Modeling frost heave in freezing soils

Abstract

A generalized model for secondary frost heave in freezing fine-grained soils is presented. The cryostatic suction effect, which causes an increase in upward water permeation, ice-lens growth during freezing, and, as a consequence, the increase of soil heave, is considered to be the main mechanism of moisture transfer. Although the model in this paper has a number of approaches in common with the model of Fowler and Krantz (1994) it differs in at least several important respects. We recognize the need to determine the distribution of the moisture within the frozen fringe by approximation of the experimental data for the equilibrium unfrozen water content. This distribution is the result of the complicated interaction between water, ice and the mineral skeleton during the freezing process. The generalization of the Clapeyron relation, which is used in the work cited above, only estimates the drop in initial freezing temperature and does not define the connection with the external temperature gradient ∇T, which is responsible for the frost heave process. This very important aspect is discussed in detail in the Introduction to our paper. Another difference is the fact that our solution is based on a dimensionless system of equations. We take into account the ratio Pe/Ste ≠ 1 (where Pe << 1). This approach allows us to obtain both a more general solution as well as analyze frost heave and propagation of the freezing front as they depend upon the convective (Pe) and phase transition (Ste) characteristics (criteria) of the process. The theoretical results derived from our solution of the analysis for fine-grained soils are compared, in good agreement, with experimental investigations and numerical models. A singularity of the solution at the initial point in time is discussed. In this respect the asymptotic solution for short and long times is obtained. The results are compared with both solutions (modeling and asymptotic). The model presented predicts the frost heave and freezing processes in porous media with reasonable accuracy and satisfactorily reflects observed phenomena, and thus can be suitable for engineering practice.