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 technique of local averaging is applied to obta, in general equations which describe mass and momentum transport in porous media. The averaging is performed without significantly idealizing either the porous medium or the pertinent fluid mechanical relations. The resulting general flow equation is simplified to treat flow of a Newtonian fluid in a slowly deforming solid matrix for two special cases. For flow in an isotropic medium where convective and inertial terms are important, an equation is developed which is dependent only on five medium parameters which could be evaluated by experiment. Flow in an anisotropic medium is also analyzed, and the general equation is reduced to Darcy's law when the convective and inertial terms are neglected.

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Broad-band electromagnetic induction (EMI) methods are promising in the detection and discrimination of subsurface metallic targets. In this paper, the quasi-magnetostatic solution for a conducting and permeable prolate spheroid under arbitrary excitation by a time-harmonic primary field is obtained by using the separation of variables method with vector spheroidal wave functions. Numerical results for the induced dipole moments are presented for uniform axial and transverse excitations, where the primary field is oriented along the major and minor axis of the prolate spheroid, respectively. We show that the EMI frequency responses are sensitive to the orientation and permeability of the spheroid. An approximation is also developed that aims to extend the exact solution to higher frequencies by assuming slight penetration of the primary field into the spheroid. Under this approximation, a system of equations that refers only to the external field expansions is derived. It is shown that, for spheroids with high relative permeability, this approximation is in fact capable of yielding an accurate broad-band response even for highly elongated spheroids.