Processus de
versants
1
Hillslope Processes
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 soil
and sediment are moved over time via the
mediums of air, water, and ice often under
the direct influence of gravity.
2
Hillslope Processes
Fabriques of weak materials
Physical 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
Surface runoff
Wet
Debris flow
Landslide
Solifluction
Rock falls
Soil creep
Dry
Shallow sliding
M. Summerfield, Global Geomophology,1991
Fast
Slow
Soil creep
4
Hillslope Transport
Surface runoff
Debris flow
Landslide
Solifluction
Rock fall
Soil creep
Shallow sliding
M. Summerfield, Global Geomophology,1991
Soil creep
5
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 bouncing
a few times as they move very rapidly down
slope.
Rock falls are very dangerous because they
can 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
Debris flow
Landslide
Solifluction
Rock fall
Soil creep
Shallow sliding
M. Summerfield, Global Geomophology,1991
Soil creep
7
Hillslope Transport
Rock 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 (usually
where one layer of sediment or sedimentary
rock is in contact with another layer), planes
of cleavage (determined by mineral foliation)
within metamorphic rocks, or a fracture (fault
or joint) within a body of rock. Rock slides
can 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 be
triggered by earthquakes or by the
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saturation of a slope with water.
Hillslope Transport
Surface runoff
Debris flow
Landslide
Solifluction
Rock fall
Soil creep
Shallow sliding
M. Summerfield, Global Geomophology,1991
Soil creep
9
Hillslope Transport
before
after
As the name implies, this type of flow contains a
variety of particles or fragments, mainly small
to 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 fairly
high velocity for some distance from where they
originated. Debris flows tend to follow the paths
of pre-existing stream channels and valleys, but
debris flows are much denser than water, so
they can destroy anything in their paths such as
houses, bridges, or highways.
In volcanically active regions, ash on the slopes
of volcanoes can readily mix with water from
rainfall or snowmelt. When this occurs, a lowviscosity debris flow, called by the Indonesian
term lahar, can form and move very rapidly down
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slope.
Hillslope Transport
Surface runoff
Debris flow
Landslide
Solifluction
Rock fall
Soil creep
Shallow sliding
M. Summerfield, Global Geomophology,1991
Soil creep
11
Hillslope Transport
12
Hillslope Transport
This is the slowest type of mass wasting, requiring years of gradual
movement to have a pronounced effect on a slope. Slopes creep
due 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 lacking
vegetative ground cover even dry sediment will creep due to daily
13
heating and cooling of surface sediment grains.
Hillslope Transport
Surface runoff
Debris flow
Landslide
Solifluction
Rock fall
Soil creep
Shallow sliding
M. Summerfield, Global Geomophology,1991
Soil creep
14
Hillslope Transport
Mass movement of soil and regolith
affected by alternate freezing and
thawing. Characteristic of saturated
soils 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, after
snow melt and heavy rainfall
• frost-susceptible
materials,
with
significant contents of silt and clay,
at least at depth
• extensive regolith across a range of
slope angles
15
Hillslope Transport
Surface runoff
Debris flow
Landslide
Solifluction
Rock fall
Soil creep
Shallow sliding
Soil creep
16
Hillslope Stability
17
Hillslope Stability
18
Hillslope Stability
Angle of repose
19
Hillslope Stability
Every body knows about friction !
Static friction
Sliding friction
20
Hillslope Stability
Pore pressure
21
Slope Stability Analysis
volume fraction solids
wet bulk density
ρ b = υ s ρ s + m(1 − υ s ) ρ w
h
σb
σ b = ρ b gh cos α
water
density
solid
density
τb
fraction of soil
depth saturated
ρb
α
normal stress
cohesion
shear stress
τ b = ρ b gh sin α
friction
sb = c + (σ b − Pp ) μ = c + (σ b − Pp ) tan φ
resisting stress
pore pressure
internal friction
angle
22
Slope Stability Analysis
τb
F=1
F<1
sb
μ
C
F>1
σb
23
Slope Stability Analysis
h
soil surface
water table
Pp = ρ w gmh cos α
impermeable horizon
mh
F=
c + (σ b − Pp ) tan φ
τb
c + ( ρ b − ρ w m) gh cos α tan φ
=
ρ b gh sin α
(c / gh) + ( ρ s − ρ w m)υ s cos α tan φ
=
(υ s ρ s + m(1 − υ s ) ρ w ) sin α
24
Slope Stability Analysis
Implication for dry cohesionless soil
(c / gh) + ( ρ s − ρ w m)υ s cos α tan φ
F=
(υ s ρ s + m(1 − υ s ) ρ w ) sin α
m=0 c=0
ρ sυ s cos α tan φ tan φ
F=
=
υ s ρ s sin α
tan α
F=1 at maximum stable slope
angle of repose = angle of internal friction!
