## 7 Conclusions  
Based on the numerical simulation and field measurement of the irregular horizontal freezing reinforcement adopted in the shield repairmen project, the characteristics and influencing factors of the freezing temperature field of the irregular horizontal freezing are obtained, and the principal findings are as follows:  
(1) The extension length of the outer ring pipe has an approximately linear effect on the thickness and average temperature of the frozen wall. The frozen thickness increases by 0.25 m on average, and the average temperature decreases by 1.25 \({}^{\circ}\)C when the extension length increases by 1 m on average. The lap time decreases by 13 days when the extension length increases from 3.53 m to 4 m, while the lap time only decreases by 5 days when the lap time increases from 4.99 m to 5.47 m. In this project, the best extension length of the outer ring pipe is 5 m, and the thickness of the frozen wall of the weak path 3 can reach 5.24 m to meet the design requirements. (2) The temperature of the weak point in the center increases approximately linearly with the increase in the relative ratio of the axial angle between the two adjacent tubes. The midpoint temperature of the two tubes increases by 3.3 \({}^{\circ}\)C for every unit increase in the angle coefficient. Therefore, reducing the axial angle near the weak link of the outer ring hole to a certain extent will improve the stability of the weak region, and it will also help to reduce the total length of the freezing pipe when the horizontal length of the outer ring pipe is constant. (3) The influence of the opening angle of the inner ring hole on the thickness and average temperature is almost negligible, and the fluctuation is not more than 0.15 m and 0.6 \({}^{\circ}\)C, respectively. At the same time, the center temperature of the inner ring angle gradually increases as the opening angle increases. Therefore, appropriately reducing the angle of the inner tube will help to improve the stability of the frozen wall without greatly affecting the thickness or the average temperature. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(\backslash\)d & \(\backslash\)\({}^{\circ}\)C & **Numeric** & **Measured** & **Numeric** & **Measured** & **Numeric** & **Measured** \\  & **T1-6** & **T1-6** & **T2-3** & **T2-3** & **T2-4** & **T2-4** \\ \hline
30 & \(-\)4.159 & \(-\)1.500 & \(-\)7.444 & \(-\)5.844 & \(-\)7.395 & \(-\)5.095 \\
60 & \(-\)15.450 & \(-\)13.264 & \(-\)11.264 & \(-\)11.400 & \(-\)14.715 & \(-\)13.415 \\
90 & \(-\)18.959 & \(-\)15.481 & \(-\)13.481 & \(-\)13.900 & \(-\)17.450 & \(-\)16.500 \\
120 & \(-\)20.336 & \(-\)16.380 & \(-\)15.800 & \(-\)16.500 & \(-\)18.567 & \(-\)18.067 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The numerical and measured temperature comparison of each measuring point. (4) The average temperature of the weak line composed of weak points shows a trend of decreasing first and then increasing along the shield advance under the irregular horizontal freezing form. It reaches the minimum value while the distribution of freezing pipes near the cutter head is dense relatively, and there is no freezing end effect or convective heat transfer. The data conclusions obtained in this paper are based on COMSOL numerical simulation software. More than 1000 high-level papers related to freezing have been published through this software, which is enough to prove its applicability and accuracy in the field of freezing. At the same time, the temperature data collected by thermocouple field measurement are used as comparative analysis, which further strengthens the correctness of numerical simulation data and shows the applicability of the conclusions in this paper. In the future, the spatial and temporal evolution law of freezing temperature field with irregular hole arrangement can be further studied, and the universal law of the influence of different hole arrangement methods on temperature field can be obtained, and the results can be extended to any underground freezing reinforcement project.