Deformation of subglacial till

We have known for decades that ice moving over granular subglacial materials can deform these materials. (Herein, the term "granular material" should be understood to include materials with significant amounts of clay, although a distinction between granular materials and clays is usually made in the soil mechanics literature.) Commonly, the granular material is till, either formed by erosion during the present glacial cycle, or left from a previous one. Recently it has become clear that a large fraction of the surface velocity of a glacier may be a result of deformation of such till (Figure 5.5).

Intense interest in the rheology of till dates from work on Whillans Ice Stream in Antarctica where studies of seismic velocities suggested that a layer with high porosity, saturated with water under high pressure, and 2-13 m thick was present beneath the ice (Blankenship et al., 1986). The high porosity suggested active deformation, facilitated by the high water pressure. Thus, the high speed of the ice stream, about 450 ma-1, was attributed to deformation of the till. Subsequent drilling revealed that the ice stream was, indeed, underlain by till, and also confirmed that the water pressure was close to the overburden pressure (Engelhardt et al., 1990). A key question, then, is whether the till is deforming, or alternatively whether the high water pressures have simply decoupled the ice stream from the till. Experiments addressing this question will be described later in this chapter.

More recently, some scientists studying the Quaternary period have suggested that the large volumes of material found in till sheets in the midwestern United States and the large volumes of glacigenic material found in some submarine fans surrounding the Barents Sea could only have been transported to their present locations in deforming subglacial till layers (e.g. Alley, 1991; Hooke and Elverhai, 1996). It is estimated that the amount of material that could be transported in basal ice or by subglacial melt streams is too low to account for the volumes of these deposits in the time inferred to be available for their formation. In the Barents Sea case, calculated basal melt rates are so high that little material is likely to have been entrained by basal ice, and yet they are too low to provide the water volumes required for significant fluvial transport.

Because glacial till is a granular material, its rheology is quite different from that of ice. Granular materials normally have a yield strength below which they deform only elastically. This yield strength, i, is related to two physical properties of the material, the cohesion, c, and the angle of internal friction, <, by the classical Mohr-Coulomb relation:

Figure 7.13. Relation between s and Ne obtained from a laboratory test on a sample of till from beneath Storglaciaren (Iverson, unpublished data). Inset shows, schematically, how s may actually vary with Ne at low effective pressures.

100 200 Effective normal pressure, Ne, kPa

100 200 Effective normal pressure, Ne, kPa

Figure 7.13. Relation between s and Ne obtained from a laboratory test on a sample of till from beneath Storglaciaren (Iverson, unpublished data). Inset shows, schematically, how s may actually vary with Ne at low effective pressures.

where Ne is the effective normal pressure. To determine c and y, laboratory tests are conducted in which the stress needed to initiate deformation of a material is measured at various effective normal pressures. When i varies linearly with Ne (Figure 7.13), the slope of the line is tan y, and the intercept is the apparent cohesion.

The term apparent cohesion is used because detailed measurements often show that the variation of i with Ne is not linear at low effective normal pressures, but rather is as shown by the dashed line in the inset in Figure 7.13. The true cohesion is the value of i at the intercept of this dashed line with the ordinate. Because the apparent cohesion varies directly with the true cohesion, however, we normally will not draw a distinction between the two quantities.

Let us now examine the physics involved in cohesion, and the physical significance of y.

Cohesion

True cohesion in soils is a consequence of cementation, of electromagnetic forces between clay particles, and of electrostatic forces resulting from charge imbalances among ions absorbed on clay minerals (Mitchell, 1993, pp. 125, 373-374). Cementation is the major source of cohesion in subaerial soils, but would not be significant in continuously deforming subglacial tills. Thus, the magnitude of c in such tills is determined primarily by the amount and species of clay minerals present.

In situ deforming subglacial tills formed by erosion in the current cycle of glaciation do not seem to have much clay-sized material unless the glacier has moved over a bed containing such material. Furthermore, most of the clay-sized particles that are present in such clay-poor tills are not clay minerals. Thus, c may be small in such tills. For example, records from tiltmeters emplaced in till beneath Storglaciaren demonstrate that this till is deforming. However, only ~5.4% (by weight) of the particles in samples collected through boreholes are less than 2 ¡m, and these particles are largely quartz and hornblende (Iverson, unpublished data). Laboratory tests yield c = 8 kPa for this till (Figure 7.13). Similar tests on till samples collected from beneath Whillans ice stream, containing ~35% clay, gave c = 3 ± 1.3 kPa (Tulaczyk et al., 2000a). (In this case, the clay-sized material, which does consist of clay minerals, is inferred to have been derived from Tertiary glaciomarine sediments (Tulaczyk et al., 1998; Kamb, 2001).) For comparison, values for silty and clayey sands are typically between 20 and 75 kPa (Hausmann, 1990).

