• A zonal geometric equivalence method simplifies the freezing curtain geometry. • An analytical steady-state solution is developed for dual-pipe freezing under seepage. • Freezing wall closure time increases with seepage velocity, with a critical limit. • Outer isotherms are heart-shaped, with flattened radial temperature gradients. Under the influence of a seepage field, the artificial freezing curtain adopts a distinct asymmetrical shape due to the combined effects of convective heat transfer induced by groundwater flow and conductive heat transfer from the freezing pipes. This study investigates the temperature field of a dual-pipe freezing system configured in a linear arrangement. Based on steady-state temperature field theory, a zonal geometric equivalence method is proposed to simplify the complex geometry of the freezing curtain. Using this approach, analytical solutions for the steady-state temperature field of an asymmetric frozen curtain in fractured rock under seepage conditions, along with formulas for calculating its thickness and average temperature, were derived. A coupled seepage–temperature numerical model for artificial freezing in fractured rock was developed using COMSOL Multiphysics to validate the accuracy and applicability of the analytical solution. The results indicated that the isotherms exhibited a distinctive “heart-shaped” pattern at the outer edge of the freezing front. The calculated temperatures along key axes showed strong agreement with the numerical simulation results, confirming the validity of the analytical solution. The time required for the frozen wall to form a closed ring increased with fracture water velocity, and a critical velocity was identified beyond which complete closure could not occur. Overall, the steady-state analytical solution developed in this study accurately captured the temperature distribution of artificial freezing under coupled seepage–thermal conditions and provides a valuable reference for analyzing dual-pipe freezing temperature fields in fractured, highly permeable formations with strong seepage.
Shi et al. (Sat,) studied this question.