Radius of particle mm

1000

accommodated largely by regelation and for large clasts accommodated largely by plastic deformation (Figure 7.25). Whether a clast ploughs or not will be dependent upon the strength of the till, which is controlled by the effective pressure. However, based on Figure 7.25, it appears that clasts in the 20-40 mm size range will be the first to move.

Depth of deformation in a subglacial till

Let us now address two questions, to which there are currently no firm answers: (1) what controls the thickness of the layer of subglacial till that can be mobilized by an overriding glacier; and (2) what is the shape of the velocity profile through this layer?

Evidence for thick layers of deforming till is ambiguous. As noted, Alley (1991) and Hooke and Elverh0i (1996) have suggested that, during the Pleistocene, huge amounts of sediment must have been moved long distances in deforming subglacial layers of till. This would seem to require layers at least a few meters thick. However, studies of cores of subglacial till obtained through boreholes that penetrated the kilometer-thick Whillans Ice Stream revealed little evidence for deformation (Tulaczyk et al., 1998; Kamb, 2001,p. 172). Clasts were not striated and there were no distinct shears or other visible macroscopic or microscopic fabrics or textures suggestive of deformation. On the other hand, diatoms of different ages were mixed together, requiring some sort of deep deformation process.

Analysis of the variation of t and Ne with depth provides a basis for calculating the thicknesses of deforming layers and velocity profiles in them. Beneath a glacier of thickness h with surface slope a and a horizontal bed:

Here pi, pt and pw are the density of ice, the bulk density of the till, and the density of water, respectively, subscript b refers to the conditions at the ice-till interface, and z is measured downward from the interface. Alley (1989b) refers to the second of Equations (7.26) as a hydrostatic variation of Ne with depth because the pressure in the water increases as pwgz. Assuming pt « 2000 kg m-3, and taking derivatives with respect to z yields:

For typical surface slopes, the rate of increase of Ne with depth clearly exceeds that of t ,sothe strength of the till should increase faster than the applied stress. Thus, the decrease in ¿in the till is likely to be nonlinear, and deformation will cease at the depth at which s exceeds t .

Elaborating on this approach, Iverson and Iverson (2001) calculated the velocity profile shown in Figure 7.26. In their model, displacements are assumed to occur across shear zones several millimeters thick when grain bridges fail. Their analysis is based on the assumptions that: (1) the deforming part of the till can be viewed as consisting of a stack of shear zones, (2) slip on any given shear zone occurs intermittently, (3) the frequency of slip is the same on all shear zones, and (4) the amount of slip on a shear zone during a given event decreases with depth owing to the relative rates of change of Ne and t with depth. By varying some of their less well-constrained parameters within reasonable limits, they were able to match a profile measured in a coarse-grained till quite well.

In situations in which water is produced by melting at the ice-till interface and is lost downward by flow through a permeable substrate, the hydraulic head must decrease downward through the till. Then dNe/dz will be higher than in the purely hydrostatic case represented by the second of Equations (7.27), and the deforming layer should be thinner than otherwise (Alley, 1989b).

On the other hand, Tulaczyk et al. (2001a) found that in sediment cores, up to 3 m long, obtained from beneath Whillans Ice Stream the

Figure 7.26. Velocity profile in a deforming subglacial till calculated by Iverson and Iverson (2001). See text for explanation. (Modified from Iverson and Iverson, 2001, Figure 3. Reproduced with permission of the authors and the International Glaciological Society.)

Velocity, m a

void ratio did not vary with depth. This suggests that dNe/dz = 0 (Figure 7.16). Alley (1989b) refers to this as a lithostatic variation of Ne with depth because the pressure in the water increases as ptgz. Such a situation would seem to be possible only in situations in which the permeability of the till was quite low and the till was at least occasionally deforming to depths of at least 3 m.

To actually measure the ratio of till deformation to sliding at an ice-till interface, Engelhardt and Kamb (1998) implanted stakes in the till, again through boreholes drilled for the purpose. As the ice moved away from a stake, a wire attached to the stake was pulled off of a spool anchored in the basal ice and the rate of rotation of the spool was measured. In such a "tethered-stake" experiment on Whillans Ice Stream, the top of the stake was believed to be about 30 mm below the base of the ice, and the rate of relative motion between the spool and the stake was ~1.0 m d-1,or 83% of the surface speed. Thus, sliding and deformation in the top 30 mm of the till accounted for most of the ice movement. The remaining 17% could have been either internal deformation of the ice or deformation deeper in the till layer.

