1 High mobility of subaqueous debris flows and the lubricating layer model Anders Elverhøi Fabio De Blasio Trygve Ilstad Dieter Issler Carl B. Harbitz.

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High mobility of subaqueous debris flows and

the lubricating layer modelAnders ElverhøiFabio De Blasio

Trygve IlstadDieter Issler

Carl B. Harbitz

International Centre for GeohazardsNorwegian Geotechnical Institute, Norway

Dep. of Geosciences, University of Oslo, Norway..

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Debris flow

How can we explain that 10 - 1000 km3 of sediments can

• move100 - > 200 km• on < 1 degree slopes• at high velocities ( -20 - > 60 km/h)

Basic problem!

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Experimental settingsSt. Anthony Falls Laboratory

10 m

turbidity current

debris flow

6° slope

Experimental Flume: “Fish Tank”

Video (regular and high speed) and

pore- and total pressure measurements

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Flow behavior Clay rich debris flows

Hydroplaning front “Auto-acephalation” 32.5 wt% clay cited from G. Parker

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Pressure measurements at the base of a clay rich debris flow as pressure develops during the flow

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Flow behavior:Debris flow at high mass fraction of clay

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Material from the base of the debris flow is eroded and incorporated into the lubricating layer.

L1

L2

Ls

H1

H2Hs

Downslope gravitational forces

Bottom shear stresses

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Grossly simplified detachment/stretching dynamics

• Tensile force in the neck• Viscoplastic stretching of the neck is volume-

conserving– The growth rate of the length is the product of the

stretching rate with the neck length

• Solution of the simplified stretching equations:– The neck stretches and thins at a rate that increases

with time, until the height becomes zero after a finite time

• detachment occurs

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Neglected physics:• Changing tension due to slope and velocity

changes• Friction, drag and inertial forces on neck• Changes in material parameters of neck due to

– shear thinning, accumulated strain and wetting, crack formation

More sophisticated treatment is possible Coupled nonlinear equations, use a numerical modelMain difficulty is quantitative treatment of crack

formation and wetting effects

Detachment/stretching dynamics

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Tension in the “neck”:

Viscoplastic stretching of the neck is volume-conserving:

Solution of the simplified stretching equations:

Grossly simplified detachment dynamics:

ssss

s

ytyt

LdtdLHdtdH

aH

b

/,/

''

)(sin')(sin' 22222

11111 U

H

Lg

H

HLU

H

Lg

H

HL

sssst

)(

)0()0()(,1)0()(

'/

tH

HLtLeHtH

s

sss

t

y

t

y

tss

y

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Simulation of the giant Storegga slide400-500 km runout

• Clay-rich sediments– Visco-plastic

materials:

• Model approach:– “Classical” BING– BING: Remolding of

the sediment during flow

– H-BING: Hydroplaning

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Velocity profile of debris flows Bingham fluid

shear stress

yield strength

dynamic viscosity

shear rate

y

uy

Plug layer

Shear layer

Yield strength: constant during flow

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Water film shear stress reduction in a Bingham fluid

Water, w, w, uw

Mudm, m, um

Lid(Debris flow)

=1=1-

u=1

Shear layer

Plug layer

1+

R(1+)/

1

1+

1

1

1-

u(R-)/

1

1u

1

1-

Velocity Shear stress

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Simulation: final deposit of the large-scale Storegga

Initial deposits

Present deposits

= 10 kPa

= 10 kPa with remoulding to 0,5 kPa

= 10 kPa with remoulding to 0,1 kPa

= 5 kPa with hydroplaning

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Conclusions• Experiments

– water enhances the mobility of debris flows via the formation of a lubricating layer/stretching

• The giant Storegga slide – BING

• reproduced with extremely low yield stresses, 200-300 Pa

– R-BING• starting from yield stresses between 6 and 10kPa, residual

stress of 200 Pa

– Hydroplaning • extreme runout distances, even with stiff sediments

independence of sediment rheology

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Future directions (II)

• Modification of the existing models– Incorporation of water in the slurry – Detachment mechanism of a hydroplaning

head

• Parameterizations of the rheological properties as a function of water content

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Subaqueous conditions -increased mobility

Basic concept – based on experimental studies:– Hydroplaning– Lubricating– Stretching (not yet implemented)

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Comparison between Storegga slides and selected cases

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Future direction (I)

• Modification of the existing models– Incorporation of water in the slurry – Detachment mechanism of a hydroplaning head

• Parameterizations of the rheological properties as a function of water content (and stretching?)

• Important question: How is the basal “water” layer distributed?

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2W ten WD

1 1 1 1

FdU 1gsin C U

dt D L WD 2 L

yten

2 2 2

FdVgsin

dt L WD D

D1

D2

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Velocity profile of debris flows Bingham fluid – with remolding

Plug layer

Shear layer

Yield strength at start: high; 10–20 kPa

Yield strength at stop: low; < 1 kPa

The yield stress is allowed to vary according to:

eyyy )y,0,(,(

initial yield stress

residual yield stress

total shear deformation

dimensionless coefficient quantifying the remolding efficiency

0,y

y,