}^{\circ}\)C \\ \hline Gangwon-do & Sokcho, Gangneung, Taebaek, Cheorwon, Daegwallyeong, Chuncheon, Wonju & 8.1 \({}^{\circ}\)C\(-\)12.2 \({}^{\circ}\)C \\ \hline Chungcheongnam-do & Daejun, Buyeo, Geumsan, Cheonan, Seosan, Boryeong & 9.3 \({}^{\circ}\)C\(-\)12.3 \({}^{\circ}\)C \\ \hline Chungcheongbuk-do & Chungju, Cheongju, Chupungyeong, Jecheon, Boeun & 9.5 \({}^{\circ}\)C\(-\)12.6 \({}^{\circ}\)C \\ \hline Jeollanam-do & Gwangju, Mokpo, Suncheon, Jangheung, Goheung & 7.6 \({}^{\circ}\)C\(-\)11.2 \({}^{\circ}\)C \\ \hline Jeollabuk-do & Jeonju, Gunsan, Buan, Jeongup, Imsilsi, Namwon, Jangsu & 8.0 \({}^{\circ}\)C\(-\)12.2 \({}^{\circ}\)C \\ \hline Gyeongsangnam-do & Busan, Ulsan, Changwon, Jinju, Miryang, Geochang, Hapcheon & 8.4 \({}^{\circ}\)C\(-\)13.3 \({}^{\circ}\)C \\ \hline Gyeongsangbuk-do & Pohang, Daegu, Yeongju, Munyyeong, Yeongdeok, Uiseong, Gumi, Yeongcheon & 8.4 \({}^{\circ}\)C\(-\)14.8 \({}^{\circ}\)C \\ \hline \multicolumn{3}{c}{Average DTR in winter} & 10.5 \({}^{\circ}\)C \\ \hline \end{tabular}
\end{table}
Table 1: Korean winter DTR average value (1991–2020).  
Figure 4: The change in the energy rate and air temperature over time. (**a**) Correlation between the energy rate and air temperature change [17]; (**b**) Outside air temperature change and DTR.  
The data were selected when the outside air temperature maintained a constant diurnal temperature range (DTR) and a minimum temperature to analyze the change in the air temperature inside the tunnel. In the case of the measured data, the minimum outside air temperature dropped below \(-8\)\({}^{\circ}\)C and lasted for about 6 to 7 days from 8 February 2019. The air temperature change by the tunnel length (0 m, 120 m, 880 m, 1740 m, and 3270 m) from the entrance is shown in Figure 6. The relationship between the minimum outside and inside air temperatures was analyzed. The minimum temperature at the tunnel entrance dropped to between \(-11.2\)\({}^{\circ}\)C and \(-8.01\)\({}^{\circ}\)C and gradually increased toward the tunnel midpoint. The DTR inside the tunnel decreased as the tunnel length increased from the entrance.  
Figure 5: Schematic of thermometer box installation. (**a**) Tunnel cross-section; (**b**) Thermometer box installation; (**c**) Tunnel longitudinal section.  
Figure 6: Air temperature changes at each tunnel length over time.