Theoretical Studies of Ice Segregation in Soil

• Published in: Journal of Glaciology
• Main Author: Arakawa, Kiyoshi
• Format: Article in Journal/Newspaper
• Language: English
• Published: Cambridge University Press (CUP) 1966
• Subjects: Earth-Surface Processes; Journal of Glaciology
• Online Access: http://dx.doi.org/10.1017/s0022143000019274; https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000019274

Abstract The mathematical theory of heat conduction is applied to the analysis of ice segregation processes in soil. A diffusion equation is first employed for the flow of soil moisture. Two new quantities, the rate of ice segregation,σ and the segregation efficiency, E , are introduced. The first is the rate of ice growth measured as mass per area per time. The latter is defined as E = σL /( K 1 ∂T 1 / ∂x − K 2 ∂T 2 / ∂x ), where L is the latent heat of fusion of ice, T 1 and K 1 are the temperature and thermal conductivity of frozen soil, and T 2 and K 2 are the temperature and thermal conductivity of unfrozen soil. Three types of soil freezing can be classified in terms of E : freezing of non-frost-susceptible soil ( E = 0), perfect segregation ( E = 1) and imperfect segregation (0 < E < 1). Finally, the mathematical boundary conditions at an advancing frost line are obtained in freezing, frost-susceptible soil ( E ≠ 0). Two parameters related to the structure of soil are pointed out, which seem to be valid criteria of frost susceptibility. The amount of frost-heaving is derived under special conditions.