Shear dilation of subglacial till results in time-dependent sliding laws

Abstract

The dynamics of glacial sliding over water-saturated tills are poorly constrained and difficult to capture realistically in large-scale models. Experiments characterize till as a plastic material with a pressure-dependent yield stress, but the subglacial water pressure may fluctuate on annual to daily timescales, leading to transient adjustment of the till. We construct a continuum two-phase model of coupled fluid and solid deformation, describing the movement of water through the pore space of a till that is itself dilating and deforming. By forcing the model with time-dependent effective pressure at the ice–till interface, we infer the resulting relationships between basal traction, solid fraction and rate of deformation. We find that shear dilation introduces internal pressure variations and transient dilatant strengthening emerges, leading to hysteretic behaviour in low-permeability materials. The result is a time-dependent effective sliding law, with permeability-dependent lag between changes in effective pressure and the slidingspeed. 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.

Squishy oscillations

“…Such forcing might be found in the perivascular system surrounding arterial blood vessels in the brain (e.g. Kelley 2021), the forcing by ocean tides of melt-water flows in sub-glacial till (Warburton, Hewitt & Neufeld 2023), and the response of ground water to solid-Earth tides (Allègre et al. 2016), to give just a few examples in very different contexts and at vastly different scales.…”

Advances in monitoring glaciological processes in Kalallit Nunaat (Greenland) over the past decades

“…Over the past decades, two lines of inquiry have motivated extensive research into Greenland's basal processes: i) the percentage of the bed undergoing slip, and ii) the relationship between ice speed and basal traction (commonly referred to as the slip law). In recent years, emerging evidence also suggests that transient forcings occurring on timescales of days to weeks may push sliding dynamics beyond "steady state" conditions typically assumed in ice flow models [190][191][192][193][194]. Given the scale of this problem, diverse methodologies have been used to probe these questions over the past two decades, such as custom borehole instrumentation [195,196], geophysics [197][198][199][200], laboratory experiments [201], and large-scale inversions for basal drag using satellite imagery [202][203][204].…”

Two-layer gravity currents of generalized Newtonian fluids

“…Determining the relationship between an ice sheet's sliding velocity and the rheology of the subglacial till (as well as the bed topography) has received significant attention over many decades [1,2,[30][31][32][33][34]. Motivated by this problem, we quantify the lubricating effect of a thin lower layer of generalized Newtonian fluid via asymptotic analysis.…”