A mechanism for differential frost heave and its implications for patterned-ground formation

The genesis of some types of patterned ground, including hummocks, frost boils and sorted stone circles, has been attributed to differential frost heave (DFH). However, a theoretical model that adequately describes DFH has yet to be developed and validated. In this paper, we present a mathematical model for the initiation of DFH, and discuss how variations in physical (i.e. soil/vegetation properties) and environmental (i.e. ground/air temperatures) properties affect its occurrence and length scale. Using the Fowler and Krantz multidimensional frost-heave equations, a linear stability analysis and a quasi-steady-state real-time analysis are performed. Results indicate that the following conditions positively affect the spontaneous initiation of DFH: silty soil, small Young's modulus, small non-uniform surface heat transfer or cold uniform surface temperatures, and small freezing depths. The initiating mechanism for DFH is multidimensional heat transfer within the freezing soil. Numerical integration of the linear growth rates indicates that expression of surface patterns can become evident on the 10-100 year time-scale.