Applicability of two-phase modeling with compression experiments for snow compaction dynamics

Compaction is a rheological process which, in many fields, has been modeled using a 1-D two-phase continuum framework. However, only recently has it been posed as a promising method for modeling the densification of snow into glacial ice, where the conventional model is empirical or semi-empirical. Here, we explore the applicability of a standard one-dimensional two-phase continuum framework for modeling snow compaction through theoretical and laboratory methods by analyzing and simplifying theory, and then experimentally constraining the model coefficient. We find in our theory analysis that the limit of slow compaction is reached such that air evacuation during the compaction process does not impede the deformation of ice grains. Model-data comparisons are performed using data from a series of uniaxial compression experiments of snow samples under a range of compaction rates (1 × 10⁻⁶ to 3 × 10⁻⁵ m s⁻¹) and densities (250 to 450 kg m⁻³) at −10° and –20 °C, which show good measures of fit ($r^2$>0.996). By defining a linear effective pressure function, we then constrain the model parameter by tuning against the data. While our model follows proper simplification of theory, the temperature and microstructural dependence are determined exclusively by the model parameter in a rheological formulation with the strain rate, and much scatter still exists. Within the selected range of compaction rates and densities, our results indicate that a 1-D two-phase model with a continuum framework alone does not likely capture important processes involved in the compaction process.