HR: 0800h
AN: C31A-1120    [Abstracts]
TI: The Stefan Problem Revisited: A Continuum Model of Frost Heave
AU: * Rempel, A w
EM: rempel@uoregon.edu
AF: University of Oregon, Department of Geological Sciences, Eugene, OR 97403
AB: The classical Stefan problem describes the motion of a solidification front through a uniform half-space in response to a step change in temperature on its boundary. The predictions of such a model can be applied quite accurately to the freezing of water in a porous medium so long as the pore geometry remains unaltered by the passing solidification front. It is observed, however, that in fine-grained porous media, ice has a tendency to form in segregated horizontal bands, known as ice lenses, that disrupt the regular pattern of heat flow through their enhanced consumption of latent heat. This process, known as frost heave, causes significant ground deformation in regions subject to prolonged freezing, and is one of the most important weathering processes in polar and alpine regions. Recent improvements to our understanding of the mechanics of ice lens nucleation and growth are applied here to predict the conditions and characteristics of frost heave in a step-freezing configuration. We find that heave is possible only when the imposed effective stress -- the overburden less the fluid pressure -- is less than P_max≡ L/T_m[φ S_s(T_m-T_s)-∫_Ts^T_fφ S_s dT], where L is the latent heat of fusion per unit volume of ice, T_m is the normal bulk melting temperature, φ is the pore volume fraction, S_s(T) is the ice saturation level, and T_s is the surface temperature. At lower overburdens, a lens forms and we track the motion of its boundary and the evolving thickness of the partially frozen fringe beneath. We identify parameter regimes in which: 1. the lens grows more rapidly than the square root of time, leading eventually to the disappearance of the frozen fringe and the slowly decaying growth of a solitary lens; 2. the lens growth is slower than √t, its temperature decreases and new lenses are initiated to form a sequence of lenses; and 3. the lens grows in proportion to √t and the system evolution closely mirrors that of the classical Stefan problem.
DE: 0700 CRYOSPHERE (4540)
DE: 0704 Seasonally frozen ground
DE: 0706 Active layer
DE: 0710 Periglacial processes
DE: 0738 Ice (1863)
SC: Cryosphere [C]
MN: Fall Meeting 2005