# Longitudinal Stress

## Deviatoric stress

Normal stress is the stress acting on the bed in the vertical direction. Ice tends to spread out under its own weight, so normal stresses act in all other directions. If the ice is subject to other pushes and pulls, the stresses at location x may differ from the average value[1].

The difference between a stress at location x and the regional mean normal stress is the deviatoric stress; it represents a deviation from the mean.

The deviatoric stress in a given direction is compressive if the normal stress is greater than the mean, and tensile if the normal stress is less than the mean.

Tensile and compressive stresses are greatest at 45° from the shear plane, and zero across the shear plane. As ice is subject to unequal normal stresses, it will also experience shear stresses in directions oblique to the normal stress axis[1]. This shear stress is therefore zero parallel to the normal shear stress maximum, and is at its greatest at 45° to the normal shear stress maximum.

Therefore, a shear stress in one direction results in a deviatoric stress in other directions.

Shear stresses and deviatoric stresses in ice flow. After Benn and Evans 2010, Cuffey and Patterson 2010.

## Longitudinal stress

Longitudinal stresses modify, enhance and resist the basal shear stress in a glacier. They comprise both pushing and pulling stresses, and are essentially the pushing and pulling effect of the ice. The spatial variations in these pushing and pulling forces yield longitudinal stress gradients. The longitudinal stress gradient is the result of variations in along-flow directed deviatoric stresses[1].

In a simple, idealised glacier, the accumulation area is dominated by extension. Particles are driven downwards. The ablation area is dominated by compression. Particles are driven upwards.

Compressive and extensional ice flow drives thinning and movement of particles.

In the accumulation area, the along-flow compressive deviatoric stresses decrease down-glacier. The glacier is pushed along from behind. Tensile stresses dominate, opening up transverse crevasses. The ice thins downstream. The valley narrows and flowlines converge.

In the ablation area, the along-flow compressive deviatoric stresses increase down-glacier and the glacier is held back from in front. There is a compressive flow with sideways extension towards the glacier terminus, which results in splaying crevasses.

Longitudinal stresses and resulting crevasse patterns.

## Patterns of crevasses

Crevasses are tensional fractures in ice. They form characteristic patterns that are related to the principle stresses. Crevasses open in the direction of maximum tension[2].

Extending flow in the accumulation area tends to result in concave transverse crevasses, orientated at 90° to the direction of flow. Velocity increases downstream.

In the more central parts of the glacier, the shear stress exerted by the valley walls results in marginal crevasses.

In the lower parts of the glacier, velocity decreases downstream. There is a small tensile principle stress inclined at more than 45° to the x axis, and a large compressive principle stress; the crevasses therefore meet the valley sides at angles greater than 45°.

At the glacier snout, flowlines often diverge. This sets up tension parallel to the ice margin and opens crevasses perpendicular to the ice margin.

After formation, crevasses are rotated, bent and moved by ice movement. Marginal crevasses may rotate so that they no longer point at 45° up-glacier, and may even point down-glacier. Crevasses may close, and remain visible as crevasse traces. Irregular bedrock, subglacial hills and promontories may also cause crevasse formation.

Crevasses on a glacier

## References

1. Benn, D.I. and D.J.A. Evans, Glaciers & Glaciation. 2010, London: Hodder Education. 802.
2. Cuffey, K.M. and W.S.B. Paterson, The Physics of Glaciers, 4th edition. 2010: Academic Press. 704.

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