第46卷第6期 中南大学学报（自然科学版） .46No.6 2015年6月 Journal of Central South University (Science and Technology) June 2015 D0:10.11817i.issn.1672-7207.2015.06. 环形单圈管冻结稳态温度场一般解析解 胡向东3，韩延广12 (1同济大学岩土及地下工程教育部重点实验室，上海，200092： 2.同济大学地下建筑与工程系，上海，200092) 摘要：隧道联络通道和矿山竖井冻结法施工经常采用环形布置冻结管。对于环形布管冻结温度场的解，目前仅有 冻结圈内完全冻实的单圈管冻结温度场解析解，但现实冻结工程中，内部通常是未冻实的。首先应用保角变换将 环形单圈管冻结模型变换为易于求解的特殊的直线型挂布的模型，再结合调和方程的边界条件可分离的性质，将 日分去雀挂鬼实指杨的最后藏单要管快表森实物鞋华气析华。一九子玫值模8 对解析解的验证结果表明：在冻土幕充分交圈后， 果基木 致，得到的解析解具有 高的精度。同时本文解析解也适用于冻结圈内完全冻实的温度场。 关键词：人工地层冻结法：环形单圆冻结管：温度场：解析解：保角变换：调和方程 中图分类号：TK124 文献标志码：A 文章编号：1672-7207201506-2342-08 General analytical solution to steady-state temperature field of single-circle-pipe freezing HU Xiangdong',HAN Yanguang (1.Key Laboratory of Geotechnical and Underground of the Ministry of Education Tongji University.Shanghai 200092.China: 2.Department of Geotechnical Engineering Tongji University.Shanghai00092.China) :Single-circ-ipenthd sha present,there is only one analytical solution which is aimed at the situation that the ground inside the freezing-pipe circl s frozen solid.However,a more usual situation is that the area enclosed inside the freezing-pipe circle is not frozen completely.For this situation,an analytical solution to the steady-state temperature field of single-circle-pipe freezing was proposed.The solution was derived by converting the sing-r-pipefreezing model toa special single-row-pipe freezing model using conformal mapping.and then decomposing the single-row-pipe freezine model into the single-row-pipe freezing model and a linear temperature field model according to the separability of boundary conditions for harmonic qtions.Comprison of the analytical solution with the numerical thermal analysis shows that the Key words:artificial gr mapping:harmonic equation 自然科学基 资助项日(5117836,51478340：浙江省自然科学基金资助项目(LZ13E08002XPot(51178336 nce foun .du.c 1994-2016 China Academic Joumal Electronic Publishing House.All rights reserved.http://www.cnki.ne第 46 卷第 6 期 中南大学学报(自然科学版) Vol.46 No.6 2015 年 6 月 Journal of Central South University (Science and Technology) June 2015 DOI: 10.11817/j.issn.1672-7207.2015.06. 环形单圈管冻结稳态温度场一般解析解 胡向东 1, 2，韩延广 1, 2 (1. 同济大学 岩土及地下工程教育部重点实验室，上海，200092； 2. 同济大学 地下建筑与工程系，上海，200092) 摘要：隧道联络通道和矿山竖井冻结法施工经常采用环形布置冻结管。对于环形布管冻结温度场的解，目前仅有 冻结圈内完全冻实的单圈管冻结温度场解析解，但现实冻结工程中，内部通常是未冻实的。首先应用保角变换将 环形单圈管冻结模型变换为易于求解的特殊的直线型排布的模型，再结合调和方程的边界条件可分离的性质，将 问题分解为单排问题和线性温度场问题，最后完成单圈管冻结圈内未冻实的温度场解析解。热力学数值模拟计算 对解析解的验证结果表明：在冻土帷幕充分交圈后，数值模拟结果和解析解结果基本一致，得到的解析解具有较 高的精度。同时本文解析解也适用于冻结圈内完全冻实的温度场。 关键词：人工地层冻结法；环形单圈冻结管；温度场；解析解；保角变换；调和方程 中图分类号：TK124 文献标志码：A 文章编号：1672−7207(2015)06−2342−08 General analytical solution to steady-state temperature field of single-circle-pipe freezing HU Xiangdong1, 2, HAN Yanguang1, 2 (1. Key Laboratory of Geotechnical and Underground Engineering of the Ministry of Education, Tongji University, Shanghai 200092, China; 2. Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China) Abstract: Single-circle-pipe freezing method is often applied in cross passage construction and mine shaft sinking. At present, there is only one analytical solution which is aimed at the situation that the ground inside the freezing-pipe circle is frozen solid. However, a more usual situation is that the area enclosed inside the freezing-pipe circle is not frozen completely. For this situation, an analytical solution to the steady-state temperature field of single-circle-pipe freezing was proposed. The solution was derived by converting the single-circle-pipe freezing model to a special single-row-pipe freezing model using conformal mapping, and then decomposing the single-row-pipe freezing model into the single-row-pipe freezing model and a linear temperature field model according to the separability of boundary conditions for harmonic equations. Comparison of the analytical solution with the numerical thermal analysis shows that the analytical solution is precise enough. Furthermore, the solution can also be employed for the temperature field of the frozen-solid situation. Key words: artificial ground freezing; single-circle-pipe freezing; temperature field; analytical solution; conformal mapping; harmonic equations 收稿日期：2014−04−13；修回日期：2014−08−20 基金项目(Foundation item)：国家自然科学基金资助项目(51178336，51478340)；浙江省自然科学基金资助项目(LZ13E080002)(Project (51178336, 51478340) supported by the National Natural Science Foundation of China; Project (LZ13E080002) supported by the Natural Science Foundation of Zhejiang Province, China) 通信作者：胡向东，副教授，博士生导师，从事隧道及地下工程研究；E-mail：anton.geotech@tongji.edu.cn