## Mechanisms Of Ice Flow

A glacier flows because the ice within it deforms in response to gravity. This gravitational force is derived from the fact that glaciers slope towards their termini as a result of the spatial imbalance between accumulation and ablation discussed in the previous section. If there is no surface slope - no imbalance between accumulation and ablation - the glacier would not flow. The force per unit area set up within a mass of ice by gravity which causes it to deform is known as the shear stress. The level of shear stress experienced within an ice mass at any point is dependent upon the ice thickness and the surface slope of the glacier. This can be summarised in the equation:

t = pg(s — z) sin a where t is the shear stress at a point within the glacier, p is the density of ice, g is the acceleration due to gravity, a is the surface slope of the glacier, s is the surface elevation and z is the elevation of a point within the glacier.

At the base of a glacier the product of (s - z) will be equal to the ice thickness so that the shear stress at the base of a glacier, its basal shear stress, is given by:

t = pgh sin a where t is shear stress, p is the density of ice, g is the acceleration due to gravity, h is the thickness of the glacier and a is the surface slope of the glacier. This equation predicts that basal shear stress will vary with glacier thickness and with surface slope and that high basal shear stress values occur where the ice is both thick and steep.

Different materials can withstand different values of shear stress before they will deform or fracture. In the case of ice, deformation occurs under relatively low values of shear stress and the values obtained from beneath glaciers are remarkably constant. In most situations shear stress at the base of a glacier flowing over bedrock varies between about 50 and 100 kPa (100 kPa = 1.0 bars or kg per cm2). Ice does not normally deform at levels less than 50 kPa and it cannot usually withstand a shear stress of more than 150 kPa. Glaciers flow because the spatial imbalance between accumulation and ablation leads to an increase in the surface slope, causing the shear stress to increase until the ice deforms or flows.

Values of basal shear stress may be much lower where the glacier flows over a bed that is not rigid but composed of deformable sediment. In this situation a large proportion of the forward movement of the glacier may be produced by flow within this deformable sediment as the stress within the glacier is transferred to the bed. Consequently movement may not be controlled primarily by the properties of the ice but by the mechanical and hydrological properties of the sediment below (see Section 3.3.3).

The relatively constant values of shear stress found beneath glaciers flowing over rigid bedrock is an important characteristic and explains why most ice bodies have a parabolic profile; that is, a glacier slope which is steep at the margin and flattens

Soft-deforming sediment

Figure 3.6 Schematic cross-section through an ice sheet to illustrate how an area of deformable subglacial sediment might influence the ice-surface profile. [Modified from: Boulton (1993) in Holmes' Principles of Physical Geology (ed. P.McL.D. Duff), Chapman and Hall, figure

Soft-deforming sediment

Figure 3.6 Schematic cross-section through an ice sheet to illustrate how an area of deformable subglacial sediment might influence the ice-surface profile. [Modified from: Boulton (1993) in Holmes' Principles of Physical Geology (ed. P.McL.D. Duff), Chapman and Hall, figure

off towards the centre. If shear stress is constant it follows from the equation above that a large ice thickness must be associated with a small surface slope, and a small ice thickness with a large surface slope. The longitudinal profile of a glacier will therefore have a parabolic form, with high slopes at the margin and low slopes in the accumulation zone. The slope of this profile may be reduced or modified if the glacier flows over a layer of deformable sediment (Figure 3.6). This consistency of ice-surface profile makes it possible to reconstruct the form of Cenozoic ice sheets that have long since disappeared if their former margin is known (Box 3.2). The consistency of basal shear stress values is also of importance in providing a way of

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