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Slope Stability Analysis
τb
τb
σb
σb
The saturation of soil
materials increases the
weight of slope materials
The presence of bedding planes in the
hillslope material can cause material
above a particular plane below ground
level to slide along a surface
lubricated by percolating moisture
Saturation of soil materials
can reduce the cohesive
bonds between individual
soil particles resulting in the
reduction of the internal
strength of the hillslope
τb
σb
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Hillslope Transport
Surface runoff
Debris flow
Landslide
Solifluction
Rock fall
Soil creep
Shallow sliding
Soil creep
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Overland Flow
28
Overland Flow
29
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 intensity31R
• Bedrock rugosity k
Overland Flow
Dimensionless number
Reynolds number
Re =
inertial forces V .D
=
viscous forces
ν
Low Re laminar flow - sheet
High Re turbulent flow – rills & gullies
Froude number
inertial forces
V
Fr =
=
gravitational forces
gh
Fr < 1 subcritical flow – fluvial
Fr > 1 supercritical flow - torrential
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Hillslope Transport
Surface runoff
Debris flow
Landslide
Solifluction
Rock fall
Soil creep
Shallow sliding
Soil creep
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Soil Creep
Instant and delayed compression
Total
volumetric
strain
Deformation
during primary
consolidation Effective
creep time
t’ = t-τc
ln τc
εc
ε
ln t
μ*
compression
index
time scale
parameter
34
Madurapperuma & Puswewala, 2008
Hillslope Evolution
Heimstat et al., 1997
∂qs
∂h
= production − transport = P −
∂t
∂x
35
Hillslope Evolution
Production
Maximum of soil
production
Exposed bedrock
samples
P~e
− ah
36
Heimstat et al., 2001
Hillslope Evolution
Transport
C
oa
st
al
C
al
ifo
rn
ia
The flux of sediment is
proportional to the hillslope
gradient
in
Alp
e
pe
o
l
s
l
h il
∂h
qs = −κ
∂x
Diffusivity in units of L2/T
Dietrich et al., 2003
37
Hillslope Evolution
Diffusion law
The flux of sediment is proportional to the
hillslope gradient
∂h
qs = −κ
∂x
Conservation of mass: an increase or a
decrease in the elevation is equal the change
in flux per unit length
∂qs
∂h
=−
∂t
∂x
Diffusion law
∂h
∂ 2h
=κ 2
∂t
∂x
⎛ ∂ 2h ∂ 2h ⎞
∂h
= κ ⎜⎜ 2 + 2 ⎟⎟ = κ∇ 2 h
∂t
∂y ⎠
⎝ ∂x
38
Hillslope Evolution
Diffusion law
∂h
∂ 2h
=κ 2
∂t
∂x
h
L
x
Assuming a constant incision rate
1. 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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Hillslope Evolution
Diffusion law
Lachlan Valley, SE Australia
Diffusion model leads to a parabolic elevation profile
40
Hillslope Evolution
Diffusion law
Surface runoff
Debris flow
Landslide
Solifluction
Rock falls
Slope < 20°
Diffusion
Soil creep
Shallow sliding
Soil creep
The applicability of the diffusion model to hillslope
evolution depends on both the local slope and the
processes acting to move sediment on the hillslope. 41
Hillslope Evolution
Non-linear erosion law
Anderson, 1994
Shoalhaven valley, SE Australia
42
Hillslope Evolution
Non-linear erosion law
Sc
∂h
qs = −κ
∂x
Roering et al., 2001
⎡
⎤
⎢
⎥
1
∂h ⎢
⎥
qs = −κ
∂x ⎢ ⎛ 1 ∂h ⎞ 2 ⎥
⎢1 − ⎜
⎥
⎟
⎢⎣ ⎜⎝ S c ∂x ⎟⎠ ⎥⎦
43
Hillslope Evolution
Non-linear erosion law
Roering et al., 2001
44
Hillslope Evolution
Non-linear erosion law
Montgomery & Brandon, 2002
45
Hillslope Evolution
Non-linear erosion law
Taiwan
SE Australia
Lesser Himalaya
Alps
SE Australia
46
Montgomery & Brandon, 2002
Hillslope Evolution
Non-linear erosion law
Montgomery & Brandon, 2002
47
Hillslope Evolution and Processes
Tectonic activity
Hillslope process
Sediment flux
low
diffusion
continuous
sliding
high
rock fall
stochastic48
Hillslope Evolution and Processes
Dietrich et al., Nature, 2006
49