Key concepts
• Failure of slopes depends on direction of
groundwater flow, but in many cases surface parallel
flow is an adequate assumption
• Failure also depends on a balance between the
intensity and duration of rainfall
• Larger landslides have relatively longer runout
distances, and therefore lower ‘effective’ friction.
• Wet material can have extremely long runout
distances
Key concepts
• Debris flows vs. landslides: It is all about the
water!
• Critical state porosity in soils
• Characteristics of debris flows
–
–
–
–
Long runout
Kinematic sorting
Erosion of landscapes
Supply and storage of sediment
• Colluvial hollow cycling and triggering
Eroding Landscapes
Hillslope sediment transport
What follows is a long derivation of
the mass balance of a hillslope soil
Q: Why go through this?
A1: It serves as the basis for all quantitative
hillslope studies
A2: The thought process is the same for
channels, glaciers, etc.
Alan Howard
Meaningful predictions require
quantitative analyses!
Q: Suppose IPCC says rainfall will increase by
25% in 2080. How much more sediment is
going to come from these slopes?
Alan Howard
Meaningful predictions require
quantitative analyses!
Alan Howard
Q: Suppose IPCC says rainfall will increase by
25% in 2080. How much more sediment is
going to come from these slopes?
Why would you want to know?
Landslide risk
Soil loss
Changing soil properties changes hydrology
Downstream effects
Meaningful predictions require
quantitative analyses!
Q: Suppose IPCC says rainfall will
increase by 25% in 2080. How
much more sediment is going to
come from these slopes?
A1: Qualitative: More sediment will
come out.
A2: Quantitative: There is a 50%
chance that erosion rates will
increase from 0.1mm/yr to
0.17mm/yr, leading to 30% greater
risk of flooding in your town.
Alan Howard
What is this course about? Many
kinds of eroding landscapes
Chinese Loess Plateau
Chinese karst terrain
Upper Mekong River Basin
Basic
observations
about
hillslopes
and rivers
• Hillslopes
tend to be
round.
• Valleys
frequently
have regular
spacing.
Roering et al. (2007), EPSL
Basic
observations
about
hillslopes
and rivers
• Slope area
data
(sometimes)
shows a
‘boomerang’
pattern.
Grieve, PhD (former GPG student!)
Now for the mass balance (this will
be done on the board but these
notes accompany the lecture)
Alan Howard
Here is a landscape with some rivers
and hillslopes
Zoom in
For convenience, pick a planar hillslope
(i.e., not convergent, not divergent)
A generic hillslope strip
Now look from
the side
Side
view
Look
at
mass
in and
out
Ignore
mass
exchange
at the
surface
Aside: dimensions and units
• Express dimensions in
– M for mass
– L for length
– T for time
• Units can be
– Mass: kilograms, grams, etc.
– Length: metres, cm
– Time: seconds, hours, days, etc
Mass in box: Check dimensions
• Mass in box is: ρs*h*dA
– Dimensions of ρs: M/L3
– Dimensions of h: L
– Dimension of dA: L2
• So dimensions ρs*h*dA: M*L*L2/L3 = M
• In my personal experience, this is the easiest
way to check if you are doing things correctly.
r is the
density
of the
parent
material
What could determine qs?
• What we need is a ‘sediment flux law’
Sediment flux laws
A sediment flux law tells us how qs varies as a
function of the properties of the landscape
Sediment flux laws
So, you tell me the slope angle, or the amount
of overland flow, or the number of gophers,
and I’ll tell you how much dirt is moving on
your hillslope
A very simple case
The steeper
the slope,
the more
sediment
flux
A very simple case
The steeper
the slope,
the more
sediment
flux
This is called a
‘linear’
sediment
flux law
Proposed by Culling, W.E.H., 1960. Analytical Theory of Erosion. Journal of
Geology, 68(3): 336-344.
