Dilation of subglacial sediment governs incipient surge motion in glaciers with deformable beds

Abstract

Glacier surges are quasi-periodic episodes of rapid ice flow that arise from increases in slip-rate at the ice-bed interface. The mechanisms that trigger and sustain surges are not well-understood. Here, we develop a new model of incipient surge motion for glaciers underlain by sediments to explore how surges may arise from slip instabilities within a thin layer of saturated, deforming subglacial till. Our model represents the evolution of internal friction, porosity, and pore water pressure within the till as functions of the rate and history of shear deformation, and couples the till mechanics to a simple ice-flow model. Changes in pore water pressure govern incipient surge motion, with less-permeable till facilitating surging because dilation-driven reductions in pore-water pressure slow the rate at which till tends toward a new steady-state, thereby allowing time for the glacier to thin dynamically. The reduction of overburden (and thus effective) pressure at the bed caused by dynamic thinning of the glacier sustains surge acceleration in our model. The need for changes in both the hydromechanical properties of the till and thickness of the glacier creates restrictive conditions for surge motion that are consistent with the rarity of surge-type glaciers and their geographic clustering.

Dilation of subglacial sediment governs incipient surge motion in glaciers with deformable beds

“…We further simplify the expression for dynamical thinning by neglecting extensional strain rates (consistent with the assumptions in § 2 c), yielding where is the balance velocity. Finally, the rate of change in surface slope becomes where equation ( 3.4 b ) follows from the assumption of a parabolic surface profile for the glacier [ 92 ]. These approximations complete the quasi-one-dimensional model, and we solve equations ( 2.4 ), ( 2.17 ), ( 2.27 ), ( 3.3 ) and (3.4) using the same parameters, initial conditions and numerical solver as in § 3 b.…”

“…Assuming that individual grains in the till are rigid, strain within the till will be accommodated by changes in porosity. Adopting an elastic–plastic model for the deformation of granular till, wherein the total strain is equal to the sum of the elastic and plastic strains, we separate porosity changes into an elastic component and a plastic component such that [ 78 , 91 ] where is the till compressibility and ϵ e is the elastic compressibility coefficient, taken to be in the range ϵ e ∼ 10 −3 –10 −1 [ 92 ]. Following work by Segall & Rice [ 78 ] and Segall et al [ 53 ] on slow-slip events on tectonic faults, we take the plastic component of porosity to have the same form as the evolution component of the rate-and-state model for till shear strength (equation ( 2.1 )), namely where ϕ c is a (constant) characteristic porosity and ϵ p is a dilatancy coefficient, a dimensionless parameter hereafter assumed constant and in the range 10 −4 ≤ ϵ p ≤ 10 −2 [ 53 ].…”

A theory of glacier dynamics and instabilities Part 1: Topographically confined glaciers

“…Some glaciers are known to surge periodically, a phenomenon that has long intrigued glaciologists and is the subject of extensive studies and reviews (Meier and Post, 1969;Clarke, 1987;Raymond, 1987;Harrison and Post, 2003). Although many mechanisms may contribute to the initiation and termination of the surge, such as the drainage switch (Kamb and others, 1985;Murray and others, 2003;Benn and others, 2019), the till instability (Kamb, 1991;Boulton and others, 1996;Nolan, 2003;Minchew and Meyer, 2020) or the pulsed englacial water storage (Lingle and Fatland, 2003), the thermal switch (Clarke, 1976;Fowler and others, 2001) remains one of the most viable in producing the self-oscillation.…”