Practical models describing hysteresis behavior of unfrozen water in frozen soil based on similarity analysis

Abstract

Hysteresis behavior of unfrozen water in frozen soil is investigated, and practical models which predict the soil thawing characteristic (STC) curve from the soil freezing characteristic (SFC) curve are developed. By comparing the Gibbs-Thomson equation in frozen soil with the Young-Laplace equation in unsaturated soil, a similarity theory is established, which indicates that formulas and models describing liquid water in unsaturated soil can be applied to describe unfrozen water in frozen soil using the same form. Five models describing hysteresis behavior of unfrozen water are then developed from theories of unsaturated soil. Comparisons between model predictions and measured results in literature are conducted. The predicted results of three models are in good agreement with measured data, and these three models are derived from the formulas of Pham et al. (2003), Van Genuchten (1980) and Fredlund and Xing (1994), respectively. The concept of average relative error is introduced to investigate the accuracy of different models in a quantitative way, and the results show that the model derived from the formula of Fredlund and Xing (1994) has the best performance in describing hysteresis behavior of unfrozen water in frozen soil.