考虑水分迁移及相变对温度场影响的渠道冻胀模型

    Frost heave model of canal considering influence of moisture migration and phase transformation on temperature field

    • 摘要: 冬季渠基冻土中水分迁移及相变产生的巨大潜热对温度场影响显著,由此,该文建立了考虑水分迁移与相变潜热的渠基土体冻胀模型。模型将冻土视为低温膨胀性材料,将相变潜热作为材料的等效热容加入热传导方程中;根据Clapeyron方程和达西定律建立饱和冻土冻结锋面处水分迁移表达式,并以迁移水相变潜热作为热传导方程热源项;采用COMSOL对模型算例求解,与不考虑相变和水分迁移的模型比较发现:相变作用对渠道温度场和变形场影响较大,考虑相变后,冻深推进缓慢,且冻深减小,衬砌板变形整体减小,较不考虑相变的模拟结果更接近实际情况,验证了本模型的合理性,为寒区工程冻胀设计提供参考。

       

      Abstract: Abstract: The great latent heat of the water transfer and phase transformation in the winter has a significant effect on the temperature field of the canal base soil. The researches on the freezing-thawing of frozen soil with moisture phase change are mostly based on the road foundation, buried pipe, and so on. The study on frost heave damage of lining canal is relatively less. As the canal is in water-carrying condition for a long time, the moisture content of canal foundation soil is high, especially in excavation canal because of the high groundwater table caused by moisture convergence. Under the preceding special geological conditions, as the canal foundation soil is freezing, not only is the water frozen in situ, but also the unfrozen water migrates to the freezing front and changes phase, and then the temperature field and displacement field in canal foundation are influenced by reason of tremendous latent heat of phase change. Although in some past thermal-mechanics coupling calculations the latent heat of moisture phase change is in consideration, the source of moisture with phase change is not completely considered, the computed results of temperature field are not precise enough, and the inaccuracy of the results can lead to the error of frost heave deformation calculated by thermal-mechanics coupling models. So the article established a frost heave model for canal foundation frozen soil, and the water migration and phase change were taken into account in this model. The model regarded the permafrost as cryogenic expansion material, in which the latent heat was added to the conduction equation, and the latent heat is equivalent heat capacity. According to Clapeyron equation and Darcy's law, the article established the expression of moisture migration of freezing fronts in saturated freezing soil, and the latent heat of moisture migration was as the source term of conduction equation. In order to verify the reasonableness of the model, the COMSOL was used, which is a kind of large-scale software for multi-physics fields coupling for numerical calculation. Results showed that in the temperature and displacement field the phase change produced a great influence. After considering the phase change, the freezing depth of the soil advanced slowly, the maximum frozen depth was 1.5 m, and it was near to the actual value which was 1.8 m. But if the moisture phase change was not in consideration, the calculation value of maximum frozen depth was 3 m, and it was much greater than the actual value. As the moisture phase change was in consideration, the maximum normal displacements on the shady slope, sunny slop and canal bottom were 9.65, 4.81 and 2.0 cm, respectively. Compared with the model not considering phase change, the frost heave model proposed in this article is more in line with the actual situation. So in order to make the calculation results accord well with actual value, the influence of moisture phase change on temperature fields and displacement fields can't be neglected. The present results can provide reference to engineering design for frost heave resistance in cold region.

       

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