Transcript Bed Coupling - Geography

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
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
Ice surface
UF
Unfrozen
sediment
bed
US
A horizon
B horizon
UD
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 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
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
Suess Glacier
4000
Englacial facies
Distance above bed (mm)
3500
Amber facies
3000
2500
Solid facies
2000
1500
Stratified facies
1000
500
0
0
100
200
Velocity (mm.a-1)
300
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
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 f )
 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 + 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
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
Strain above critical shear stress
Flow laws proposed to describe deformation
Viscous vs. Plastic
Boulton and Hindmarsh (1987) - viscous
e
K t 0  t cr 
a
s
b
where
e = strain rate
to = shear stress
tcr = critical shear stress
s = effective normal stress
K,a,b = constants dependent
on material properties
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
Stress
Strain rate
Depth
A Horizon
below
glacier
sole
B Horizon
Sediment shear
strength
Basal shear stress

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
Three thermal conditions
 dT 
 dT 
 dT 
L s  L g  Ki 
i L s  L g  K i 
i L s  L g  K i 
i
 dH 
 dH 
 dH 
where
Ls = heat due to sliding
Lg = heat due to geothermal heating
Ki = thermal conductivity of ice
dT/dH = temperature gradient of basal ice
Ice surface
UF
Frozen
bed
UF
Unfrozen
rock bed
US
UF
US
Unfrozen A horizon
sediment
bed
B horizon
UD
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. Drybased.