Mathematical Modeling and Analysis of the Freezing Process of Drainage Channels in Cold Region Tunnels

In cold regions, the frequent occurrence of frost damage seriously affects the safety and stability of tunnel projects during construction and service time. Analyzing the formation mechanism of ice congestion in the drainage channel is of great significance for reducing the risk of frost damage. For this purpose, a mathematical model was proposed in the present work to investigate the freezing properties of water flow in the drainage channel. In this model, the latent heat of the water–ice phase change was taken into account to describe the formation process of frazil ice. Combined with the method of energy conservation, the critical distance of water freezing was derived theoretically. The field experiment and computational fluid dynamics (CFD) simulation were carried out to verify the accuracy and effectiveness of the proposed model. It showed that the estimated critical position of water freezing agreed well with the experimental and simulation results. Subsequently, the effects of hydraulic and thermodynamic factors on the freezing process of water flow were further discussed. As a practical application, the proposed mathematical model is utilized to evaluate the safety of the drainage channel of a railway tunnel in cold regions. The results demonstrate that when the flow discharge is smaller than 2,600 m3/day, there is a risk of ice congestion in the drainage channel within a range of about 960 m from the water outlet. Therefore, freeze-proof measures such as (1) thermal insulation cover plate, (2) electric heat tracing system, and (3) ground-source heat pump system should be employed in this range.