The absence of clay-sized material in deforming tills is likely to be largely a consequence of flushing by subglacial streams. In addition, however, it is noteworthy that the deviatoric stress required to fracture a grain increases as the particle size decreases, and that in the limit very fine grains deform plastically rather than fracture into still smaller particles (Kendall, 1978). That the clay-sized particles present in such tills tend not to be clay minerals is the result of the absence of subaerial weathering processes. Higher concentrations of clay-sized particles and of clay minerals in Pleistocene tills may be a consequence either of sub-aerial weathering after retreat of the ice, or of incorporation of previously weathered material over which the ice moved.

Cohesion is not increased by saturation by water unless clay minerals are present. The well-known fact that the walls of wet sand castles stand up better than dry ones is, rather, a result of surface tension. Surface tension effects are present when the sand is wet but pore spaces still contain air. This is because surface tension is a result of stresses associated with the air-water interface.

Consolidation

When a granular material accumulates gradually, it compacts under its own weight. Such a material is called normally consolidated. If an additional load, such as a shear stress, is then placed on the material, it becomes overconsolidated. The term overconsolidated is also used to describe a granular material which, after being normally consolidated, experiences a reduction in overburden pressure due to erosion or, perhaps, to melting of an overlying glacier. The highest past effective stress to which a sample has been subjected is called the preconsolidation stress.

Figure 7.14. Deformation of a granular medium involves both (a) dilation as grains move apart in order to pass Motion over one another; and

(b) friction between grains that are constrained to slide past one another.

Figure 7.14. Deformation of a granular medium involves both (a) dilation as grains move apart in order to pass Motion over one another; and

(b) friction between grains that are constrained to slide past one another.

The state of consolidation is altered whenever a granular material is sheared. Thus, for example, if a subglacial till, previously consolidated by an effective pressure of 100 kPa, is later deformed at an effective pressure of 30 kPa, the preconsolidation stress is reset to the lower value (Tulaczyk et al., 2001a).

Angle of internal friction

When an overconsolidated granular material begins to deform under a shear stress, it must dilate so that individual grains can move over one another (Figure 7.14a). A normally consolidated material may either dilate or compact slightly, depending on the granulometry (size distribution of particles) and the conditions under which it accumulated. Dilation increases pore space, which is why the high porosity of the till beneath Whillans Ice Stream suggests deformation.

Grains in such a deforming material must also slide past one another locally (Figure 7.14b). The forces resisting this sliding motion are fric-tional. Frictional forces are a consequence of the interlocking of microscopic asperities on the surfaces of the materials (Mitchell, 1993,p. 362). The maximum shearing stress that can be supported by friction between two surfaces, tp, is proportional to the effective normal pressure, Ne: tp = ¡xNe. The constant of proportionality, ¡x, is called the coefficient of friction.

Let us define ft as the angle, relative to the shear plane, that particles must ascend during dilation from an overconsolidated state (Figure 7.14a) and also define m = tan-1 x. Then y = ft + m (Iverson et al, 1996). In granular materials that do not have much clay, m is typically 20-25° and y is typically between 25° and 40° (Mitchell, 1993, pp. 343, 366). Thus, more than half of the resistance to deformation of such a material is a consequence of frictional forces, while the remainder is due to processes such as dilation and crushing (Mitchell, 1993, p. 401).

Figure 7.15. Schematic illustration of the variation of mean shear stress with time (or displacement) in a granular medium that is sheared at a constant rate.

Figure 7.15. Schematic illustration of the variation of mean shear stress with time (or displacement) in a granular medium that is sheared at a constant rate.

As a result of the dependence of y on f, y depends, also, on the granulometry of the material. For example, if spaces between particles in Figure 7.14a were filled with finer material, a particle could not settle down into the gap between subjacent particles, and thus would not have to rise so much to move over its neighbor. Then f would be lower, and hence so would y. For example, y is 31° in the sandy Storglaciaren till (Figure 7.13) and 24° in the clay-rich till from beneath Whillans Ice Stream (Tulaczyk et al., 2000a).

