Theoretical Studies of Ice Segregation in Soil

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 ₁and K ₁are 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.