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We present a finite-element-based cohesive zone model for simulating the nonlinear fracture process driving the propagation of water-filled surface crevasses in floating ice tongues. The fracture process is captured using an interface element whose constitutive behavior is described by a bilinear cohesive law, and the bulk rheology of ice is described by a nonlinear elasto-viscoplastic model. The additional loading due to meltwater pressure within the crevasse is incorporated by combining the ideas of poromechanics and damage mechanics.We performed several numerical studies to explore the parametric sensitivity of surface crevasse depth to ice rheology, cohesive strength, density, and temperature for different levels of meltwater depth.We find that viscous (creep) strain accumulation promotes crevasse propagation and that surface crevasses propagate deeper in ice shelves/tongues if we consider depth-varying ice density and temperature profiles. Therefore, ice flow models must account for depth-varying density and temperature-dependent viscosity to appropriately describe calving outcomes. 

Abstract Hydrofracturing can enhance the depth to which crevasses propagate and, in some cases, allow full depth crevasse penetration and iceberg detachment. However, many existing crevasse models either do not fully account for the stress field driving the hydrofracture process and/or treat glacier ice as elastic, neglecting the non-linear viscous rheology. Here, we present a non-local continuum poro-damage mechanics (CPDM) model for hydrofracturing and implement it within a full Stokes finite element formulation. We use the CPDM model to simulate the propagation of water-filled crevasses in idealized grounded glaciers, and compare crevasse depths predicted by this model with those from linear elastic fracture mechanics (LEFM) and zero stress models. We find that the CPDM model is in good agreement with the LEFM model for isolated crevasses and with the zero stress model for closely-spaced crevasses, until the glacier approaches buoyancy. When the glacier approaches buoyancy, we find that the CPDM model does not allow the propagation of water-filled crevasses due to the much smaller size of the tensile stress region concentrated near the crevasse tip. Our study suggests that the combination of non-linear viscous and damage processes in ice near the tip of a water-filled crevasse can alter calving outcomes. 

ABSTRACT We investigate the appropriateness of calving or crevasse models from the literature using linear elastic fracture mechanics (LEFM). To this end, we compare LEFM model-predicted stress intensity factors (SIFs) against numerically computed SIFs using the displacement correlation method in conjunction with the finite element method. We present several benchmark simulations wherein we calculate the SIF at the tips of water-filled surface and basal crevasses penetrating through rectangular ice slabs under different boundary conditions, including grounded and floating conditions. Our simulation results indicate that the basal boundary condition significantly influences the SIF at the crevasse tips. We find that the existing calving models using LEFM are not generally accurate for evaluating SIFs in grounded glaciers or floating ice shelves. We also illustrate that using the ‘single edge crack’ weight function in the LEFM formulations may be appropriate for predicting calving from floating ice shelves, owing to the low fracture toughness of ice; whereas, using the ‘double edge crack’ or ‘central through crack’ weight functions is more appropriate for predicting calving from grounded glaciers. To conclude, we recommend using the displacement correlation method for SIF evaluation in real glaciers and ice shelves with complex geometries and boundary conditions.