processus de versants - géosciences montpellier · hillslope evolution diffusion law surface...

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Processus de Processus de versantsversants

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Hillslopes are an important part of the terrestrial landscape.

The Earth's landscape can be thought of as being composed of a mosaic of slope types, ranging from steep mountains and cliffs to almost flat plains.

On most hillslopes large quantities of soiland sediment are moved over time via the mediums of air, water, and ice often underthe direct influence of gravity.

Hillslope Processes

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Hillslope Processes

Fabriques of weak materialsPhysical processes

- heating and cooling cycles- freeze-thaw cycles- Dry – wet cycles …

Chemical processes (weathering)Bioturbation (fauna and flora)

Hillslope transport

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Hillslope Transport

Soil creepShallow sliding

M. Summerfield, Global Geomophology,1991

Surface runoff

Rock falls

SolifluctionLandslide

Debris flow

Soil creepDryDry

WetWet

FastFast SlowSlow

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Hillslope Transport


Surface runoff


Rock fall


Debris flow

Soil creep

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Hillslope Transport

A rock fall consists of one or maybe a few rocks that detach from the high part of a steep slope, dropping and perhaps bouncinga few times as they move very rapidly down slope.

Rock falls are very dangerous because theycan occur without warning, and because the rocks are traveling at high velocity.

You can usually tell where rock falls are common by identifying talus at the base of steep slopes.

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Hillslope Transport


Surface runoff


Rock fall


Debris flow

Soil creep

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Hillslope TransportRock slide occurs where there is a tilted, pre-existing plane of weakness within a slope which serves as a slide surface for overlying sediment/rock to move downward. Such planes of weakness are either flat sedimentary surfaces (usuallywhere one layer of sediment or sedimentaryrock is in contact with another layer), planes of cleavage (determined by mineral foliation) within metamorphic rocks, or a fracture (faultor joint) within a body of rock. Rock slidescan be massive, occasionally involving an entire mountainside, making them a real hazard in areas where a surface of weakness tilts in the same direction as the surface of the slope. Rock slides can betriggered by earthquakes or by the saturation of a slope with water.

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Hillslope Transport



Surface runoff

Rock fall


Debris flow

Soil creep

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Hillslope TransportAs the name implies, this type of flow contains a variety of particles or fragments, mainly smallto large rock fragments but also trees, animal carcasses, cars and buildings.Debris flows usually contain a high water content which enables them to travel at fairlyhigh velocity for some distance from where theyoriginated. Debris flows tend to follow the pathsof pre-existing stream channels and valleys, but debris flows are much denser than water, sothey can destroy anything in their paths such as houses, bridges, or highways.In volcanically active regions, ash on the slopesof volcanoes can readily mix with water fromrainfall or snowmelt. When this occurs, a low-viscosity debris flow, called by the Indonesianterm lahar, can form and move very rapidly down slope.

before

after

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Hillslope Transport


Surface runoff


Rock fall


Debris flow

Soil creep

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Hillslope Transport

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Hillslope Transport

This is the slowest type of mass wasting, requiring years of gradualmovement to have a pronounced effect on a slope. Slopes creepdue to the expansion and contraction of surface sediment, and the pull of gravity. The pull of gravity is a constant, but the forces causing expansion and contraction of sediment are not. The presence of water is generally required, but in a desert lackingvegetative ground cover even dry sediment will creep due to dailyheating and cooling of surface sediment grains.

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Hillslope Transport


Surface runoff


Rock fall


Debris flow

Soil creep

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Hillslope Transport

Mass movement of soil and regolithaffected by alternate freezing and thawing. Characteristic of saturatedsoils in high latitudes, both within and beyond the permafrost zone. A number of features contribute to active solifluction:• frequent freeze-thaw cycles• saturated soils and regolith, aftersnow melt and heavy rainfall• frost-susceptible materials, withsignificant contents of silt and clay, at least at depth• extensive regolith across a range of slope angles

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Hillslope Transport

Surface runoff


Rock fall


Debris flow

Soil creep

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Hillslope Stability

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Hillslope Stability

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Hillslope Stability

Angle of repose

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Hillslope Stability

Every body knows about friction !

