Debris-bed friction of hard-bedded glaciers

[1] Field measurements of debris-bed friction on a smooth rock tablet at the bed of Engabreen, a hard-bedded, temperate glacier in northern Norway, indicated that basal ice containing 10% debris by volume exerted local shear traction of up to 500 kPa. The corresponding bulk friction coefficient between the dirty basal ice and the tablet was between 0.05 and 0.08. A model of friction in which nonrotating spherical rock particles are held in frictional contact with the bed by bed-normal ice flow can account for these measurements if the power law exponent for ice flowing past large clasts is 1. A small exponent (n < 2) is likely because stresses in ice are small and flow is transient. Numerical calculations of the bed-normal drag force on a sphere in contact with a flat bed using n = 1 show that this force can reach values several hundred times that on a sphere isolated from the bed, thus drastically increasing frictional resistance. Various estimates of basal friction are obtained from this model. For example, the shear traction at the bed of a glacier sliding at 20 m a−1 with a geothermally induced melt rate of 0.006 m a−1 and an effective pressure of 300 kPa can exceed 100 kPa. Debris-bed friction can therefore be a major component of sliding resistance, contradicting the common assumption that debris-bed friction is negligible.

[1]  T. H. Jacka.  The time and strain required for development of minimum strain rates in ice , 1984 .

[2]  H. Bernard.  A Theoretical Model of Glacial Abrasion , 1979, Journal of Glaciology.

[3]  J. Harper,et al.  Depth‐varying constitutive properties observed in an isothermal glacier , 2002 .

[4]  S. Goren.  The hydrodynamic force resisting the approach of a sphere to a plane permeable wall , 1979 .

[5]  G. Boulton.  Processes and Patterns of Glacial Erosion , 1982 .

[6]  N. Glasser,et al.  Glacial erosional landforms: origins and significance for palaeoglaciology , 2004 .

[7]  John Frederick Nye,et al.  A calculation on the sliding of ice over a wavy surface using a Newtonian viscous approximation , 1969, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[8]  S. Marshall,et al.  North American Ice Sheet reconstructions at the Last Glacial Maximum , 2002 .

[9]  J. Nye.  Theory of regelation , 1967 .

[10]  H. Brenner.  The slow motion of a sphere through a viscous fluid towards a plane surface , 1961 .

[11]  B. Kamb.  Sliding motion of glaciers: Theory and observation , 1970 .

[12]  J. F. Nye,et al.  Glacier sliding without cavitation in a linear viscous approximation , 1970, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[13]  M. E. O'neill,et al.  SLOW MOTION OF A SOLID SPHERE IN THE PRESENCE OF A NATURALLY PERMEABLE SURFACE , 1991 .

[14]  M. Funk,et al.  Mechanisms of fast flow in Jakobshavns Isbræ, West Greenland: Part I. Measurements of temperature and water level in deep boreholes , 1993, Journal of Glaciology.

[15]  E. Rutter,et al.  Experimental rock‐on‐rock frictional wear: Application to subglacial abrasion , 2004 .

[16]  Peter L. Moore,et al.  Effects of Basal Debris on Glacier Flow , 2003, Science.

[17]  O. Castelnau,et al.  Compressive creep of ice containing a liquid intergranular phase: Rate‐controlling processes in the dislocation creep regime , 1999 .

[18]  L. Lliboutry.  General Theory of Subglacial Cavitation and Sliding of Temperate Glaciers , 1968, Journal of Glaciology.

[19]  G. Gudmundsson,et al.  Basal-flow characteristics of a non-linear flow sliding frictionless over strongly undulating bedrock , 1997, Journal of Glaciology.

[20]  B. Hallet.  Glacial Abrasion and Sliding: their Dependence on the Debris Concentration in Basal Ice , 1981, Annals of Glaciology.

[21]  J. Happel,et al.  Low Reynolds number hydrodynamics: with special applications to particulate media , 1973 .

[22]  L. Reynaud.  Flow of a Valley Glacier with a Solid Friction Law , 1973, Journal of Glaciology.

[23]  S. Goren.  The normal force exerted by creeping flow on a small sphere touching a plane , 1970, Journal of Fluid Mechanics.

[24]  David L. Goldsby,et al.  Superplastic deformation of ice: Experimental observations , 2001 .

[25]  L. Morland.  Glacier Sliding Down an Inclined Wavy Bed With Friction , 1976, Journal of Glaciology.

[26]  P. Jansson,et al.  Rheology of till beneath Storglaciären, Sweden , 1997 .

[27]  D. Cohen.  Rheology of ice at the bed of Engabreen, Norway , 2000, Journal of Glaciology.

[28]  W. Budd,et al.  Empirical Studies of Ice Sliding , 1979, Journal of Glaciology.

[29]  B. Hallet.  Subglacial Regelation Water Film , 1979, Journal of Glaciology.

[30]  A. Iken,et al.  The relationship between subglacial water pressure and velocity of Findelengletscher, Switzerland, during its advance and retreat , 1997 .

[31]  R. Hindmarsh.  Cavities and the effective pressure between abrading clasts and the bedrock , 1996, Annals of Glaciology.

[32]  J. Kohler,et al.  Sliding of ice past an obstacle at Engabreen, Norway , 2000, Journal of Glaciology.

[33]  J. Schweizer,et al.  The role of bed separation and friction in sliding over an undeformable bed , 1992, Journal of Glaciology.

[34]  A. Fowler,et al.  A theoretical treatment of the sliding of glaciers in the absense of cavitation , 1981, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.