Semi-Analytical Solution for the Steady-State Temperature Field of a Shallow-Buried Twin-Pipe Ground Freezing System

Accurate prediction of the temperature field around shallow-buried freezing pipes is important for the design and assessment of artificial ground freezing systems in shallow tunnel and underground structure construction. This study develops a semi-analytical series solution for the steady-state temperature field around a twin-pipe freezing unit in a semi-infinite domain under Dirichlet boundary conditions. The model assumes steady-state heat conduction in homogeneous and isotropic soil with prescribed pipe wall and ground surface temperatures; transient phase change, groundwater seepage, and thermo-hydro-mechanical coupling are not considered. Conformal mappings are used to transform the original semi-infinite and eccentric domains into bounded circular domains. The temperature field is decomposed into two subproblems by superposition, and the corresponding general solutions are expressed using Fourier series. The unknown coefficients are determined through boundary discretization and the solution of a finite linear algebraic system. The proposed method is compared with ANSYS Fluent results in the transformed domain at six selected points, yielding a pointwise NRMSE of 0.758% at a truncation order of 20. Parametric analyses further illustrate the qualitative sensitivity of the calculated temperature field to different ground surface temperatures, pipe radii, burial depths, and pipe spacings. The proposed method provides a preliminary semi-analytical framework for rapid quasi-steady temperature field estimation and qualitative parameter sensitivity analysis of shallow-buried twin-pipe artificial ground freezing systems.