General thermomechanical model of freezing soil with numerical applications

Fremond and Mikkola (1991) presented a mathematical model for the freezing of saturated soil based on the principles of continuum mechanics and of macroscopic thermodynamics. In their model, the saturated soil is considered as a mixture of skeleton, liquid water and ice. The constitutive equations of the porous medium are derived by the application of the method of the accompanying local equilibrium state choosing appropriate expressions of the free energy and the dissipation potential.

In this presentation, an application of the general model is described. The objective is to develop a formulation appropriate for numerical treatment. The complete system is reduced to a computationally convenient set of equations without losing its generality. The proposed formulation is considered from the point of view of numerical analysis, and the nature of essential material parameters is explained. The finite element implementation is done in one-dimensional case. Simulations of some experiments have been carried out and the results are presented.