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1. A non-local continuum poro-damage mechanics model for hydrofracturing of surface crevasses in grounded glaciers

   https://doi.org/10.1017/jog.2020.16  

   Duddu, Ravindra ; Jiménez, Stephen ; Bassis, Jeremy ( June 2020 , Journal of Glaciology)

   null (Ed.)

   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. 

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2. Across the Great Divide: The Flow-to-Fracture Transition and the Future of the West Antarctic Ice Sheet

   Alley, R. ( December 2018 , AGU Fall Meeting)

   Physical understanding, modeling, and available data indicate that sufficient warming and retreat of Thwaites Glacier, West Antarctica will remove its ice shelf and generate a calving cliff taller than any extant calving fronts, and that beyond some threshold this will generate faster retreat than any now observed. Persistent ice shelves are restricted to cold environments. Ice-shelf removal has been observed in response to atmospheric warming, with an important role for meltwater wedging open crevasses, and in response to oceanic warming, by mechanisms that are not fully characterized. Some marine-terminating glaciers lacking ice shelves “calve” from cliffs that are grounded at sea level or in relatively shallow water, but more-vigorous flows advance until the ice is close to flotation before calving. For these vigorous flows, a calving event shifts the ice front to a position that is slightly too thick to float, and generates a stress imbalance that causes the ice front to flow faster and thin to flotation, followed by another calving event; the rate of retreat thus is controlled by ice flow even though the retreat is achieved by fracture. Taller cliffs generate higher stresses, however, favoring fracture over flow. Deformational processes are often written as power-law functions of stress, with ice deformation increasing as approximately the third power of stress, but subcritical crack growth as roughly the thirtieth power, accelerating to elastic-wave speeds with full failure. Physical understanding, models based on this understanding, and the limited available data agree that, above some threshold height, brittle processes will become rate-limiting, generating faster calving at a rate that is not well known but could be very fast. Subaerial slumping followed by basal-crevasse growth of the unloaded ice is the most-likely path to this rapid calving. This threshold height is probably not too much greater than the tallest modern cliffs, which are roughly 100 m. 

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3. A Finite-Element-Based Cohesive Zone Model of Water-Filled Surface Crevasse Propagation in Floating Ice Tongues

   https://doi.org/10.1109/MCSE.2023.3315661  

   Gao, Yuxiang ; Ghosh, Gourab ; Jiménez, Stephen ; Duddu, Ravindra ( May 2023 , Computing in Science & Engineering)

   Irina Tezaur, Josefin Ahlkrona (Ed.)

   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. 

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4. On the evaluation of the stress intensity factor in calving models using linear elastic fracture mechanics

   https://doi.org/10.1017/jog.2018.64  

   JIMÉNEZ, STEPHEN ; DUDDU, RAVINDRA ( October 2018 , Journal of Glaciology)

   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. 

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5. Crevasse advection increases glacier calving

   https://doi.org/10.1017/jog.2022.10  

   Berg, Brandon ; Bassis, Jeremy ( January 2022 , Journal of Glaciology)

   Abstract Iceberg calving, the process where icebergs detach from glaciers, remains poorly understood. Moreover, few parameterizations of the calving process can easily be integrated into numerical models to accurately capture observations, resulting in large uncertainties in projected sea level rise. Recent efforts have focused on estimating crevasse depths assuming tensile failure occurs when crevasses fully penetrate the glacier thickness. However, these approaches often ignore the role of advecting crevasses on calculations of crevasse depth. Here, we examine a more general crevasse depth calving model that includes crevasse advection. We apply this model to idealized prograde and retrograde bed geometries as well as a prograde geometry with a sill. Neglecting crevasse advection results in steady glacier advance and ice tongue formation for all ice temperatures, sliding law coefficients and constant slope bed geometries considered. In contrast, crevasse advection suppresses ice tongue formation and increases calving rates, leading to glacier retreat. Furthermore, crevasse advection allows a grounded calving front to stabilize on top of sills. These results suggest that crevasse advection can radically alter calving rates and hint that future parameterizations of fracture and failure need to more carefully consider the lifecycle of crevasses and the role this plays in the calving process. 

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