1. Department of Geotechnical Engineering,Tongji University,Shanghai　 200092,China; 2. Key Laboratory of Geotechnical and Underground Engineering of the Ministry of Education,Tongji University,Shanghai　 200092,China; 3. Shanghai Tunnel Engineering Co. ,Ltd. ,Shanghai　 200232,China

In the artificial ground freezing project,the average temperature is the basic parameter for evaluating the fro- zen soil curtain state and the mechanical analysis of the frozen soil curtain. The average temperature calculation of the frozen soil curtain formed by the single-row pipe freezing is studied in this paper. Based on the analytical solution of the steady-state temperature field of a single-row pipe freezing,the integral calculation of the temperature is directly performed. Using the partial integral method and the integral median theorem,the calculation formula of the average temperature of the single-row tube freezing is obtained,and the formula is simplified according to the actual parameter values in the project. Considering that the temperature field analytical solution is not applicable in the frozen pipe are- a,the same integral strategy is used to solve the influence of the frozen pipe area on the average temperature calcula- tion,and the average temperature calculation formula is corrected. The results of the average temperature calculation formula were compared with the results of the thermal steady-state numerical simulation of the single-row pipe freezing using ANSYS. The pipe spacing l = 0. 4,0. 6,0. 8,1. 0,1. 2,1. 4 m,and there are six kinds of frozen development states with relative thickness ξ / l = 0. 5,0. 6,0. 7,0. 8,1. 0 and 1. 5. The values of soil parameters are taken according to the test report and the freezing parameters are commonly used in engineering. The comparison calculation results show that the formula calculation is in good agreement with the numerical calculation results. When the relative thick- ness is over more than 0． 5,the difference between the formula calculation result and the numerical calculation result is rapidly reduced to within 0． 5 ℃ with the development of the frozen soil thickness (relative thickness increase). When the relative thickness is greater than 0. 6,the difference between the results is less than 0． 2 ℃ . When the relative thickness is 1 or greater,the difference is less than 0． 1 ℃ . The accuracy of the average temperature calculation formu- la is verified by numerical simulation,and the rationality of the formula simplification and correction is also explained. The error calculated by the formula satisfies the requirements of engineering application.

国家自然科学基金资助项目（51478340）

HU Xiangdong,LIU Yanghui,HONG Zequn,et al. Calculation of average temperature of frozen soil wall by single row- piped freezing[J]. Journal of China Coal Society,2019,44(4):1092-1097.