The role of bed separation and friction in sliding over an undeformable bed

AbstractThe classic sliding theories usually assume that the sliding motion occurs frictionlessly. However, basal ice is debris-laden and friction exists between the substratum and rock particles embedded in the basal ice. The influence of debris concentration on the sliding process is investigated. The actual conditions where certain types of friction apply are defined, the effect for the case of bed separation due to a subglacial water pressure is studied and consequences for the sliding law are formulated. The numerical modelling of the sliding of an ice mass over an undulating bed, including the effect of both the subglacial water pressure and the friction, is done by using the finite-clement method. Friction, seen as a reduction of the driving shear stress due to gravity, can be included in existing sliding laws which should contain the critical pressure as an important variable. An approximate functional relationship between the sliding velocity, the effective basal shear stress and the subglacial water pressure is given.

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Basal Sliding and Bed Separation: Is There a Connection?

Journal of Glaciology ◽

10.1017/s0022143000030045 ◽

1979 ◽

Vol 23 (89) ◽

pp. 407-408 ◽

Cited By ~ 1

Author(s):

Robert Bindschadler

Keyword(s):

Shear Stress ◽

Normal Stress ◽

Water Pressure ◽

Simple Relationship ◽

Sliding Velocity ◽

Separation Parameter ◽

Basal Sliding ◽

Bed Separation ◽

Image Position ◽

Basal Shear

Abstract Analysis of field data from Variegated Glacier supports the conclusion of Meier (1968) that no simple relationship between basal shear stress and sliding velocity can be found. On the other hand, an index of bed separation is defined and evaluated that correlates very well with the longitudinal variation of summer sliding velocity inferred for Variegated Glacier. This bed separation parameter is defined as where τ is the basal shear stress and is proportional to the drop in normal stress on the down-glacier side of bedrock bumps and N eff is the effective normal stress equal to the overburden stress minus the subglacial water pressure. The water-pressure distribution is calculated assuming water flow to be confined in subglacial Röthlisberger conduits. The excellent agreement between the longitudinal profiles of I and sliding velocity suggests that calculations of the variation of bed separation can be used to deduce the variation of sliding velocity in both space and time. Further, it is possible that a functional relationship can be developed that adequately represents the geometric controls on basal sliding to permit accurate predictions of sliding velocities.

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Basal Sliding and Bed Separation: Is There a Connection?

Journal of Glaciology ◽

10.3189/s0022143000030045 ◽

1979 ◽

Vol 23 (89) ◽

pp. 407-408

Author(s):

Robert Bindschadler

Keyword(s):

Shear Stress ◽

Normal Stress ◽

Water Pressure ◽

Simple Relationship ◽

Sliding Velocity ◽

Separation Parameter ◽

Basal Sliding ◽

Bed Separation ◽

Image Position ◽

Basal Shear

AbstractAnalysis of field data from Variegated Glacier supports the conclusion of Meier (1968) that no simple relationship between basal shear stress and sliding velocity can be found. On the other hand, an index of bed separation is defined and evaluated that correlates very well with the longitudinal variation of summer sliding velocity inferred for Variegated Glacier. This bed separation parameter is defined as where τ is the basal shear stress and is proportional to the drop in normal stress on the down-glacier side of bedrock bumps and Neff is the effective normal stress equal to the overburden stress minus the subglacial water pressure. The water-pressure distribution is calculated assuming water flow to be confined in subglacial Röthlisberger conduits. The excellent agreement between the longitudinal profiles of I and sliding velocity suggests that calculations of the variation of bed separation can be used to deduce the variation of sliding velocity in both space and time. Further, it is possible that a functional relationship can be developed that adequately represents the geometric controls on basal sliding to permit accurate predictions of sliding velocities.

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Basal Water Film, Basal Water Pressure, and Velocity of Traveling Waves on Glaciers

Journal of Glaciology ◽

10.1017/s0022143000005116 ◽

1983 ◽

Vol 29 (101) ◽

pp. 20-27 ◽

Cited By ~ 15

Author(s):

J. Weertman ◽

G. E. Birchfield

Keyword(s):

Traveling Waves ◽

Traveling Wave ◽

Water Pressure ◽

Strong Support ◽

Water Film ◽

Field Measurements ◽

Surface Velocity ◽

Sliding Velocity ◽

Wave Velocities ◽

Basal Shear

Abstract The theory of Nye and of Weertman of traveling waves on glaciers is extended to cover the situation where the presence of abundant basal water or increased basal water pressure produces increased sliding of a glacier over its bed. It is found that the ratio of traveling-wave velocity to surface velocity is independent of the amount of water or the basal water pressure. The theoretical value of this ratio, about 4 to 5, agrees with that found in field measurements (the most recent data are from Mer de Glace). It is concluded that field observations of traveling-wave velocities lend strong support to any glacier sliding theory in which the sliding velocity is proportional to the basal shear stress raised to about a second to fifth power and in which the sliding velocity is a function of either or both the amount of water at the bed of a glacier and the pressure within this water.

