%A ChangWei Xie, William A. Gough
%T Comments on thaw-freeze algorithms for multilayered soil, using the Stefan equation
%0 Journal Article
%D 2017
%J Sciences in Cold and Arid Regions
%R 10.3724/SP.J.1226.2017.00525
%P 525-533
%V 9
%N 6
%U {http://www.scar.ac.cn/CN/abstract/article_48.shtml}
%8 2017-12-01
%X The Stefan equation provides a useful and widely used method for predicting the depth of thawing and freezing in a soil where little site-specific information is available. The original Stefan equation was derived for only a homogeneous medium, and some algorithms have been developed for its use in a multilayered system. However, although the Stefan equation was derived more than 100 years ago, there is not a unified understanding for its use in a multilayered system. This paper examines the use of the Stefan equation in multilayered soil, based on comparing three algorithms (JL-algorithm, NM-algorithm, and XG-algorithm). We conclude that the JL and NM algorithms are incorrect, as they arose from flawed mathematical derivations. Both of these algorithms failed to recognize that the thawing depth in a multilayered soil is a piecewise function and not a continuous function of time. This work asserts that the XG-algorithm is a correct and rigorous method to determine the freezing-thawing fronts in multilayered soil.