A stress-based poro-damage phase field model for hydrofracturing of creeping glaciers and ice shelves

Abstract

There is a need for computational models capable of predicting meltwater-assisted crevasse growth in glacial ice. Mass loss from glaciers and ice sheets is the largest contributor to sea-level rise and iceberg calving due to hydrofracture is one of the most prominent yet less understood glacial mass loss processes. To overcome the limitations of empirical and analytical approaches, we here propose a new phase field-based computational framework to simulate crevasse growth in both grounded ice sheets and floating ice shelves. The model incorporates the three elements needed to mechanistically simulate hydrofracture of surface and basal crevasses: (i) a constitutive description incorporating the non-linear viscous rheology of ice, (ii) a phase field formulation capable of capturing cracking phenomena of arbitrary complexity, such as 3D crevasse interaction, and (iii) a poro-damage representation to account for the role of meltwater pressure on crevasse growth. A stress-based phase field model is adopted to reduce the length-scale sensitivity, as needed to tackle the large scales of iceberg calving, and to adequately predict crevasse growth in tensile stress regions of incompressible solids. The potential of the computational framework presented is demonstrated by addressing a number of 2D and 3D case studies, involving single and multiple crevasses, and considering both grounded and floating conditions. The model results show a good agreement with analytical approaches when particularised to the idealised scenarios where these are relevant. More importantly, we demonstrate how the model can be used to provide the first computational predictions of crevasse interactions in floating ice shelves and 3D ice sheets, shedding new light into these phenomena. Also, the creep-assisted nucleation and growth of crevasses is simulated in a realistic geometry, corresponding to the Helheim glacier. The computational framework presented opens new horizons in the modelling of iceberg calving and, due to its ability to incorporate incompressible behaviour, can be readily incorporated into numerical ice sheet models for projecting sea-level rise.