1. 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

2. 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

3. Hillslope sediment transport
Eroding Landscapes
Hillslope sediment transport

4. 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

5. Meaningful predictions require quantitative analyses!
Q: Suppose IPCC says rainfall will increase by 25% in How much more sediment is going to come from these slopes?
Alan Howard

6. Meaningful predictions require quantitative analyses!
Q: Suppose IPCC says rainfall will increase by 25% in 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
Alan Howard

7. Meaningful predictions require quantitative analyses!
Q: Suppose IPCC says rainfall will increase by 25% in 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

8. What is this course about? Many kinds of eroding landscapes
Chinese Loess Plateau
Chinese karst terrain
Upper Mekong River Basin
What is this course about? Many kinds of eroding landscapes

9. Basic observations about hillslopes and rivers
Hillslopes tend to be round.
Valleys frequently have regular spacing.
Roering et al. (2007), EPSL

10. Basic observations about hillslopes and rivers
Slope area data (sometimes) shows a ‘boomerang’ pattern.
Grieve, PhD (former GPG student!)

11. Now for the mass balance (this will be done on the board but these notes accompany the lecture)
Alan Howard

12. Here is a landscape with some rivers and hillslopes

13. Zoom in

15. For convenience, pick a planar hillslope
(i.e., not convergent, not divergent)

16. A generic hillslope strip

20. Now look from the side

21. Side view

22. Look at mass in and out

24. Ignore mass exchange at the surface

27. 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

28. 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.

30. r is the density of the parent material

43. What could determine qs?
What we need is a ‘sediment flux law’

44. Sediment flux laws
A sediment flux law tells us how qs varies as a function of the properties of the landscape

45. 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

46. A very simple case
The steeper the slope, the more sediment flux

47. 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., Analytical Theory of Erosion. Journal of Geology, 68(3):

48. 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., Analytical Theory of Erosion. Journal of Geology, 68(3):

49. 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
Proposed by Andrews, D.J. and Bucknam, R.C., Journal of Geophysical Research-Solid Earth and Planets, 92(B12):
Popularized by Roering, J.J., Kirchner, J.W. and Dietrich, W.E., Water Resources Research, 35(3):

50. 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
Proposed by Andrews, D.J. and Bucknam, R.C., Journal of Geophysical Research-Solid Earth and Planets, 92(B12):
Popularized by Roering, J.J., Kirchner, J.W. and Dietrich, W.E., Water Resources Research, 35(3):

51. Sediment flux laws: we’ll come back to this later
First lets go back to the hillslope mass balance

52. 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?

53. Change in the amount of soil in the box
Soil production
Soil coming in minus soil going out

60. but
hnew=hold

65. Okay, lets go back to looking at the hillslope strip

67. Because it is at the divide

72. What came out of box 1 goes into box 2.

78. Sediment flux laws: reminder

80. Check dimensions

82. Implication?
Slope increases as you move away from the divide!!!

86. A steadily eroding hillslope with linear creep is convex up!

87. So that explains the top part of this profile, but not the bottom

89. Simplest creep flux law:
What about water?
Probably also depends on slope.
But also depends on how much water is there

90. Simplest sediment flux law that accounts for water:
What about water?
Simplest sediment flux law that accounts for water:
Greater slope, more transport.
More drainage area, more water
More water, faster erosion

98. This is a fundamental result in geomorphology!!

99. This is a fundamental result in geomorphology!!
Convex: creep like processes dominate
Concave: fluvial and wash processes dominate

104. Roughening and smoothing
Creep like processes smooth the landscape
Wash and fluvial processes roughen the landscape

105. Roughening and smoothing are in competition!!!
In balance at the channel head!

106. Two end members In creep-like domain: In fluvial/wash 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

107. So, looking at slope area plots:

108. Slope-area plots can be used to compare landscapes, and the competition between creep and fluvial processes

109. 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

110. Process and form
Threshold landsliding
Creep only

111. Process and form
On a theoretical basis, one could pick out process transitions from slope – contributing area relationships

112. 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

113. Calculus note