Time-dependent soft-bedded sliding laws

The dynamics of soft-bedded glacial sliding over saturated till are poorly constrained and difficult to realistically capture in large scale models. While experiments characterise till as a plastic material with a pressure dependent yield stress, large scale models rely on a viscous or power-law description of the subglacial environment to efficiently constrain the basal sliding rate of the ice. Further, the subglacial water pressure may fluctuate on timescales from annual to daily, leading to transient adjustment of the till.

We construct a continuum two-phase model of coupled fluid and solid flows, using Darcy flow for the fluid phase and a recently described saturated granular model for the solid. After verifying our model against the steady-state experiments, we force the model with a fluctuating effective pressure at the ice-till interface and infer the resulting relationships between basal traction, porosity, rate of deformation, and till flux. Shear dilation introduces internal pressure variations, leading to hysteretic behaviour in low-permeability materials, resulting in a time-dependent effective sliding law.