A constitutive relation for phase partitioning of water in unsaturated frozen soils is proposed. This relation compares well with existing experimental data on unfrozen water content as a function of temperature for different total water content values. A nonisothermal extension of the Richards equation including this formulation is able to reproduce data from two different freezing-soil column experiments.

A new constitutive relationship for phase partitioning of water in frozen soils is proposed. This relationship extends to unsaturated conditions established relationships for gas-free conditions by smoothing a thermodynamically derived relationship to eliminate a jump discontinuity at the freezing temperature. This relationship is shown to compare well with experimental data on unfrozen water content as a function of temperature for different total water content values. Using this new relationship, a modified nonisothermal Richards equation is solved for flow in freezing soil. The results based on this modified Richards equation are shown to compare well with data from two different column experiments.