Bed Coupling

1. Bed Coupling 1. Introduction 2. Sources of the idea • Boulton's experiments • Remote sensing 3. Processes • sources of strength • the Coulomb equation and pore water pressure • strain above critical shear stress 4. Additional factors • dilation • grain crushing • grain size • thermal processes • spatial variation in bed strength • decoupling

2. References Bennett, M.R. and Glasser, N.F. (1996) Glacial geology: ice sheets and landforms. Wiley, Chichester. Chapter 3

3. Introduction The bed may not be the ice-substrate An "effective“ bed The idea: • Shear stress exerted by the ice may exceed the shear strength of the sediment • Deformation penetrates the substrate to the depth at which shear strength exceeds shear stress • Shear stress diminishes with increased particle to particle contact • Pervasive deformation and forward movement sediment • aka Subsole deformation

4. UF US UD A horizon Unfrozen sediment bed B horizon Ice surface

5. Sources of ideas Pleistocene geology of North America – what was the substrate? Experiments conducted by G.S. Boulton on Breidamerkajokull an outlet glacier of Vatnajokull in Iceland • Tunnels in the cliff to access the bed • Inserted segmented rods into the substrate • Excavated several days later and found that the rods were displaced downstream

7. Sources of ideas (ctd.) A two-tired till Upper layer (A) • Porous, low density • Only 40-50% mineral grains • 0.5m thick Lower layer (B) • Denser • Limited deformation • Brittle deformation

8. Displacement constituted 80-95% of forward motion of the glacier • Pore water pressures • fluctuated on daily basis, probably linked to the production of surface melt • high pressures = high strain rates • Slurry ejected from tunnel Comment

9. Other experiments Borehole data Trapridge Glacier, Yukon (Blake et al.) Storglaciaren, Sweden (Iverson et al.) Revealed complex patterns of subsole deformation Up to69% motion Little information on stress-strain relationships Seismic data Unfrozen till beneath the Antarctic ice sheet Ice stream B (Alley et al. 1986; Blankenship et al. 1987) Shear of a thin layer of basal till of motion 69% Englehardt et al. 1998

10. Other experiments Direct observation Shear within ice-laden drift Urunqui No 1 Glacier ca 60% of total motion (Echelemyer and Wang 1987) Deformation within basal ice Suess Glacier Compound velocity profile part linear velocity profile part power law

11. Englacial facies Amber facies Solid facies Stratified facies Suess Glacier

12. Other experiments Direct observation Shear within ice-laden drift Urunqui No 1 Glacier ca 60% of total motion (Echelemyer and Wang 1987) Deformation within basal ice Suess Glacier Compound velocity profile part linear velocity profile part power law Video techniques Ice stream C

13. Processes From the field studies: • a lack of empirical data • no repetition of Boulton's experiment • influence on glacier morphology not agreed (modelling) • no agreement on how widespread Agreed: • no deformation occurs unless the yield stress or critical shear stress of the material is exceeded

14. Critical shear stress Minimum stress required to overcome the strength of material = shear strength at the onset of movement Sources of strength – cohesion and friction

15. Cohesion • electrostatic forces between particles • chemical bonds between grains • negligible for particles >1mm

16. Frictional strength • Resistance of grains to shearing and crushing • Variables • Size • Packing • Sorting • Directly proportional to normal stress

18. Frictional strength • Resistance of grains to shearing and crushing • Size • Packing • Sorting • Directly proportional to normal stress • Represented by the tangent of the angle if the normal and shear stresses are at right angles • Coefficient of the angle of friction (tan f ) • Typical values vary between 7 and 50o

20. The coulomb equation and pore water pressure s = c + s tan f Frictional strength modulated by pore water pressure • At low water contents surface tension pulls the grains together thereby increasing frictional strength • At higher water contents part of the normal stress is transferred and borne by the pore water

21. s =Pi - Pw where s = effective pressure Pi = ice overburden pressure Pw = water pressure eg saturated sand weaker than dry or damp sand Incorporated into Coulomb equation: s=c + (Pi - Pw) tan f

