The surface of ice exhibits the swath of phase-transition phenomena common to all materials and as such it acts as an ideal test bed of both theory and experiment. It is readily available, transparent, optically birefringent, and probing it in the laboratory does not require cryogenics or ultrahigh vacuum apparatus. Systematic study reveals the range of critical phenomena, equilibrium and nonequilibrium phase-transitions, and, most relevant to this review, premelting, that are traditionally studied in more simply bound solids. While this makes investigation of ice as a material appealing from the perspective of the physicist, its ubiquity and importance in the natural environment also make ice compelling to a broad range of disciplines in the Earth and planetary sciences. In this review we describe the physics of the premelting of ice and its relationship with the behavior of other materials more familiar to the condensed-matter community. A number of the many tendrils of the basic phenomena as they play out on land, in the oceans, and throughout the atmosphere and biosphere are developed.

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The physics of premelted ice and its geophysical consequences

Several mechanisms can extend the equilibrium domain of a liquid phase into the solid region of the normal phase diagram. The causes of premelting, which include surface melting, interface curvature and substrate disorder, occur in all types of substances, including H2O. In the case of H2O, premelting can have important environmental consequences, among which are the heaving of frozen ground, breakdown of rock and concrete, sintering of snow, flow of glaciers, scavenging of atmospheric trace gases by snow and ice, and the electrification of thunderclouds. The article reviews the basic mechanisms of premelting and discusses their roles in the environmental phenomena. The principal results of numerous studies are reviewed, and trends in current research are outlined.

http://iopscience.iop.org/article/10.1088/0034-4885/58/1/003/pdf

The premelting of ice and its environmental consequences

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.

Exploration of a Rigid Ice Model of Frost Heave

The range of problems that geotechnical engineers must face is increasing in complexity and scope. Often, complexity arises from the interaction between the soil and the environment – the topic of this lecture. To deal with this type of problem, the classical soil mechanics formulation is progressively generalised in order to incorporate the effects of new phenomena and new variables on soil behaviour. Recent advances in unsaturated soil mechanics are presented first: it is shown that they provide a consistent framework for understanding the engineering behaviour of unsaturated soils, and the effects of suction and moisture changes. Building on those developments, soil behaviour is further explored by considering thermal effects for two opposite cases: high temperatures, associated with the problem of storage and disposal of high-level radioactive waste; and low temperatures in problems of freezing ground. Finally, the lecture examines some issues related to chemical effects on soils and rocks, focusing i...

Soil–environment interactions in geotechnical engineering

When subjected to a uniform cooling below the freezing point a water-infiltrated porous material undergoes a cryo-deformation resulting from various combined actions: (i) the difference of density between the liquid water and the ice crystal, which results in the initial build-up of an in-pore pressure at the onset of crystallization; (ii) the interfacial effects arising between the different constituents, which eventually govern the crystallization process in connection with the pore access radius distribution; (iii) the drainage of the liquid water expelled from the freezing sites towards the air voids; (iv) the cryo-suction process, which drives liquid water towards the already frozen pores as the temperature further decreases; (v) the thermomechanical coupling between the solid matrix, the liquid water and the ice crystal. We work out a comprehensive theory able to encompass this whole set of actions. A macroscopic approach first provides the constitutive equations of freezing poroelastic materials, including the interfacial energy effects. This approach reveals the existence of a thermodynamic state function—namely the liquid saturation degree as a function of the temperature only. The macroscopic ice-dependent poroelastic properties are then upscaled from the knowledge of the elastic properties of the solid matrix, of the pore access radius distribution, and of the capillary curve. The theory is finally illustrated by analysing quantitatively the effects of the cooling rate and of the pore radius distribution upon the cryo-deformation of water-infiltrated porous materials. The theory succeeds in accounting for the experimentally observed shrinkage of embedded air voids, while predicting the partial melting of the ice already formed when the cooling suddenly stops.

Poromechanics of freezing materials

: Frost heave is analyzed for the common case in which some ice penetrates the soil. In this situation, heave is due to the accumulation of soil-free ice just within the frozen zone, behind a frozen fringe of finite thickness. Heat and mass transport within and across that fringe are crucial processes in the dynamics of heave. This analysis concentrates on activity within the fringe, also connecting that activity to heat and mass flows in the more frozen and unfrozen zones. Each component in a set of governing differential equations is developed from rational physics and thermodynamics, using previous experimental work. It is assumed that the soil ice grows through interconnected interstices; hence it constitutes and can move as a rigid body. When the assumption is translated into mathematical terms, it completes the governing equations. The model resulting from these considerations is a one-dimensional finite element computer program that solves the equations for arbitrary initial and boundary conditions. The model is used to simulate the heave history of a hypothetical soil column frozen unidirectionally and subjected to a surcharge. The results are gratifying in that they predict qualitatively the characteristics of numerous laboratory observations. Some questions about the completeness of the theory remain, and strict verification of the model awaits further experimentation and better parameter identification.

Numerical Solutions for a Rigid-Ice Model of Secondary Frost Heave,

Visions of a single mobile substance present as two rival phases more or less cleanly segregated by capillarity between rival strata of a serially porous medium (a “discontinuum”) imply explicit testable equations for externally measured capillary thermo-osmotic pressures and capillary thermo-osmosis, with implications for thermomechanical consolidation, dilation, and cracking. Underlying equations assume fluid phases governed by the laws of surface tension and viscous flow, moderated by an appropriate form of the Clapeyron equation. Derived phenomenological coefficients in macroscopic equations for steady coupled transports of mass and heat include only path-length-weighted fluid and heat conductances for rival domains and the heat of phase transformation. Expressions emphasize the phase-specific nature of Onsager's reciprocity principle and apply to serial media held within permeameters set up for measuring either “isothermal” or “adiabatic” mass transport or held within sealed containers intended for measurements of “thermal conductivities.” Results clarify unmet challenges facing modelers of similar processes and attributes in randomly porous media.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/98WR00728

Robert D. Miller

Papers

Exploration of a Rigid Ice Model of Frost Heave

Numerical Solutions for a Rigid-Ice Model of Secondary Frost Heave,

Capillary thermomechanics in serially porous media, with implications for randomly porous media