Exploration of a Rigid Ice Model of Frost Heave

Abstract

A numerical model is explored which simulates frost heave in saturated, granular, air-free, solute-free soil. It is based on equations developed from fundamental thermomechanical considerations and previous laboratory investigations. Although adequate data are lacking for strict experimental verification of the model, we note that simulations produce an overall course of events together with significant specific features which are familiar from laboratory experience. Simulated heave histories show proper sensitivities in the shapes and orders of magnitude of output responses and in the relations between crucial factors such as heave rate, freezing rate, and overburden. ed mathematical models, attempting to reduce uncertainty by including superior representations of relevant physics and thermodynamics. The overall offerings in this domain and many of the underlying concepts are reviewed by O'Neill [1983]. For further discussion of some of the basic concepts and equations adduced below, the reader is referred to this review and to the textbook treatment by Miller [1980]. Among responses to the challenge is what has been called 281 282 O'NEILL AND MILLER: FROST HEAVE MODEL the rigid ice model of frost heave. This model is comprised of a set of macroscopic equations which result from an analysis of the microscopic features of the formation of ice from water within the pores of a soil [Miller, 1978]. At present, the physical formulation is limited to solute-free, air-free soils of negligible compressibility. A simplified set of equations applicable only to very simple quasi steady states has been solved by Miller and Koslow [1980]. A strategy for obtaining numerical solutions of the full set of equations for simple boundary conditions has also been developed [O'Neill and Miller, 1982]. In this paper we expand on the physical basis of that formulation and its mathematical expression and implementation. Improved tactics have produced a more flexible model so that its behavior can be better explored. We report examples of the results of such explorations below. PHASE EQUILIBRIAConcepts of phase equilibrium applicable at a microscopic level are most familiar in the context of water and air in (ice-free) porous media. It is useful to paraphrase these to establish a rationale for the treatment of ice-water equlibria in air-free soil. The adjective microscopic, as used in this paper, refers to scales that are large relative to the dimensions of a single molecule or the length of chemical bonds but small compared to the scale of observation. Relevant scales are those comparable to the dimension of grains, interstices between them, and even "long-range" surface adsorption force fields. A well-known example of the last is the virtual force field that arises if there is a diffuse electrical double layer at a grain surface. In this discussion, no particular model of surface adsorption will be invoked. Instead, we merely use a more general proposition that for whatever reasons, liquid water very close to a grain surface is attract...

A simplified numerical solution of the Miller model of secondary frost heave

“…It is difficult to obtain, from the papers of O'Neill and Miller (1982Miller ( , 1985, all the information required for a quantitative comparison between the full system of equations and the reduced set given here. Instead we try to give a qualitative comparison of our Figs.…”

“…(For a more complete account see for example O'Neill and Miller ( 1985 ) or Fowler and Krantz (1993). ) For simplicity it is usually assumed that the soil matrix is incompressible.…”

“…Numerical solutions are presented and qualitative comparison is made with a numerical solution to the full system of equations given by O'Neill and Miller ( 1985 ). …”

A new method for calculating frost heave including solute effects

“…Under very wet conditions and in weather that promotes rapid freezing, numerous thin layers of ice may form near the soil surface [O'Neill and Miller, 1985]. Smaller-depth increments requiring more computer time would, of course, have to be used in the algorithm proposed here to reproduce that type of result.…”

“…This allowed numerical models of coupled water and heat fluxes to be developed and tested with real data. This approach has gained support O'Neill and Miller, 1985;Guymon et al, 1983].…”