Three-dimensional frost heave evaluation based on practical Takashi's equation

- We propose a practical method to expand 1D frost heave model to 3D successfully.
- We compare the stress values between experiment and 3D simulation.
- We demonstrate this practical method by comparisons with experiments.
- We explain the physical meaning of this expansion method.

Frost heave is the main cause of damage to structures in cold regions. To predict frost heave, various researches have been conducted, including evaluation of its theoretical mechanism, derivation of practical estimation equations, and large-scale experiments. Most of the currently available practical prediction methods are derived for one-dimensional frost heave and a large amount of valuable experimental data have been accumulated. However, one-dimensional analysis might not provide adequate information regarding complicated engineering situations. Therefore, three-dimensional frost heave analysis is required urgently. While planning to extend the original one-dimensional practical equations to three-dimensional space, the first issue encountered is how to deal with frost heave distribution. To solve this issue, authors have proposed a simple but effective method to allocate frost heave ratio to multiple dimensions. In this study, the practical Takashi's equation, derived from numerous one-dimensional indoor frost heave tests, is adopted as the theoretical foundation for frost heave estimation. This equation can predict the frost heave ratio in the freezing direction based on the freezing rate and constraining stress in the freezing direction. To obtain these two factors, we combine thermal and mechanical analyses by using a finite element method. In addition, with regard to the frost heave distribution in frozen soil, an anisotropic parameter β is proposed to distribute the frost heave ratio in the freezing direction and its transverse directions. By adjusting the value of this parameter, a numerical simulation can be made to reflect the actual situation well. Based on this assumed parameter, an indoor frost heave test is performed and an assumed example is considered and discussed. The applicability of the proposed method in three-dimensional space is demonstrated, and the physical meaning of the anisotropic parameter is discussed. This method can extend the applicability of most one-dimensional practical methods for evaluating frost heave in three-dimensional space.