Vulnerability of Firn to Hydrofracture, Part I: Poromechanical Modeling

Ice slabs are multi-meter thick layers of solid reforzen ice that form on top of the porous firn layer in Greenland’s wet snow zone. Recent observations in Northwest Greenland highlight the ability of this relict firn layer to store meltwater in its pores after surface meltwater drains rapidly through cracks in the overlying ice slab. Current fracture mechanics (i.e., LEFM) assumes that the stored elastic energy in an impermeable solid matrix is instantaneously dissipated by creating new crack surfaces, which only holds for impermeable solid media. To better understand the fate of meltwater in the porous firn layer beneath ice slabs, we develop a two-dimensional, poroelastic continuum model to quantify the stress and pressure changes in the porous firn during meltwater penetration.

We extend Biot’s poroelastic theory to two-phase immiscible flow by introducing meltwater saturation as an extra variable. By coupling the fluid continuity and force balance equations, we resolve the spatiotemporal evolution of 1) matrix deformations and effective stresses, 2) the water saturation field, and 3) the water pressure field. We adopt a fracture criterion for the cohesive porous firn layer: the maximum tensile effective stress should exceed the material tensile strength to generate fractures. We study the maximum tensile effective stress induced by water injection as a function of firn’s mechanical and hydraulic properties (bulk modulus, porosity, and permeability), and the infiltration conditions (constant infiltration pressure or flow rate). Our results show that the maximum tensile effective stress in the firn layer is no more than a quarter of that predicted for an equivalent solid ice column, because the imposed load is mostly transmitted into the pore pressure. Therefore our model predicts that surface-to-bed hydrofracture is unlikely to form if meltwater can leak into the firn layer. In “Vulnerability of Firn to Hydrofracture, Part II: Greenland’s Ice Slab Regions”, we apply this model to assess the vulnerability of Greenland’s ice slab regions.