A thermodynamics-based mathematical model for the frost heave of unsaturated freezing soils

Abstract

A thermodynamics-based mathematical model is presented for unsaturated freezing soils. The proposed model describes the contributions of the film water, capillary water and vapor in unsaturated freezing soils, based on hybrid mixture theory and phase field theory. A new parameter, namely φB, is introduced to describe the freezing state of the capillary water in the pore space. The proposed model can describe the primary and secondary frost heave in a consistent manner. To illustrate the proposed model, expressions for the free energy function and the dissipative potential are formulated. The surface energy potential and the strain energy that is associated with the phase transition of pore fluid are considered. The stress tensors and constitutive relationships are then derived. Finally, the undercooling of the pore fluid and its moisture migration in freezing unsaturated soils are discussed.