Freezing in porous media is associated with a host of dynamic phenomena
that stem from the presence and mobility of premelted liquid at subzero
temperatures. Accurate assessments of the progressive liquid---ice phase
transition is required for predictive models of frost damage,
glacier---till coupling, and many other cold regions processes, as well
as for evaluating the capacity for water storage in near-surface
extraterrestrial environments. We use a Monte Carlo approach to sample
the pore space in a synthetic 3D packing of poly-dispersed spherical
particles, and evaluate local geometrical constraints that allow us to
assess changes in the relative proportions of pore fluid and ice. By
approximating the phase boundary geometry in fine-grained pores while
considering both the curvature of the liquid---ice interface and wetting
interactions with matrix particles, our model predicts changes in phase
equilibrium in granular media over a broad temperature range, where
present accounting for the colligative effects of chloride and
perchlorate solutes. In addition to formulating the constitutive
behavior needed to better understand properties and processes in frozen
soils, our results also provide insight into other aspects of phase
equilibria in porous media, including the formation of methane hydrates
in permafrost and marine sediments, and the partitioning between liquid
water and vapor in the vadose zone.