Abstract
AbstractHydrofracturing 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.
Highlights
The mass loss from glaciers and ice sheets represents the largest contribution to eustatic sea level rise in the 21st century (Meier and others, 2007; Moore and others, 2013)
Through idealized simulation studies, we address two important modeling questions related to glacier calving: (1) Are the crevasse depths predicted by the CDPM model consistent with those predicted by zero stress and linear elastic fracture mechanics (LEFM) models? (2) What is the role of ice rheology and fracture process zone size on crevasse propagation and calving outcomes? In addition, we address a fundamental glacier mechanics question: ‘Can a water-filled crevasse reach the bottom surface of a glacier?’ (Weertman, 1973)
The rest of the article is organized as follows: in Section 2, we present the strong form of the governing equations of the nonlocal continuum poro-damage mechanics (CPDM) model for hydromechanical fracture, including the notion of poro-damage mechanics, constitutive models for ice, and creep damage evolution law; in Section 3, we present parametric and sensitivity studies before comparing the depths of water-filled crevasses predicted by CPDM, LEFM and zero-stress models; in Section 4, we discuss the implications of the rheology and damage model assumptions and idealized simulation results for ice fracture and calving for real glaciers; and in Section 5, we offer some concluding remarks
Summary
The mass loss from glaciers and ice sheets represents the largest contribution to eustatic sea level rise in the 21st century (Meier and others, 2007; Moore and others, 2013). Researchers sought to estimate crevasse penetration depths in glaciers and ice shelves analytically using either the zero stress model (Nye, 1957) or linear elastic fracture mechanics (LEFM) models (Weertman, 1971, 1973; Smith, 1976; van der Veen, 1998a, 1998b). The rest of the article is organized as follows: in Section 2, we present the strong form of the governing equations of the nonlocal CPDM model for hydromechanical fracture, including the notion of poro-damage mechanics, constitutive models for ice, and creep damage evolution law; in Section 3, we present parametric and sensitivity studies before comparing the depths of water-filled crevasses predicted by CPDM, LEFM and zero-stress models; in Section 4, we discuss the implications of the rheology and damage model assumptions and idealized simulation results for ice fracture and calving for real glaciers; and, we offer some concluding remarks. In the Appendices, we briefly review the formulation of the analytical zero-stress and LEFM models, and the finite element implementation of the CPDM model
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