管幕冻结特殊布管形式稳态温度场解析解

为了给管幕冻结这一新型地下工程施工方法的设计与施工提供参考，针对港珠澳大桥拱北隧道口岸暗挖段的管幕冻结工法，考虑积极冻结过程中所使用的"圆形主力冻结管"和"异形加强冻结管"2种类型冻结管的特殊布置形式，通过对实际问题进行适当简化，提出单圈冻结管错位布置的冻结模型。在此基础上，首先利用保角变换将单圈管不等距模型转化为单排管不等距模型，然后结合Laplace方程边界条件可分离的特性，利用2个单排管等间距模型叠加求解单排管不等距模型，最后得到管幕冻结法单圈管错位布置的温度场解析解。结合该解析解，选取管幕冻结法布管形式1个周期单元上3个特征位置的截面进行温度分析，并利用ANSYS数值软件对特征面上的理论温度分布进行对比验证，最后根据拱北隧道实际施工参数对其管幕冻结效果进行求解分析和直观的温度场云图展示。研究结果表明：在管幕冻结法冻结管单圈错位布置形式下，各特征面的温度均能降至较低的负温，远低于土体冻结温度，"管间封水"的效果能够得到保证；对比而言主面上温度最低，较近两冻结管之间的界面1温度略低于主面温度，在冻结管布置圈径上，各组参数下界面1的温度均能达到-15℃以下，且温度随着冻结管错位角度减小而降低；各特征面上，温差最大位置出现在冻结管布置轴面上，温度差异随着冻结过程的进行逐渐减小，冻土帷幕内的温度分布趋于稳定。

Analytical Solution to Steady-state Temperature Field of Freeze-sealing Pipe-roof with Specific Freezing Pipe Arrangement

A special circle-pipe freezing model with different pipe spacing based on simplification of the dark excavation section of the Gongbei tunnel in Hong Kong-Zhuhai-Macao Bridge is proposed to provide reference for the design and construction of freeze-sealing pipe roof (FSPR), which is a new underground construction method, considering the special arrangement of two types of freezing pipes ("circular master freezing pipe" and "profiled enhancing freezing pipe") used in active freezing period. In order to obtain the analytical solution of this special model, the circle-pipe model was first converted to row-pipe model with non-equal spacing between adjacent freezing pipes using conformal mapping method. Then, two simple single-row pipe models with equal spacing were superposed to obtain the analytical solution of this row-pipe model according to the separability of boundary conditions for Laplace equations. The analytical solution of the circle-pipe model was then determined by the corresponding law of parameters in conformal mapping. Three characteristic sections in a periodic unit of this special freezing model were analyzed, and the correctness of the analytical solution was verified by comparing the results with the numerical simulation results calculated using ANSYS software. The freezing effect of FSPR in the Gongbei tunnel was also analyzed and visual display with temperature cloud figures was implemented based on the analytical solution. The results show that the temperature of all characteristic sections can be frozen to a sufficiently low negative value, which is far below the soil freezing temperature, and the sealing effect of FSPR between two adjacent jacking pipes can be fully guaranteed. Intersection 1 passes through the middle of two adjacent jacking pipes, so the temperature on this section is slightly higher than that on the main section and can be lower than -15℃; this value also decreases with the offset angle of the freezing pipes. Besides, the maximum temperature difference occurs on the axis section and decreases gradually with the freezing process. Meanwhile, the temperature distribution in the frozen soil curtain also shows a tendency toward stabilization.