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Cyclic Surging of Glaciers

Journal of Glaciology ◽

10.3189/s002214300002267x ◽

1973 ◽

Vol 12 (64) ◽

pp. 3-18 ◽

Cited By ~ 2

Author(s):

G. de Q. Robin ◽

J. Weertman

Keyword(s):

Shear Stress ◽

Pressure Gradient ◽

Water Pressure ◽

Stress Gradient ◽

Longitudinal Direction ◽

Phenomenological Theory ◽

Trigger Zone ◽

Basal Shear ◽

Velocity Zone ◽

Theory And Model

AbstractA partly phenomenological theory and model are constructed of cyclically surging glaciers. During the after-surge portion of a surge cycle the lower portion of a glacier becomes increasingly stagnant. The upper part of the glacier gradually becomes more active as both its thickness and the magnitude of its basal shear stress increase. In the region between these two parts, called by us the trigger zone, the value of the derivative of the basal shear stress in the longitudinal direction of the glacier gradually increases with time. The pressure gradient in the water at the base of a glacier is related to the derivative of the basal shear stress. The pressure gradient decreases as the basal shear-stress gradient increases. The pressure gradient actually can take on negative values, a condition which produces “up-hill” water flow at the base of a glacier. A surge is started in the trigger zone when water is dammed there by a zero water-pressure gradient. The zone of fast-sliding velocities propagates up the glacier from the trigger zone with a velocity of the order of a surge velocity. The fast-sliding velocity zone also propagates down the glacier because of increased melt-water production.

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Debris-bed friction during glacier sliding with ice–bed separation

Annals of Glaciology ◽

10.1017/aog.2019.46 ◽

2019 ◽

Vol 60 (80) ◽

pp. 30-36 ◽

Cited By ~ 1

Author(s):

Neal R. Iverson ◽

Christian Helanow ◽

Lucas K. Zoet

Keyword(s):

Shear Stress ◽

Slip Velocity ◽

Contact Forces ◽

Debris Particles ◽

Rock Bed ◽

Bed Separation ◽

Particle Bed ◽

Basal Shear ◽

Bed Friction ◽

Theory And Experiments

AbstractTheory and experiments indicate that ice–bed separation during glacier slip over 2-D hard beds causes basal shear stress to reach a maximum at a particular slip velocity and decrease at higher velocities. We use the sliding theory of Lliboutry (1968) to explore how friction between debris particles in sliding ice and a rock bed affects this relationship between shear stress and slip velocity. Particle–bed contact forces and associated debris friction increase with increasing slip velocity, owing to increased rates of ice convergence with up-glacier facing surfaces. However, debris friction on diminished areas of the bed counteracts this effect as cavities grow. Thus, friction from debris alone increases only slightly with slip velocity, and for sediment particles larger than ~60 mm in diameter, debris friction peaks and decreases with increasing slip velocity. The effect on the sliding relationship is to steepen its rising limb and shift its shear stress peak to a slightly higher velocity. These results, which exclude the effect of debris friction on cavity size and debris concentrations above ~15%, indicate that the effect of debris in ice is to increase basal shear stress but not significantly change the form of the sliding relationship.

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Channelized subglacial drainage over a deformable bed

Journal of Glaciology ◽

10.3189/s0022143000003750 ◽

1994 ◽

Vol 40 (134) ◽

pp. 3-15 ◽

Cited By ~ 21

Author(s):

Joseph S. Walder ◽

Andrew Fowler

Keyword(s):

Water Pressure ◽

Ice Sheets ◽

Drainage System ◽

West Antarctica ◽

Plausible Assumption ◽

Basal Ice ◽

Ice Stream B ◽

Steep Slopes ◽

Subglacial Drainage

AbstractWe develop theoretically a description of a possible subglacial drainage mechanism for glaciers and ice sheets moving over saturated, deformable till. The model is based on the plausible assumption that flow of water in a thin film at the ice-till interface is unstable to the formation of a channelized drainage system, and is restricted to the case in which meltwater cannot escape through the till to an underlying aquifer. In describing the physics of such channelized drainage, we have generalized and extended Röthlisberger’s model of channels cut into basal ice to include “canals” cut into the till, paying particular attention to the role of sediment properties and the mechanics of sediment transport. We show that sediment-floored Röthlisberger (R) channels can exist for high effective pressures, and wide, shallow, ice-roofed canals cut into the till for low effective pressures. Canals should form a distributed, non-arborescent system, unlike R channels. For steep slopes typical of alpine glaciers, both drainage systems can exist, but with the water pressure lower in the R channels than in the canals; the canal drainage should therefore be unstable in the presence of channels. For small slopes typical of ice sheets, only canals can exist and we therefore predict that, if channelized meltwater flow occurs under ice sheets moving over deformable till, it takes the form of shallow, distributed canals at low effective pressure, similar to that measured at Ice Stream B in West Antarctica. Geologic evidence derived from land forms and deposits left by the Pleistocene ice sheets in North America and Europe is also consistent with predictions of the model.

