Artificial ground freezing is widely used in the construction of underground engineering. The calculation of freezing temperature field is not only the basement of theory research on artificial ground freezing

but also an important basis of the freezing construction design. Single-circle-pipe freezing method is often applied to artificial ground freezing projects

while the analytical solution of this situation has never been published. Thus it’s necessary to get the solution to benefit our engineering practice. Based on the theory of analogy between thermal and hydraulic problems

using conformal mapping

mirror reflection of sources and sinks

and the superposition of potential function

this paper gives an analytical solution to the steady-state temperature field of single-circle-pipe freezing and demonstrates its correctness by numerical thermal analysis. Comparison of the analytical solution with the numerical thermal analysis shows that the analytical solution is precise enough and will afford reasonable guidance in single-circle-pipe freezing projects. A simplified formula is also given and is proven to be precise enough. Based on the simplified formula

the thickness formula of the outer part of frozen wall is derived. The analytical solution

simplified formula and thickness formula can provide guidance and theoretical basement for construction and design of single-circle-pipe freezing projects.