Bed Coupling1. 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

References

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

USUF UD

A horizon

B horizon

Unfrozen sediment bed

Ice surface

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

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

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

Other experiments

Borehole dataTrapridge Glacier, Yukon (Blake et al.)Storglaciaren, Sweden (Iverson et al.)Revealed complex patterns of subsole deformationUp to69% motionLittle information on stress-strain relationships

Seismic dataUnfrozen 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

Other experiments

Direct observationShear within ice-laden drift Urunqui No 1 Glacierca 60% of total motion (Echelemyer and Wang 1987)

Deformation within basal ice Suess GlacierCompound velocity profile

part linear velocity profilepart power law

0

500

1000

1500

2000

2500

3000

3500

4000

0 100 200 300

Velocity (mm.a-1)

Dis

tan

ce a

bo

ve b

ed (

mm

)

Stratified facies

Englacial facies

Solid facies

Amber facies

Suess Glacier

Other experiments

Direct observationShear within ice-laden drift Urunqui No 1 Glacierca 60% of total motion (Echelemyer and Wang 1987)

Deformation within basal ice Suess GlacierCompound velocity profile

part linear velocity profilepart power law

Video techniquesIce stream C

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

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

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

Frictional strength Resistance of grains to shearing and crushing Variables

Size Packing Sorting

Directly proportional to normal stress

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 ) Typical values vary between 7 and 50o

Typical cohesion values and friction angles for some geological materials Material Cohesion (kPa) Friction Angle (o) Dense sand (well sorted) 0 32-40

Dense sand (poorly sorted) 0 38-46

Gravel (well sorted) 0 34-37

Gravel (poorly sorted) 0 45-48

Bentonite clay 10-20 7-13

Soft glacial clay 30-70 27-32

Stiff glacial clay 70-150 30-32

Till (mixed grain size) 150-250 32-35

Soft sedimentary rock 1,000-20,000 25-35

Igneous rock 35,000-55,000 35-45

Source: Selby (1982)

The coulomb equation and pore water pressure

s = c + tan

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

=Pi - Pw

where

= 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

Strain above critical shear stress

Flow laws proposed to describe deformationViscous vs. Plastic

Boulton and Hindmarsh (1987) - viscous

where = strain rateo = shear stresscr = critical shear stress

= effective normal stressK,a,b = constants dependent on material properties

b

acrK

0

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

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

Basal shear stress

Sediment shear strength

Stress

Depth

below

glacier

sole

Strain rate

A Horizon

B Horizon

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

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

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

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

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

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

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

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)

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)

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

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

Basal thermodynamics: thermal control of glacial erosion and deposition

where

s = heat due to sliding

g = heat due to geothermal heating

Ki = thermal conductivity of ice

T/H = temperature gradient of basal ice

iH

TK igs

iH

TK igs

iH

TK igs

Three thermal conditions

US

Unfrozen rock bed

UFUF

Frozen bed

Ice surface

USUF UD

A horizon

B horizon

Unfrozen sediment bed

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.