Till rheology

To simulate the mechanics and dynamics of soft-bedded ice streams, and glaciers, it is necessary to quantitatively capture till rheology. Early treatments of soft-bedded ice-stream motion focused on the mildly non-linear till model with stress exponent in the till flow law of ca. 1-2 (e.g. Alley et al., 1987b, 1989). This was a convenient choice because such mildly non-linear rheology is in many ways similar to ice rheology. Hence, shear deformation of a till layer was treated quantitatively just as shear deformation of an unusually soft basal ice layer (e.g. MacAyeal, 1989a,b, 1992b). However, laboratory tests on samples of till recovered from beneath WIS have shown that this material behaves as a Coulomb-plastic material whose strength is (nearly) independent of strain rates and depends mainly on effective stress (Kamb, 1991; Tulaczyk et al., 2000a). The values of stress exponents implied by the laboratory data are ca. 50-100. These findings were corroborated by in situ and laboratory studies of other tills that also supported the highly non-linear, nearly plastic nature of till rheology (e.g. Fischer & Clarke, 1994; Iverson et al., 1997, 1998; Hooke et al., 1997).

There are still some reservations about applying a rheological till model, based on data derived from small laboratory samples and localized in situ studies (spatial scales of ca. 0.1-1.0m), in simulations of soft-bedded ice masses, for which the length-scales relevant to determining the ice flow rate are several orders of magnitude larger (ca. 100-1000m) (Hindmarsh, 1997; Fowler, 2002, 2003). One of the most prominent arguments advanced against the (nearly) Coulomb-plastic model of till rheology is based on the fact that ice flow rates in soft-bedded systems appear to be less temporally variable than one would expect if all of the flow resistance were provided by a bed with no significant strain-rate-dependence of strength (Hindmarsh, 1997). However, there are two important problems with this argument. Firstly, much of the flow resistance in soft-bedded ice streams appears to come from sources other than the bed (e.g. shear margins). It is sufficient to look at ice shelves to see ice bodies with no direct velocity control from the base, which, nonetheless, have a relatively narrow and stable range of velocities because the flow rates are controlled ultimately by the mildly non-linear rheology of ice itself (e.g. MacAyeal & Lange, 1988; MacAyeal, 1989a,b). The second important fact, which undermines the arguments against the (nearly) Coulomb-plastic rheology of till, stems from the recent observations of highly variable velocities on the ice plain of Whillans Ice Stream (Bindschadler et al., 2003). There, the ice stream accelerates from a stationary state to velocities greater than ca. 10kmyr-1 within minutes and comes back to a stationary state within a similar time period. These wild velocity fluctuations occur in response to small tidally driven stress perturbations. Such behaviour cannot be reconciled easily with the viscous bed model proposed previously for this ice stream (e.g. Alley et al., 1987b, 1989) but is fully consistent with the (nearly) Coulomb-plastic till rheology observed in laboratory tests on samples recovered from beneath the ice stream ca. 200 km upstream of the ice plain (Kamb, 1991; Tulaczyk et al., 2000a). These observations demonstrate that at least in the case of Whillans Ice Stream, small-scale laboratory rheological tests and regional in situ observations are both consistent with highly non-linear till rheology and inconsistent with nearly linear viscous till rheology.

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