冻结法施工中，冻结管的布置间距往往大于单管冻结锋面半径，且考虑到冻结管影响范围有限, 为增强冻结温度场计算的准确性，基于势函数叠加原理，推导双管冻结叠加稳态温度场的计算公式，并将其周期化得到单排等距多管稳态温度场。结合依托工程的地层参数，通过数值模拟对推导公式进行验证。研究表明: 1)考虑相邻冻结管叠加影响范围有限性的双管稳态温度场计算公式能较准确地预测出一般冻结期内的温度分布规律； 2)在双管温度叠加区内, 冻结管连线中点为中垂线温度的最低点，且随着冻结管间距的减小，该点温度不断下降，但中垂线上冻结壁厚度并不改变； 3)随着冻结壁厚度的增加，双管稳态温度场接近加强单管稳态温度场。
In ground freezing construction, the spacing of
freezing tubes is always larger than the freezing front radius of a single pipe
and the influence range of the freezing tubes is limited. To improve the
calculation accuracy of freezing temperature field, a formula for the
superimposed steadystate temperature field for doubletube freezing is derived based on the superimposition principle of
potential function. And it is periodized to obtain a singlerow equidistant multitube steadystate temperature field, which is verified by numerical simulation
according to the formation parameters of the engineering project. The results
of the study indicate the following: (1) The formula for calculating the doubletube steadystate temperature field,
considering the finiteness of the superimposed range of influence of the
adjacent frozen tubes, can accurately predict the temperature distribution
during freezing. (2) In the temperature superimposition zone of the doubletube, the midpoint of the freezingpipe
connection line is the lowest temperature point on the midperpendicular line, and as the spacing of the freezing tubes
decreases, the temperature at this point decreases, while the thickness of the
frozen wall does not change across the midperpendicular
line. (3) As the thickness of the frozen wall increases, the doubletube steadystate temperature field
approaches the enhanced singletube steadystate temperature field.
