Cryo-Hydrogeological Dynamics of a Variable-Aperture Fracture Under Freeze-Thaw Conditions

Cryo-hydrogeological behaviour of groundwater flow through a saturated variable-aperture fracture is numerically simulated in three dimensions. Simulations are carried out using the finite element Heatflow/Smoker model for groundwater flow and heat transport with freeze/thaw and latent heat. We test the effects of fracture aperture distributions and thermo-hydraulic conditions on fluid flow and heat transport through a thawing fracture within an initially frozen porous matrix, and evaluate the relationships between the pre-defined (input) local-scale freezing functions (FFs) and the derived mean (fracture-averaged) freezing functions. Simulations are carried out on a 1x1x0.4 m³ porous medium block with a single variable-aperture horizontal fracture under variable temperature conditions and hydrological forcings, and fracture statistical variables. Results show that hydraulic conditions play a more important role than fracture geometry in determining how fractures open and thaw as heat flows through the system. Derived mean freezing functions differ from the input local-scale freezing functions because of a complex interaction among several factors including heat loss to the matrix, the influence of the hydraulic gradient on fluid flow, and variations in fracture aperture. These elements combine in complex ways, affecting how temperature and unfrozen water content evolve in space and time. Nevertheless, for mean negative temperatures, the simulated mean FFs for a fracture tend to be similar to the local-scale FFs, suggesting applicability to larger fracture systems which assume metre-scale uniform apertures. Under sufficient hydraulic gradients, variable aperture fields are also crucial as they enable preferential flow which helps keep the system open, while with an equivalent mean aperture, the lack of variability results in more uniform cooling and freezing, causing the system to close more rapidly. The results also underscore the pivotal role of the frozen matrix as a thermal sink especially in scenarios characterized by extensive cooling and fracture closure, reducing advective heat transport through the fracture, and steering the system toward a conduction-dominated regime. The numerical simulations enhance our understanding of internal flow dynamics during freezing and thawing in variable-aperture fractures, providing valuable insights for experimental investigations and larger-scale numerical simulations.