A time-dependent sliding law for granular till

The dynamics of soft-bedded glacial sliding over water-saturated tills 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 annual to daily timescales, leading to transient adjustment of the till.

Here, we construct a continuum two-phase model of coupled fluid and solid flows, using Darcy flow to describe the movement of water through the pore space of the till that deforms according to a granular-inspired rheology. After calibrating our model against steady-state experiments, we force the model with a fluctuating effective pressure at the ice-till interface to infer the resulting relationships between basal traction, solid fraction, rate of deformation, and till flux. Shear dilation introduces internal pressure variations and transient dilatant strengthening emerges, leading to hysteretic behaviour in low-permeability materials.

Our model predicts a time-dependent effective sliding law, with permeability-dependent lag between changes in effective pressure and the sliding speed. This deviation from traditional steady-state sliding laws may play an important role in a wide range of transient ice-sheet phenomena, from glacier surges to the tidal response of ice streams.