22. Strain above critical shear stress Flow laws proposed to describe deformation Viscous vs. Plastic Boulton and Hindmarsh (1987) - viscous where e = strain rate to = shear stress tcr = critical shear stress s = effective normal stress K,a,b = constants dependent on material properties

23. This "law" states that: • the strain rate rises as shear stress becomes greater than critical shear stress • the strain rate increases as effective normal pressure increases In ice strain is independent of normal stress

24. How do the equations describe subsole deformation: • The deforming layer is confined to the upper part of the bed because the normal stress and the frictional strength increase in a downward direction • Therefore there will be a cross-over and deformation will cease at some depth • Therefore changes in pore water pressure could result in thinning and/or thickening of the deforming layer

25. Stress Strain rate A Horizon Depth below glacier sole B Horizon Sediment shear strength Basal shear stress

26. Shear strain rates increase upwards where normal stress is at a minimum • Strain rates increase with pore water pressure due to the influence on effective normal stress and intergranular friction • Therefore inefficient drainage is conducive to high strain

27. There are, however, several additional factors that may be important: • Dilation • Grain crushing • Grain size • Thermal processes • Spatial variations in bed strength • Decoupling of the bed

28. Dilation Why the low density of the tills at Breidamerkurjokull? Attributed to the dilation during shear How? It has been suggested that a critical shear is required to sustain dilation

30. Dilated sediment is weaker • Decreased packing • Decreased contact area Feedback mechanisms (positive, or self-enhancing) • As strain rises, dilation occurs, further weakening, therefore further shear • Converse: As strain rates lower, sediment collapses, increased strength, further decreased shear Implications • temporal scaling • flow law jumps

31. Grain crushing Shearing by crushing (Hooke and Iversen) Only works if shear strength is greater than grain strength • Stress concentrations? Probably only important is strong, stiff, non dilatent material Not likely when pore water pressures are high

32. Sediment grain size Partly in the Coulomb equation • Coarse, poorly sorted have high strength • Fine, well sorted low strength Influence of water flow and pore water pressure • Permeability, related to pore space which is in turn related to size • Fine grained sediment more likely to deform

33. Thermal processes Cannot be considered separately from thermal processes considered previously Expect a wide range of ice, debris and water mixtures Therefore a wide variety of flow behavior More later

34. Spatial variations in bed strength Observations of "sticky spots" on glacier beds within otherwise low strength beds Large boulders providing "bridging” through the deforming layer and resting on stronger till Typical ice stream behaviour (explains lack of run-away motion?) Kamb (1991) and Alley (1993) Modelling may lead to error if the bed is treated as homogeneous (rates + processes)

35. Decoupling Very high water pressures may lead to decreases in strain rates in bed materials Self organisation of a distributed hydro system at the ice-till interface (if there is such an interface) Canal networks postulated (Walder and Fowler 1994)

36. Decoupling Canal networks postulated (Walder and Fowler 1994) The model suggests that: At low pore pressures high sed strength limits deformation • ice will tend to infiltrate the bed coupling it to the glacier • possible "ploughing" of the bed At higher pore pressures sediment strength is reduced encouraging deformation • at a critical limit dilation is pervasive and flow occurs • rising pore pressures reduce the tendency for ice to penetrate the sediment and decoupling occurs

37. Decoupling At very high pore pressures a distributed drainage system develops at the ice-sediment interface • Decoupling • Sliding is very efficient • May not change total glacier velocity

39. Basal thermodynamics: thermal control of glacial erosion and deposition where Ls = heat due to sliding Lg = heat due to geothermal heating Ki = thermal conductivity of ice dT/dH = temperature gradient of basal ice Three thermal conditions

40. Ice surface UF UF US UF US UD Frozen bed Unfrozen rock bed A horizon Unfrozen sediment bed B horizon

41. Case 1: Temperature gradient is insufficient to drain away heat supplied to the basal debris zone. Melting and sliding results. Case 2: Temperature gradient is just sufficient to conduct heat from the bed, an approximate balance between melting and freezing. Regelation takes place readily and sliding occurs. Case 3: The temperature gradient is more than sufficient to conduct all the heat from the bed. Dry-based.