Application of practical one-dimensional frost heave estimation method in two-dimensional situation

Most of the presently available practical frost heave prediction methods were derived from and for one-dimensional (1D) situations. However, the real desire of engineers is a multi-dimensional frost heave analysis. It is convenient to simply accumulate numerous experimental data on original 1D practical methods and then expand them for multi-dimensional applications. However, when such equations are applied to multi-dimensional situations, the first issue encountered is how to deal with the distribution of frost heave. To solve this issue, the authors propose one simple, but effective, method for allocating the frost heave ratio in multi-dimensional spaces. Takashi׳s equation is taken as an example to demonstrate this proposed distribution method. The equation was originally derived from 1D indoor frost heave experiments. It can predict the frost heave ratio in the freezing direction based on the freezing rate and the constraining stress. To obtain these two factors, thermal and mechanical analyses are combined together. With respect to the heat transfer process, the latent heat produced by the phase change of water is carefully evaluated by the equivalent heat capacity method. Concerning the distribution of the frost heave ratio, anisotropic parameter β is proposed to assign the frost heave ratio in the freezing direction and its transverse direction. By adjusting the value of β, the simulation results can very closely reflect the situation in reality. In addition, the authors discuss the relationship between frost heave and anisotropic parameter β in detail. Based on this assumption, the results of indoor frost heave tests and a large-scale field experiment are illustrated to verify this method, which simultaneously provides valuable examples for a multi-dimensional frost heave evaluation.