Static friction

Sliding friction

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Hillslope Stability

Pore pressure

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Slope Stability Analysis

bτα

wsssb m ρυρυρ )1( −+=h

bρ

fraction of soildepth saturated

volume fraction solids

soliddensity

water densitywet bulk density

αρτ singhbb =

αρσ cosghbb =

bσ

normal stressshear stress

φσμσ tan)()( pbpbb PcPcs −+=−+=

resisting stress

cohesion

pore pressure

internal friction angle

friction

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σb

τb

F<1

F>1

F=1sb

C

μ

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Slope Stability Analysish

mh

soil surface

impermeable horizon

water table

αρ cosgmhP wp =

αρυρυφαυρρ

αρφαρρ

τφσ

sin))1((tancos)()/(

sintancos)(

tan)(

wsss

sws

b

wb

b

pb

mmghc

ghghmc

PcF

−+−+

=

−+=

−+=

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αφ

αρυφαυρ

αρυρυφαυρρ

tantan

sintancos

00sin))1((

tancos)()/(

==

==−+

−+=

ss

ss

wsss

sws

F

cmm

mghcF

Implication for dry cohesionless soil

F=1 at maximum stable slope

angle of repose = angle of internal friction!

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σb

τb

The saturation of soilmaterials increases the weight of slope materials

Saturation of soil materialscan reduce the cohesivebonds between individualsoil particles resulting in the reduction of the internalstrength of the hillslope

The presence of bedding planes in the hillslope material can cause materialabove a particular plane below groundlevel to slide along a surface lubricated by percolating moisture

σb

τb

σb

τb

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Hillslope Transport

Surface runoff


Rock fall


Debris flow

Soil creep

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Overland Flow

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Overland Flow

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Overland Flow

Rills Gullies

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Overland Flow

L

Geometric parameters• Length L• Width D• Slope S0

Physical parameters• Mean water velocity V• Water discharge q• Sediment discharge qs• kinematic viscosity ν

• Water thickness h• Basal shear stress τc• Rainfall intensity R• Bedrock rugosity k

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Overland Flow

Dimensionless number

Reynolds number

νDV

forcesviscousforcesinertial .Re ==

Low Re laminar flow - sheetHigh Re turbulent flow – rills & gullies

ghV

forcesnalgravitatioforcesinertialFr ==

Froude number

Fr < 1 subcritical flow – fluvialFr > 1 supercritical flow - torrential

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Hillslope Transport

Surface runoff


Rock fall


Debris flow

Soil creep

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Soil Creep

compression index

Total volumetric

strain

Deformationduring primaryconsolidation Effective

creep time

time scaleparameter

Madurapperuma & Puswewala, 2008

Instant and delayed compression

ε

ln t

t’ = t-τc

εc

ln τc

μ*

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Hillslope Evolution

xqPtransportproduction

th s

∂∂

−=−=∂∂

Heimstat et al., 1997

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Hillslope EvolutionProduction

Heimstat et al., 2001

Exposed bedrocksamples

Maximum of soilproduction

aheP −~

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Hillslope EvolutionTransport

Dietrich et al., 2003

Coasta

l Cali

fornia

Alpine hillslope

The flux of sediment isproportional to the hillslopegradient

xhqs ∂∂

−= κ

Diffusivity in units of L2/T

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Hillslope EvolutionDiffusion law

The flux of sediment is proportional to the hillslope gradient x

hqs ∂∂

−= κ

Conservation of mass: an increase or a decrease in the elevation is equal the change in flux per unit length x

qth s

∂∂

−=∂∂

Diffusion law

hyh

xh

th

xh

th

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2

2

2

2

2

∇=⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+∂∂

=∂∂

∂∂

=∂∂

κκ

κ

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L

x

h2

2

xh

th

∂∂

=∂∂ κ

Assuming a constant incision rate1. Find the equation associated with the hillslope geometry.2. What is the maximum variation in elevation ?3. Where is the highest slope ?4. Give its expression.

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Lachlan Valley, SE Australia

Diffusion model leads to a parabolic elevation profile

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Surface runoff


Rock falls


Debris flow

Soil creepDiffusion

Slope < 20°

The applicability of the diffusion model to hillslopeevolution depends on both the local slope and the processes acting to move sediment on the hillslope.

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Hillslope EvolutionNon-linear erosion law

Shoalhaven valley, SE AustraliaAnderson, 1994

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Roering et al., 2001

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

−∂∂

−= 211

1

xh

S

xhq

c

s κ

xhqs ∂∂

−= κ

S c

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Roering et al., 2001

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Montgomery & Brandon, 2002

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Alps

Lesser Himalaya

Taiwan

SE Australia

SE Australia

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Hillslope Evolution and Processes

Tectonic activity low highHillslope process diffusion sliding rock fallSediment flux continuous stochastic

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Hillslope Evolution and Processes

Dietrich et al., Nature, 2006

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