Wu Wentao, Guo Jiaqi, Wang Xiaochuan, Hu Huanmeng, Zhao Pengyu
School of Civil Engineering, Henan Polytechnic University, Jiaozuo, Henan, China.
School of Highway, Chang'an University, Xi'an, Shaanxi, China.
Heliyon. 2024 Aug 22;10(17):e36672. doi: 10.1016/j.heliyon.2024.e36672. eCollection 2024 Sep 15.
The temperature of the surrounding rock in cold-region tunnels is crucial for antifreeze design, and the water-ice phase transition is essential to addressing the temperature field. This paper proposes a refined method that equates the latent heat of the ice-water phase transition to heat capacity and establishes a one-dimensional radial heat transfer model considering phase change. By defining an average thermal diffusivity coefficient through the concept of equal accumulated temperature, this method overcomes the limitations of classical heat transfer theory in directly solving the temperature field of three zone (unfrozen zone, freezing zone and frozen zone). Additionally, by employing the variable separation method and Fourier integral transformation method, the analytical formula for the transient temperature field considering phase change is derived. Then, the analytical solution was verified based on the field data. The results calculated using this method exhibit greater consistency with field temperature data and outperform the modified Stephan formula in determining the maximum frozen depth of the surrounding rock. Finally, the simplified form of the established analytical solution was further discussed. The research results can provide a theoretical basis for the analysis of the temperature field of the surrounding rock of the tunnel in cold regions and its antifreeze design.
寒冷地区隧道围岩温度对于防冻设计至关重要，水 - 冰相变对于解决温度场问题必不可少。本文提出一种将冰水相变潜热等效为热容的精细化方法，并建立了考虑相变的一维径向传热模型。通过采用等效累积温度概念定义平均热扩散系数，该方法克服了经典传热理论在直接求解三区（未冻区、冻结区和已冻区）温度场方面的局限性。此外，通过运用变量分离法和傅里叶积分变换法，推导了考虑相变的瞬态温度场解析公式。然后，基于现场数据对解析解进行了验证。使用该方法计算得到的结果与现场温度数据具有更高的一致性，并且在确定围岩最大冻结深度方面优于修正的斯蒂芬公式。最后，进一步讨论了所建立解析解的简化形式。研究结果可为寒冷地区隧道围岩温度场分析及其防冻设计提供理论依据。
