Heat-Flow Coupling Law for Freezing a Pipe Reinforcement with Varying Curvatures

Abstract

Using the temperature and seepage field-coupling module within COMSOL Multiphysics software, we examined freezing behavior and its evolving patterns in curved underground freezing pipes. This study employed transient states, with the Darcy’s law and porous-media heat-transfer options activated in the Physical Field Interface of the Physical Field and Variable Selection column. The models were created to establish numerical models of freezing reinforcement for both single and multiple pipes with various curvatures. These models were designed to simulate the evolving temperature and seepage fields of soil under diverse freezing conditions. Subsequently, this research utilized the models to simulate the freezing and consolidation conditions of a shallowly buried tunnel within the context of shallow tunnel conditions. The study reveals that after freezing a single pipe using water flow, the change in thickness of the frozen wall in curved pipes is notably smaller than that in straight pipes. This difference is particularly pronounced in the upstream section. Specifically, at a distance of −2000 mm from the main surface, the change in thickness of the frozen wall in straight pipes exceeds that in s = 7 curved pipes by approximately 350 mm. The smaller the long arc ratio s, the greater the arc of the freezing tube and the better the water-blocking effect. In the multi-pipe freezing model, the s = 7 curved pipes exhibit a frozen-wall thickness approximately 120 mm greater than that of straight pipes at a distance of −2000 mm from the main surface. Under the condition of a shallow buried concealed excavation with surging water, a pipe with a long arc ratio s = 7 arc freezing at 46 d attains a permafrost curtain thickness that is equivalent to that achieved by the straight pipe freezing at 58 d. This reduction in thickness shortens the working period by 12 days, resulting in a more efficient process. The successful application of the freezing method in the water-rich aquifer is expected to be a valuable reference for similar projects in the future.