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The sliding velocity over a sinusoidal bed at high water pressure

Journal of Glaciology ◽

10.1017/s0022143000002707 ◽

1998 ◽

Vol 44 (147) ◽

pp. 379-382 ◽

Cited By ~ 6

Author(s):

Martin Truffer ◽

Almut Iken

Keyword(s):

Contact Area ◽

Critical Pressure ◽

Water Pressure ◽

Wave Length ◽

High Water ◽

Force Balance ◽

Sliding Velocity ◽

Pressurized Water ◽

Overburden Pressure ◽

Basal Shear

AbstractUnder idealized conditions, when pressurized water has access to all low-pressure areas at the glacier bed, a sliding instability exists at a critical pressure,pc,well below the overburden pressure,p0.The critical pressure is given by, wherelis the wave length andais the amplitude of a sinusoidal bedrock, andTis the basal shear stress. When the subglacial water pressure, pw, approaches this critical value, the area of ice-bed contact,△l,becomes very small and the pressure on the contact area becomes very large. This pressure is calculated from a force balance and the corresponding rate of compression is obtained using Glen’s flow law for ice. On the assumption that compression in the vicinity of the contact area occurs over a distance of the order of the size of this area,Δl,a deformational velocity is estimated. The resultant sliding velocity shows the expected instability at the critical water pressure. The dependency on other parameters, such as wavelengthland roughnessa/l,was found to be the same as for sliding without bed separation.

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In search of ice-stream sticky spots

Journal of Glaciology ◽

10.3189/s0022143000016336 ◽

1993 ◽

Vol 39 (133) ◽

pp. 447-454 ◽

Cited By ~ 7

Author(s):

Richard B. Alley

Keyword(s):

Shear Stress ◽

Large Scale ◽

Water Pressure ◽

Pressure Measurements ◽

West Antarctica ◽

Ice Surface ◽

Ice Stream ◽

Bed Roughness ◽

Basal Shear

AbstractThe basal shear stress of an ice stream may be supported disproportionately on localized regions or “sticky spots”. The drag induced by large bedrock bumps sticking into the base of an ice stream is the most likely cause of sticky spots. Discontinuity of lubricating till can cause sticky spots, but they will collect lubricating water and therefore are unlikely to support a shear stress of more than a few tenths of a bar unless they contain abundant large bumps. Raised regions on the ice-air surface can also cause moderate increases in the shear stress supported on the bed beneath. Surveys of large-scale bed roughness would identify sticky spots caused by bedrock bumps, water-pressure measurements in regions of thin or zero till might reveal whether they were sticky spots, and strain grids across the margins of ice-surface highs would show whether the highs were causing sticky spots. Sticky spots probably are not dominant in controlling Ice Stream Β near the Upstream Β camp, West Antarctica.

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Cyclic Surging of Glaciers

Journal of Glaciology ◽

10.1017/s002214300002267x ◽

1973 ◽

Vol 12 (64) ◽

pp. 3-18 ◽

Cited By ~ 65

Author(s):

G. de Q. Robin ◽

J. Weertman

Keyword(s):

Shear Stress ◽

Pressure Gradient ◽

Water Pressure ◽

Stress Gradient ◽

Longitudinal Direction ◽

Phenomenological Theory ◽

Trigger Zone ◽

Basal Shear ◽

Velocity Zone ◽

Theory And Model

AbstractA partly phenomenological theory and model are constructed of cyclically surging glaciers. During the after-surge portion of a surge cycle the lower portion of a glacier becomes increasingly stagnant. The upper part of the glacier gradually becomes more active as both its thickness and the magnitude of its basal shear stress increase. In the region between these two parts, called by us the trigger zone, the value of the derivative of the basal shear stress in the longitudinal direction of the glacier gradually increases with time. The pressure gradient in the water at the base of a glacier is related to the derivative of the basal shear stress. The pressure gradient decreases as the basal shear-stress gradient increases. The pressure gradient actually can take on negative values, a condition which produces “up-hill” water flow at the base of a glacier. A surge is started in the trigger zone when water is dammed there by a zero water-pressure gradient. The zone of fast-sliding velocities propagates up the glacier from the trigger zone with a velocity of the order of a surge velocity. The fast-sliding velocity zone also propagates down the glacier because of increased melt-water production.

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