A Generalized Secondary Frost Heave Model

A generalized model for secondary frost heave is developed based on the one-dimensional model of O'Neill and Miller. Secondary frost heave arises during freezing owing to cryostatic suction effects that can increase the upward water permeation to facilitate ice-lens growth and increased heave. Nondimensionalization and scaling are used to simplify the model equations and to identify a dimensionless group whose magnitude characterizes the nature of secondary frost heave in different soils. Computational problems encountered by O'Neill and Miller are avoided by recognizing the boundary layer nature of the water permeation and by reducing the frozen fringe, wherein freezing and ice-lens growth occur, to a moving planar boundary across which jump boundary conditions are prescribed. This generalized model can predict the frost heave behavior of different soils. Its predictions for the initiation time, spacing, and thickness of sequential ice lenses agree with the results of qualitative observations. This model also can be used to predict differential frost heave and hence may be able to predict the occurrence of patterned ground forms influenced by secondary frost heave.