A very simple case
The steeper
the slope,
the more
sediment
flux
qs  KS
This is called a
‘linear’
sediment
flux law
Proposed by Culling, W.E.H., 1960. Analytical Theory of Erosion. Journal of
Geology, 68(3): 336-344.
Slightly more complex
When the slope gets very
steep (near the angle
of repose), particles
start to slide
downslope. This
sediment transport
gets very fast as the
slope approaches
some critical value
qs  KS
Proposed by Andrews, D.J. and Bucknam, R.C., 1987. Journal of Geophysical
Research-Solid Earth and Planets, 92(B12): 12857-12867.
Popularized by Roering, J.J., Kirchner, J.W. and Dietrich, W.E., 1999. Water
Resources Research, 35(3): 853-870.
Slightly more complex
When the slope gets very
steep (near the angle
of repose), particles
start to slide
downslope. This
sediment transport
gets very fast as the
slope approaches
some critical value
KS
qs 
2
1  S Sc 
qs  KS
Proposed by Andrews, D.J. and Bucknam, R.C., 1987. Journal of Geophysical
Research-Solid Earth and Planets, 92(B12): 12857-12867.
Popularized by Roering, J.J., Kirchner, J.W. and Dietrich, W.E., 1999. Water
Resources Research, 35(3): 853-870.
Sediment flux laws: we’ll come back to
this later
First lets
go back
to the
hillslope
mass
balance
qs  KS
Introduce a concept: Steady state:
• Steady state refers to a condition in which
something doesn't change in time.
• What is ‘something’?
• Topography?
• Topography relative to some moving datum?
• Soil thickness?
• Soil production?
Change in the amount of
soil in the box
Soil production
Soil coming in minus soil going out
but
hnew=hold
Okay, lets go back to
looking at the hillslope
strip
Because it is at the divide
What came out of box 1 goes into box 2.
Sediment flux laws: reminder
qs  KS
Check dimensions
Implication?
• Slope increases as you move away from the
divide!!!
A steadily eroding
hillslope with
linear creep is
convex up!
So that explains the top
part of this profile, but
not the bottom
Simplest creep flux law:
qs  KS
What about water?
Probably also depends on slope.
But also depends on how much
water is there
qs  KS ( A  Ac )
What about water?
Simplest sediment flux law
that accounts for water:
qs  KS ( A)
Greater slope, more transport.
2
More drainage area, more water
More water, faster erosion
This is a fundamental result in
geomorphology!!
This is a fundamental result in
geomorphology!!
Convex:
creep like
processes
dominate
Concave:
fluvial and
wash
processes
dominate
Roughening
and
smoothing
Creep like
processes
smooth the
landscape
Wash and fluvial
processes
roughen the
landscape
Roughening and smoothing are in competition!!!
In balance at the channel head!
Two end members
• In creep-like domain:
– Greater area means you need greater
slope to erode at the same rate, since
you have more sediment to transport
and sediment transport depends only
on slope
• In fluvial/wash domain:
– Greater area means you need a
gentler slope to erode at the same
rate because the water you gain is
very efficient at eroding and
transporting sediment
So, looking at slope area plots:
Slope-area
plots can be
used to
compare
landscapes,
and the
competition
between
creep and
fluvial
processes
• Relationship between valley spacing and uplift
rates unclear (hard to distinguish from climate,
parent material, etc)
• But transition between channel and hillslope can
now be determined for large areas using digital
elevation models
Roering et al. (2007), EPSL
Process and form
Threshold landsliding
Creep only
Process and form
On a theoretical basis, one
could pick out process
transitions from slope –
contributing area relationships
Key points
• Creep leads to fundamentally different
topography than water transport
• Creep smoothes the landscape, water
roughens it
• One can search for different process regimes
by looking at S-A plots
Reading: Anderson and Anderson Chapter 10
and section on page 592 about derivatives
Calculus note
dy
y( x  dx)  y( x)
 lim
dx dx0
dx