Modelling sediment compaction beneath ice lenses during frost heave

Frost heave occurs when the ground swells during freezing conditions due to the growth of ice lenses in the subsurface. The mechanics of ice-infiltrated sediment, or frozen fringe, influences the formation and evolution of ice lenses. As the frozen fringe thickens during freezing, progressive unloading can result in dilation of the pore space and the formation of new ice lenses. Compaction can also occur as water is expelled from the pore space and freezes onto the ice lenses. We introduce a mathematical model for compaction within frozen fringe to explore how internal variability influences the fundamental characteristics of frost heave cycles. At faster freezing rates, compaction below ice lenses can generate complex dynamics and chaos when the frozen fringe follows a consolidation law based solely on the sediment yield stress. The complex oscillations arise because a downward water flux below the compacting zone generates a distributed zone of weakening. We introduce viscous effects into the compaction law through a bulk viscosity to determine how the cycles could be influenced by the creep of ice through the pore space. Localized zones of decompaction in the viscoplastic model can prevent the feedback mechanisms that cause complex oscillations in the perfectly plastic model.