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Ice-lens formation and geometrical supercooling in soils and other colloidal materials

Robert W. Style, Stephen S. L. Peppin, Alan C. F. Cocks, and J. S. Wettlaufer
Phys. Rev. E 84, 041402 – Published 14 October 2011
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Abstract

We present a physically intuitive model of ice-lens formation and growth during the freezing of soils and other dense, particulate suspensions. Motivated by experimental evidence, we consider the growth of an ice-filled crack in a freezing soil. At low temperatures, ice in the crack exerts large pressures on the crack walls that will eventually cause the crack to split open. We show that the crack will then propagate across the soil to form a new lens. The process is controlled by two factors: the cohesion of the soil and the geometrical supercooling of the water in the soil, a new concept introduced to measure the energy available to form a new ice lens. When the supercooling exceeds a critical amount (proportional to the cohesive strength of the soil) a new ice lens forms. This condition for ice-lens formation and growth does not appeal to any ad hoc, empirical assumptions, and explains how periodic ice lenses can form with or without the presence of a frozen fringe. The proposed mechanism is in good agreement with experiments, in particular explaining ice-lens pattern formation and surges in heave rate associated with the growth of new lenses. Importantly for systems with no frozen fringe, ice-lens formation and frost heave can be predicted given only the unfrozen properties of the soil. We use our theory to estimate ice-lens growth temperatures obtaining quantitative agreement with the limited experimental data that are currently available. Finally we suggest experiments that might be performed in order to verify this theory in more detail. The theory is generalizable to complex natural-soil scenarios and should therefore be useful in the prediction of macroscopic frost-heave rates.

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  • Received 26 July 2011

DOI:https://doi.org/10.1103/PhysRevE.84.041402

©2011 American Physical Society

Authors & Affiliations

Robert W. Style* and Stephen S. L. Peppin

  • Oxford Centre for Collaborative Applied Mathematics, Mathematical Institute, University of Oxford, Oxford, UK

Alan C. F. Cocks

  • Department of Engineering Science, University of Oxford, Oxford, UK

J. S. Wettlaufer

  • Department of Geology and Geophysics, Department of Physics and Program in Applied Mathematics, Yale University, New Haven, Connecticut, USA and NORDITA, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden

  • *style@maths.ox.ac.uk

See Also

The Menace of Underground Ice

Don Monroe
Phys. Rev. Focus 28, 15 (2011)

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Issue

Vol. 84, Iss. 4 — October 2011

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