Abstract A one-dimensional thawing process of frozen soil under a uniform initial temperature and a step increase of boundary temperature is investigated. The classical thaw consolidation model developed by Morgenstern and Nixon is extended by including unfrozen water in frozen soil and time-varying loads under two types of drainage boundaries. It is proven that the thawing front advances in proportion to the square root of time even with the unfrozen water effect included. It is also indicated that a certain form of superposition principle is applicable to the consolidation process even with the presence of a moving interface. An analytical solution for the external load in the form of a power function is developed using the similarity transformation technique, and this solution can be applied to construct the analytical solution for an arbitrary external load using the superposition principle. A numerical solution for the problem is also developed. Computational examples are presented. First, the correctness of the analytical solution and the numerical solution is verified. Second, thaw consolidation processes under an instant load and a corresponding exponential load are compared and discussed. Third, the effects of unfrozen water and drainage types on the thaw consolidation behavior are investigated.

中文翻译：

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考虑不冻水效应和时变载荷的经典一维融结固结模型解析解

摘要 研究了初始温度均匀、边界温度逐步升高的冻土一维解冻过程。Morgenstern 和 Nixon 开发的经典解冻固结模型通过在两种类型的排水边界下包括冻土中的未冻结水和时变载荷进行扩展。事实证明，即使包括解冻水效应，解冻前沿也与时间的平方根成正比。还表明，即使存在移动界面，某种形式的叠加原理也适用于固结过程。使用相似变换技术开发了幂函数形式的外部载荷的解析解，并且该解可用于使用叠加原理构造任意外部载荷的解析解。还开发了该问题的数值解。给出了计算示例。首先验证解析解和数值解的正确性。其次，比较和讨论了瞬时载荷和相应指数载荷下的解冻固结过程。第三，研究了未冻结水和排水类型对解冻固结行为的影响。比较和讨论了瞬时载荷和相应指数载荷下的解冻固结过程。第三，研究了未冻结水和排水类型对解冻固结行为的影响。比较和讨论了瞬时载荷和相应指数载荷下的解冻固结过程。第三，研究了未冻结水和排水类型对解冻固结行为的影响。