Modeling hydraulic fracture of glaciers using continuum damage mechanics

Abstract

ABSTRACT. The presence of water-filled crevasses is known to increase the penetration depth of crevasses and this has been hypothesized to play an important role controlling iceberg calving rate. Here, we develop a continuum-damage-based poro-mechanics formulation that enables the simulation of water-filled basal and surface crevasse propagation. The formulation incorporates a scalar isotropic damage variable into a Maxwell-type viscoelastic constitutive model for glacial ice, and the effect of the water pressure on fracture propagation using the concept of effective solid stress. We illustrate the model by simulating quasi-static hydrofracture in idealized rectangular slabs of ice in contact with the ocean. Our results indicate that water-filled basal crevasses only propagate when the water pressure is sufficiently large, and that the interaction between simultaneously propagating water-filled surface and basal crevasses can have a mutually positive influence leading to deeper crevasse propagation, which can critically affect glacial stability. Therefore, this study supports the hypothesis that hydraulic fracture is a plausible mechanism for the accelerated breakdown of glaciers.

Boundary layer models for calving marine outlet glaciers

“…More recently, others have extended the linear elastic fracture mechanics approach of Weertman (1973Weertman ( , 1980 and van der Veen (1998a, b) to include effects such as the role of distributed damage due to the formation of microcracks in initiating crevasse formation, the blunting of cracked tips due to viscous deformation and the presence of significant torques near the calving front (Krug et al, 2014;Mobasher et al, 2016;Jiménez et al, 2017;Yu et al, 2017). The complexity of these processes however makes them difficult to parameterize in a model that does not resolve the scale of individual crevasses, and we do not consider them here.…”

Ice shelf fracture parameterization in an ice sheet model

“…1). Therefore, the scalar damage variable, D (x, y, z) ∈ [0, 1), employed in vertically varying models (Pralong and Funk, 2005;Jouvet et al, 2011;Keller and Hutter, 2014;Krug et al, 2014;Bassis and Ma, 2015;Mobasher et al, 2016) takes on either the value 0 (in the central layer) or 1 (in the upper and lower layers). The principal damage variable in our model is d (x, y) ∈ [0, h (x, y)), the vertical integral of D(x y z), and our closest analogue to the usual D is its vertical average,…”

“…Notice that damage affects only the deviatoric stress (as in Jouvet et al, 2011;Krug et al, 2014) and does not affect the gravitational driving stress. We might expect such a modification if we had instead modified the full Cauchy stress (as in Pralong and Funk, 2005;Bassis and Ma, 2015;Mobasher et al, 2016), but we have assumed that damage has no impact with respect to isotropic compression or vertical shear, so that the usual hydrostatic vertical stress balance and the usual vertical integral of the resulting horizontal pressure gradient hold. This is analogous to assuming that the crevasses are filled with an inviscid material having the same density as ice.…”

Bounds on the calving cliff height of marine terminating glaciers

“…We also assume that crevasses are sufficiently narrow, that they have little effect on the stress field, and use the stress field diagnostically to deduce the depth of crevasses. Previous work using much more complex viscoelastic damage models suggest that this is a reasonable first‐order approximation [ Duddu et al , ; Mobasher et al , ]. At the end of each time step, we also remesh after advecting all the nodes along their own nodal velocity vector to maintain a constant mesh quality throughout the simulation, and the locations of existing crevasse paths are stored.…”

“…The most promising approach in this family involves methods that seek to predict the depth of surface and basal crevasses penetration, assuming that an iceberg will detach when surface and basal crevasses intersect and isolate an iceberg [e.g., Benn et al , ; Nick et al , ; Bassis , ; Bassis and Ma , ]. Crevasse penetration depths are often computed assuming that crevasses penetrate to the depth where the tensile stress vanishes (e.g., the Nye zero stress model [ Nye , ; Benn et al , , ; Otero et al , ; Nick et al , ; Cook et al , ; van der Veen , ], Linear Elastic Fracture Mechanics [e.g., Smith , ; van der Veen , , ; Rist et al , ], or various flavors of continuum damage mechanics [e.g., Pralong and Funk , ; Borstad et al , ; Albrecht and Levermann , ; Duddu et al , ; Albrecht and Levermann , ; Krug et al , ; Bassis and Ma , ; Mobasher et al , ]).…”