Frost heave in freezing soils: A quasi-static model for ice lens growth

Abstract

Frost heave can have a very destructive impact on infrastructure in permafrost regions. The complexity of nanoscale ice-mineral interactions and their relation to the macroscale frost heave phenomenon make ice lens growth modeling an interesting but challenging task. Taking into account the limiting assumption of the constant segregation temperature in the segregation potential model, we propose here a new quasi-static model for ice lens growth under a time varying temperature based on the water activity criterion. In this model, the conventional pressure potential gradient in Darcy's law is replaced by a water activity based chemical potential gradient for the calculation of water flow velocity, which provides a better prediction of ice lens growth and is useful to describe the ice nucleation and the state of water at a specific temperature. Moreover, based on the analysis of the new developed model, a mathematical description of the segregation potential is provided here. The modified Kozeny-Carman equation is applied to determine the water permeability of a given soil. In our new model, the effects of the equivalent water pressure are taken into account to modify the freezing characteristic function. Hence, the temperature- and equivalent water pressure- dependent hydraulic permeability in the frozen fringe is mathematically determined and improved. By coupling the quasi-static model with the modified hydraulic permeability function, the numerical calculation of ice lens growth is validated based on the experimental data of the temperature of the ice lens measured in the laboratory. The prediction of ice lens growth using the proposed method contributes and facilitates the simplified calculation of frost heave in the field and/or laboratory scenarios at a quasi-static state, and thus enables a better understanding of phase change and fluid flow in partially frozen granular media (soils).