Normal pressures suppress dilation and also force particles into firmer contact, thus increasing rp. These two factors account for the dependence of s on Ne.

When a granular material is deformed at a constant strain rate (with the shear stress, r, being measured as a function of time or displacement), r first increases rapidly to a peak. The initial linear portion of the rise reflects elastic (recoverable) deformation. The point at which the rise begins to deviate from linearity is called the yield strength (Figure 7.15). Subsequent strain reflects irrecoverable visco-plastic deformation. The peak of the curve is the failure strength. If the material was initially overconsolidated, r then declines slightly before reaching a constant value. The final value of r, normally reached after a shear strain of the order of only 10%, is called the residual or ultimate strength (Skempton, 1985). The difference between the peak and the residual strength reflects the additional stress needed to induce dilation. The decrease from the peak to the residual strength reflects a decrease in f and hence in y. Once dilated, the material remains dilated as long as Ne remains constant. Thus, the stress required for deformation remains constant. (In materials in which clay-sized particles are abundant (>20%) and are predominantly clay minerals, a further decline in strength may occur as the platy clay particles become aligned parallel to the direction of shear.)

Figure 7.16. Schematic diagram showing variation of void ratio with effective normal pressure. See text for explanation.

Void ratio

The void ratio, e, is the ratio of the volume of pores, Vp, to the volume of solids, Vs: e = Vp/ Vs. (Note that this is not the same as porosity; porosity is the percentage of voids in the total volume.) The void ratio varies with Ne, thus:

Neo where eo is the void ratio at an effective normal pressure of Neo, and Cp is a dimensionless coefficient of compressibility (e.g. Tulaczyk et al., 2000a).

As a normally consolidated material accumulates, the void ratio will decrease as shown, schematically, by the line labeled NCL (normal consolidation line) in Figure 7.16. The slope of this line is — Cp. In an overconsolidated material, the void ratio will be below the NCL. If the material is sufficiently overconsolidated and is then sheared, resulting in dilation, the void ratio will increase initially and then reach a steady value shown by the line labeled CSL (critical state line) in Figure 7.16. Note that the CSL is below the NCL so if deformation stops, the material will not consolidate again unless Ne is increased by more than the amount indicated by the horizontal spacing between the two lines. If the load on a consolidated material is relaxed, the material will expand elastically along a path like the one labeled URL (unloading-reloading line) in Figure 7.16. Upon reloading, it will follow the same path back to its original position, and will then begin to consolidate further along the NCL line. By collecting an undisturbed sample in the field and subjecting it to a gradually increasing load in the laboratory, in what is called

Figure 7.17. Variation in local pressure with time in a granular medium, ~55 mm thick, as it is deformed in a ring shear experiment. (Data courtesy of N. R. Iverson and T. S. Hooyer.)

CO CO 0

VI A. '

—w — w

^^^ : Mean normal /

load

Shearing displacement, mm

1200

a preconsolidation test, this property can be exploited to determine the maximum effective normal pressure, Nemax, to which the sample has been subjected.

Hooyer and Iverson (2002) did such preconsolidation tests on several samples of till deposited by the Des Moines Lobe, a lobe of the Laurentide ice sheet that advanced out of North Dakota into Minnesota and Iowa about 13 800 radiocarbon years ago. Their values of Nemax ranged from 120 to 300 kPa. These values are quite low, considering the probable ice thickness, suggesting that pore water pressures beneath the lobe were high. This, in turn, implies that motion of the lobe could have been largely by a combination of sliding over the underlying till and deformation of that till, thus providing an explanation for the considerable extent of the lobe despite other evidence suggesting that driving stresses were quite low.

Grain fracture and the granulometry of deforming subglacial till

If a granular medium is sheared at a constant rate between moving platens, in one of which there is a pressure sensor that is many times the diameter of individual grains but much smaller than the platen itself, the pressure recorded by this sensor varies with time (Figure 7.17) (Mandl et al., 1977; Iverson et al., 1996). Sometimes it exceeds the mean normal load on the sample by as much as 25%, while at other times it is significantly less than the mean. One logical explanation for this is that grains in the medium become aligned to form bridges such as that shown in Figure 7.18a. When traced through a granular material of significant thickness, these bridges are much more complicated than suggested by the simple sketch in Figure 7.18a; high contact stresses are distributed s s s

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