A mathematical model of frost heave in granular materials
An initial review of the various theories of frost heave indicated that Miller's theory of secondary heave was the most convincing. The crucial area in this is the representation of the behaviour in the partially frozen region, known as the frozen fringe, which exists below the lowest ice lens. However, the computational difficulties of the associated mathematical model were likely to limit its application. A simpler quasi-static approach for a semi-infinite region had therefore been initiated, for a restricted range of conditions, by Holden. The work described in this thesis traces the development of the quasi-static approach and its application to the unidirectional freezing of a finite soil column. The resulting generalised model successfully predicts the freezing behaviour under a wide range of conditions. In particular, it is applicable to all overburden pressures, including zero. At low overburdens the frozen fringe disappears, but the final phase is nevertheless modelled to its ultimate equilibrium state. The predictions of the model agree with published experimental data from a number of investigators, and thus support the validity of Miller's theory. Parametric studies with the model have highlighted the importance of the hydraulic conductivity and the relationship between suction, temperature and ice content in the frozen fringe. Simulations are relatively insensitive to variations in thermal conductivity. The model has proved to be robust and stable and should form a sound basis for further studies. However, its full application will depend on the development of experimental techniques to determine the hydraulic conductivity in the frozen fringe.