Capillary bundle model of hydraulic conductivity for frozen soil

• Published in: Water resources research Vol. 44; no. 12
• Main Authors: Watanabe, Kunio, Flury, Markus
• Format: Journal Article
• Language: English
• Published: 01.12.2008
• Subjects: capillarity; frozen soils; groundwater flow; hydraulic conductivity; hydrologic models; ice; mathematical models; sandy soils; saturated flow; saturated hydraulic conductivity; silt loam soils; simulation models; soil temperature; soil water; unsaturated flow; unsaturated hydraulic conductivity
• ISSN: 0043-1397; 1944-7973
• DOI: 10.1029/2008WR007012

We developed a capillary bundle model to describe water flow in frozen soil. We assume that the soil can be represented as a bundle of cylindrical capillaries. We consider that the freezing point in the capillaries is depressed according to the Gibbs-Thomson effect and that when stable ice forms in a capillary, the ice forms in the center of the capillaries, leaving a circular annulus open for liquid water flow. We use the model to demonstrate how the hydraulic conductivity changes as a function of temperature for both saturated and unsaturated soils, using a sand and two silt loam soils as examples. As temperature decreases, more and more ice forms, and the water flux consequently decreases. In frozen soil near 0°C, water predominantly flows through ice-free capillaries, so that the hydraulic conductivity of frozen soil is similar to that of an unfrozen soil with a water content equal to the unfrozen water content of the frozen soil. At low temperatures, however, ice forms in almost all capillaries, and the hydraulic conductivity of frozen soil is greater than that of unfrozen soil with the same water potential.