ECCOMAS 2024

A Novel Multi-Scale Thermo-Hydro-Mechanical Model for Hydro-Fracture through Ice-Sheets

  • Hageman, Tim (University of Oxford)
  • Martínez-Pañeda, Emilio (University of Oxford)

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Greenland and Antarctic ice-sheets are prone to sudden fracture: Due to increasing temperatures, melting causes water to accumulate at the surface. This water flows into pre-existing crevasses in the ice-sheet, pressurising them and eventually propagating cracks through the full thickness of ice-sheets \cite{bib1}. Throughout this propagation process, the fluid flow produces thermal energy, heating up and melting the surrounding ice, while the cold surrounding the crevasse will leach energy from the fluid-filled fracture trying to freeze it shut and halt propagation. This process is characterised by a large range of length scales: Millimetres of freezing or melting will decide whether cracks with opening apertures of centimetres can propagate through kilometre thick ice-sheets. To fully capture these phenomena, multi-scale methods are required to couple these length-scales in an efficient manner to enable the simulation of glacier-scale problems. Here, a novel multi-scale thermo-hydro-mechanical model will be presented for turbulent flows within propagating crevasses. While the phase-field fracture framework will be utilised, the opening height of the crevasse is reconstructed to accurately capture the capacity of the crevasse \cite{bib2}, fluid flows, and small-scale thermal phenomena. These small-scale phenomena are then up-scaled to perform the role of driving forces for the large-scale crevassing. This scheme is implemented within a finite element framework, in which care is taken to consistently couple the small scale formulation to the global tangent stiffness matrix, resulting in a well-converging and stable scheme. Further stabilisation is applied to prevent ill-conditioning and unconstrained degrees of freedom for the not-yet-fractured ice-sheet, where the low to zero porosity removes capacity terms for the fluid flow equations. While application to supra-glacial lake drainage for ice-sheets is demonstrated within this presentation, the derived scheme is more widely applicable to hydro-fracture problems.