In a similar tethered-stake experiment on Bindschadler Ice Stream, however, the sliding speed, including deformation in the upper 0.34 m of the till, was only 10%-20% of the 1 m d-1 surface speed (Kamb, 2001). As the driving stress was too low to cause significant internal ice deformation, Kamb attributed the remaining 80%-90%

of the motion to deformation below the level of emplacement of the stake.

In another experiment, observations in a tunnel beneath the glacier Breidamerkurjokull in Iceland demonstrated that within about 0.5 m of the glacier sole deformation of the till was pervasive, while at greater depths it was localized in shear zones (Boulton and Hindmarsh, 1987). Such shear zones are characteristic of virtually all laboratory experiments on granular materials, and similar zones are a well known characteristic of granular materials that have been overridden by glaciers (Brown et al., 1987; Menzies and Shilts, 1996, pp. 48-49).

Evidence for still deeper deformation comes from an experiment on Black Rapids Glacier in Alaska. Truffer et al. (2000) emplaced tilt-meters at depths of ~0.1, 1, and 2 m in a 7-m thick till layer beneath the glacier. The tiltmeters recorded little deformation of the till in 410 days, despite the fact that the base of the glacier and the 2 m of till containing the tiltmeters moved 35-45 m during that time interval. They concluded that the motion must be along one or more shear zones at greater depths in the till.

Iverson et al. (1998) have proposed a mechanism for distributing deformation through a significant thickness of till as observed in the upper 0.5 m of till at Breidamerkurjokull. They suggest that deformation starts in a thin shear zone which then dilates. Dilatant hardening then strengthens the zone, causing the locus of deformation to shift. The process is facilitated by frequent water-pressure fluctuations because a dilated zone will begin to consolidate back to its original porosity when the water pressure drops (Figure 7.16), so the next episode of deformation may initiate a shear zone in a quite different place.

Tulaczyk (1999) has suggested two possible physical explanations for concentration of deformation in a single shear zone at depth, as inferred from the Black Rapids data.

(1) If the basal water pressure fluctuates, alternating waves of high and low pressure will penetrate into the till much as seasonal temperature waves penetrate into the surface of a glacier (see Figure 6.8). The rate at which these waves penetrate depends on the hydraulic diffu-sivity of the till. If we presume that the till is homogeneous and that deformation occurs in a relatively narrow shear zone at the weakest point in it - namely the point where the water pressure is highest -then this shear zone will migrate downward through the till with the pressure wave. According to the calculations of Tulaczyk et al. (2000a), diurnal pressure fluctuations could distribute shear through ~0.07 m of till like that from the bed of Whillans Ice Stream and through over a meter of a coarser till typical of valley glaciers.

(2) Alternatively, because the peak strength of a non-deforming till is greater than the residual strength (Figure 7.15), shear zones may not migrate readily. In this case, the strength of the till may be determined by the maximum effective pressure that the material experiences during a water pressure cycle. A shear zone could develop and persist at the depth at which this maximum pressure was lowest. Till above this level would move as a plug without significant internal deformation.

In the case of Black Rapids Glacier, calculations suggested that the lowest maximum effective pressure in an annual cycle would be between 3.5 and 4.6 m below the ice-till interface (Truffer et al., 2000). Thus, Tulaczyk's second explanation could explain the lack of deformation in the uppermost 2 m of this till.

In summary, first-order models suggest that layers of deforming till should be relatively thin, particularly in fine-grained tills, and some measurements support this interpretation. However, other observations suggest that layers may be meters thick in certain situations, and more sophisticated models are emerging that explain such layers. The seemingly contradictory evidence from till from beneath Whillans Ice Stream, in which diatoms of different ages were mixed but few deformation structures were found, may be explained by the cushioning effect of soft clay minerals, which comprise ~35% of the matrix of this till. Cushioning would inhibit formation of striations and other deformation structures.

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