# A Study on the Heat Transfer of Surrounding Rock-Supporting Structures in High-Geothermal Tunnels
## 3 Field Test
### Test Results  
As shown in Figure 8, the temperatures of both surrounding rock and lining structure decrease over the exposure time of excavation, but there exists a relatively large difference in rate and amplitude of decline. Apparently, the reduction of rock temperature near the tunnel sidewall is more significant than that in surrounding rock farther away. In Test Location 1 (the initial rock temperature was 47 \({}^{\circ}\)C), it can be seen that the temperature of sensors, located 1.2 meters away from the wall, decreased by  
Figure 6: A cross-section of the tunnel.  
Figure 7: Layout of temperature monitoring points in lining structure: **(a)** primary lining and **(b)** secondary lining.  
almost 7 \({}^{\circ}\)C. The minimum reduction of temperature is 0.3 \({}^{\circ}\)C with sensors at 17.9 meters away from the wall, and the reduction of temperature is below 1 \({}^{\circ}\)C when the distance away from the wall is over six meters. Similar test results can be obtained in Test Location 2 (the initial rock temperature was 62 \({}^{\circ}\)C). However, the decline of temperature in Test Location 2 ranges from 0.5 to 11 \({}^{\circ}\)C and the reduction of temperature is below 1 \({}^{\circ}\)C when the distance away from the wall is over 8.9 meters. The final steady air temperatures of Test Locations 1 and 2 are 34 \({}^{\circ}\)C and 40 \({}^{\circ}\)C, respectively.  
As for the temperature of lining structure, it can be seen in Figures 7 and 8 that the temperature distribution of the primary lining was in the range from 37.2 to 46.5 \({}^{\circ}\)C and 42.8 to 61.3 \({}^{\circ}\)C, respectively, while the variation ranges of the secondary lining are 35.1-54.1 \({}^{\circ}\)C and 41.3-59.8 \({}^{\circ}\)C. Moreover, it appears that there is a temperature rise of 2-3 \({}^{\circ}\)C in the primary lining after the accomplishment of the secondary lining construction. The initial temperature of the concrete decreased from a high level and showed a rapid decline rate within seven days. After almost one week, the decline rate slowed down noticeably at first and then gradually stabilized. It is noticeable, however, that the final temperature of the concrete lining was a little lower than the rock temperature and the temperature of primary lining was a little higher than that of the secondary lining because of heat dissipation at the free face.  
MATLAB has a powerful calculating capacity and strict rules of solution, which is significant in equations' solution for its reliability and quickness. According to the formula deduced above and on-site conditions, the temperature field of the high geothermal tunnel is obtained by using MATLAB programming. The equivalent radius was 4.2 m. The time step \(\Delta\tau\) was taken as 0.5 h and the space step is 0.1 m. Calculation thermodynamic parameters of the surrounding rock and lining concrete are shown in Table 1. Iterative calculations are performed by inputting initial parameters, which were obtained from numerous surveys and experiments [30; 31].  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Materials**} & **Density** & **Thickness** & **Thermal Conductivity** & **Specific Heat** & **Convective Heat Transfer** \\  & **kg\(\cdot\)m\({}^{-3}\)** & **m** & **W-(m\({}^{-2}\)C)\({}^{-1}\)** & **J-(kg \({}^{-2}\)C)\({}^{-1}\)** & **Coefficient W/m\({}^{2\cdot 0}\)C** \\ \hline Initial support & 2200 & 0.25 & 2.9 & 960 & 13.96 \\ Second lining & 2200 & 0.45 & 2.9 & 960 & 13.96 \\ Surrounding rock & 2800 & - & 3.2 & 722.1 & - \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of heat material.  
Figure 8: Variation in temperature of the surrounding rock and lining structure during construction: **(a)** Test Location 1 and **(b)** Test Location 2.