Premelting dynamics in a continuum model of frost heave

Frost heave is the process by which the freezing of water-saturated soil causes the deformation and upward thrust of the ground surface. We describe the fundamental interactions between phase change and fluid flow in partially frozen, saturated porous media (soils) that are responsible for frost heave. Water remains only partially frozen in a porous medium at temperatures below $0\,^\circ$C owing both to the depression of the freezing temperature at curved phase boundaries and to interfacial premelting caused by long-range intermolecular forces. We show that while the former contributes to the geometry of fluid pathways, it is solely the latter effect that generates the forces necessary for frost heave. We develop a simple model describing the formation and evolution of the ice lenses (layers of ice devoid of soil particles) that drive heave, based on integral force balances. We determine conditions under which either (i) a single ice lens propagates with no leading frozen fringe, or (ii) a single, propagating ice lens is separated from unfrozen soil by a partially frozen fringe, or (iii) multiple ice lenses form.

[1]  M. Worster,et al.  Interfacial premelting and the thermomolecular force: thermodynamic buoyancy. , 2001, Physical review letters.

[2]  J. C. Brice,et al.  The Growth of Crystals from the Melt , 1967 .

[3]  Wettlaufer,et al.  Dynamics of premelted films: Frost heave in a capillary. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[4]  M. Mizoguchi,et al.  Ice configuration near a growing ice lens in a freezing porous medium consisting of micro glass particles , 2000 .

[5]  D. H. Everett.  The thermodynamics of frost damage to porous solids , 1961 .

[6]  Sing,et al.  Frost heave in argon , 2000, Physical review letters.

[7]  U. Raviv,et al.  Fluidity of Bound Hydration Layers , 2002, Science.

[8]  Gunnar Beskow,et al.  Soil freezing and frost heaving with special application to roads and railroads : with a special supplement for the English translation of progress form 1935 to 1946 , 1948 .

[9]  J. Indekeu.  INTRODUCTION TO WETTING PHENOMENA , 1995 .

[10]  J. Wettlaufer.  Ice surfaces: macroscopic effects of microscopic structure , 1999, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[11]  M. Worster,et al.  The interaction between a particle and an advancing solidification front , 1999 .

[12]  Andrew C. Fowler,et al.  Mathematical Models in the Applied Sciences , 1997 .

[13]  R. R. Gilpin,et al.  A model of the “liquid-like” layer between ice and a substrate with applications to wire regelation and particle migration , 1979 .

[14]  S. Taber.  The Mechanics of Frost Heaving , 1930, The Journal of Geology.

[15]  John S. Wettlaufer,et al.  The premelting of ice and its environmental consequences , 1995 .

[16]  M. Vignes-Adler.  On the origin of the water aspiration in a freezing dispersed medium , 1977 .

[17]  J. G. Dash,et al.  Thermomolecular Pressure in Surface Melting: Motivation for Frost Heave , 1989, Science.

[18]  G. Ewing,et al.  Interfacial melting of thin ice films: An infrared study , 2002 .

[19]  O. M. Phillips,et al.  Flow and Reactions in Permeable Rocks , 1991 .

[20]  Wilen,et al.  A theory of premelting dynamics for all power law forces. , 1996, Physical review letters.

[21]  A. Rempela,et al.  Particle trapping at an advancing solidification front with interfacial-curvature effects , 2001 .

[22]  M. Mizoguchi,et al.  MICROSCOPIC OBSERVATION OF ICE LENSING AND FROST HEAVE IN GLASS BEADS , 1998 .

[23]  M. Mizoguchi,et al.  Amount of unfrozen water in frozen porous media saturated with solution , 2002 .

[24]  S. Taber,et al.  Frost Heaving , 1929, The Journal of Geology.

[25]  J. Cahn,et al.  Theory of ice premelting in monosized powders , 1992 .

[26]  M. Baker,et al.  Charge transfer in thunderstorms and the surface melting of ice , 1989 .

[27]  A. Fowler.  Secondary frost heave in freezing soils , 1989 .

[28]  B. Derjaguin,et al.  The theory of frost heaving , 1978 .

[29]  J. Wettlaufer.  Impurity Effects in the Premelting of Ice , 1999 .

[30]  Kevin O'Neill,et al.  Exploration of a Rigid Ice Model of Frost Heave , 1985 .

[31]  Wilen,et al.  Frost heave dynamics at a single crystal interface. , 1995, Physical review letters.

[32]  M. Hiroi,et al.  Frost heave in He , 1995 .

[33]  R. R. Gilpin.  A Model for the Prediction of Ice Lensing and Frost Heave in Soils , 1980 .

[34]  G. Batchelor,et al.  An Introduction to Fluid Dynamics , 1968 .

[35]  S. Herminghaus,et al.  Wetting: Statics and dynamics , 1997 .