Analytical solution for classical one-dimensional thaw consolidation model considering unfrozen water effect and time-varying load

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.