Mathematical model explains frost heave in granular soils

This study developed a generalized quasi-static mathematical model to describe frost heave in granular materials and applied it to the unidirectional freezing of a finite soil column. The model reproduces freezing behavior across a wide range of conditions, including all overburden pressures and the case where the frozen fringe disappears at low pressures.

Model predictions agree with published experimental data and emphasize the importance of hydraulic conductivity and the link between suction, temperature and ice content in the frozen fringe. The method is stable and robust, and further progress depends on measuring hydraulic conductivity within the frozen fringe.

What the study examined

The research built a generalized quasi-static mathematical model to represent freezing in granular materials, focusing on the zone below the lowest ice lens known as the frozen fringe. The work traced development of this approach and applied it to one-dimensional freezing in a finite soil column.

The effort aimed to make a simpler, computationally tractable alternative to more complex formulations, while retaining key features of prevailing theories of ice segregation and secondary heave.

Key findings

The model successfully predicts freezing behavior under a wide range of conditions and is applicable to all overburden pressures, including zero. At low overburdens the frozen fringe can disappear, yet the model continues to represent the system through to its final equilibrium state.

• Predictions from the model match published experimental data, supporting the underlying theory used to represent ice growth and soil response.
• Parametric studies highlight the crucial role of hydraulic conductivity and the relationship among suction, temperature and ice content inside the frozen fringe.
• Simulations show relatively low sensitivity to variations in thermal conductivity.

Why it matters

The model provides a robust and stable computational framework for studying freezing in granular media and for testing ideas about ice lens formation and secondary heave. Agreement with experimental results lends confidence in the approach and in the theoretical representation of the partially frozen region.

Future application of the model depends on improved experimental determination of hydraulic conductivity inside the frozen fringe, which would allow more complete use of the method for prediction and further study.