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水工建筑物在高寒区具有广泛的应用,因此对高寒区水工建筑物稳定性的研究就显得尤为重要。通过从理论上和实际应用上的分析与研究,指出:(1)非渗流土坝温度场在明确给定条件下可计算热导率微分方程。在非稳定温度条件下以傅立叶方程为理论依据,在稳定温度条件下以拉普拉斯方程为理论依据。主要的解决方法有:图表分析法、数值有限差分法、数值法;(2)自然冻结大坝在非恒温状况可用保角映射法、热平衡法、热液建模法。在恒温状况下可用保角映射法、热平衡法;(3)人工冻结大坝冻结钻孔周围土壤冻结问题的数学公式由N.A.Charny提出,公式为d~2t/dx~2+dt/rdr=0。还有众多学者也对此问题的解决提供了方案。
Hydraulic structures have a wide range of applications in the alpine region, so the study on the stability of the hydraulic structures in the alpine region becomes more and more important. Through the analysis and research in theory and practice, it is pointed out that: (1) The differential equations of thermal conductivity can be calculated under the given conditions in the temperature field of non-seepage dam. Under the condition of unstable temperature, based on the Fourier equation, Laplace equation is taken as a theoretical basis under the condition of stable temperature. The main solutions are: chart analysis, numerical finite difference method, numerical method; (2) natural freezing dam can be used in non-isothermal conformal mapping method, thermal equilibrium method, hydrothermal modeling method. Conformal mapping method and thermal equilibrium method can be used at constant temperature; (3) Mathematical formula of soil freezing problem around freezing freezing hole of artificial freezing dam is proposed by NACharny, the formula is d ~ 2t / dx ~ 2 + dt / rdr = 0 . There are many scholars also provide a solution to this problem.