When common rock forming minerals are weathered the typical reaction results in some loss of cations and the production of clays Because silicate mineral weathering consumes CO 2 weathering can influence global climate ID: 634035
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Slide1
Last Lecture
Chemical weathering: main driver is acidic waterWhen common rock forming minerals are weathered the typical reaction results in some loss of cations and the production of claysBecause silicate mineral weathering consumes CO2, weathering can influence global climateSlide2
Sediment transport on hillslopes
Hillslope hydrologySlope stability
Today’s lectureSlide3
What might the rate of these processes depend on?
Physical WeatheringSlide4
Two prevailing theories:
Physical WeatheringSlide5
alpha
Quantifying Physical Weathering Rates
Cosmogenic Radionuclides:
neutron
CRNs produced in rock and soil
We know how fast
Can give age / erosion rateSlide6
Heimsath et al., 1999
Coastal California
Heimsath et al. 2000
SE Australia
Does soil production vary with soil depth?Slide7
Heimsath et al. 2001
Oregon Coast Range
Wilkinson et al. 2005
Blue Mountains, Australia
Does soil production vary with soil depth?
YES!
Evidence for both peaked and exponential soil production functions depending on where you areSlide8
Stability vs InstabilitySlide9
p = Production rate
W = Production rate when there is no soil
= A length that tells you how
much the production rate decreases with increasing soil thickness
h = Soil thickness
Place
W in mm/yr
in m
Reference
Australia (1)
0.143
0.238
Heimsath et al., Quat. Int., 2001
California
0.077
0.435
Heimsath et al. Geomorph. 1999
Oregon
0.268
0.333
Heimsath et al. ESPL 2001
Australia (2)
0.053
0.5
Heimsath et al., Geology 2000
This is what the soil production function looks likeSlide10
This is what the soil production function looks likeSlide11
This is what the soil production function looks likeSlide12
This is what the soil production function looks likeSlide13
Natural erosion rates can on sloping lands range from 1 metre per million years to several mm per year (1 mm/
yr = 1km/million years)Disturbance (e.g., humans) can raise rates by 100 times or more!Soil can be stripped in decades
Human DisturbanceSlide14
If you strip the soil, how long does it take to recover?
Mass balance: The rate of change of soil thickness is equal to the rate of soil production minus the rate of erosion:
Human DisturbanceSlide15
Take a very simple situation. You strip away all the soil, and then you manage to reduce the erosion rate to zero:
Time it takes soil to recover
0Slide16
Take a very simple situation. You strip away all the soil, and then you manage to reduce the erosion rate to zero:
And remember, soil production is a function of depth:
Time it takes soil to recover
0Slide17
So putting these two together you get:
It turns out you can solve this equation, to find out how long it takes for the soil to reach some thickness h:
Time it takes soil to recoverSlide18
H = 0.2m
h = 0.5m
1230 yrs
4296 yrs
1530 yrs
7990 yrs
2460 yrs
8590 yrs
3060 yrs
16000 yrs
So soil conservation is important because once it is gone, it is gone for a very long time!
How long does it take?Slide19
Late Holocene (last 4ka) uplift/subsidence rates (mm/
yr)
Late Holocene surface change
Shennan and Horton (2001),
J. Quat Sci.
, 17, 511-526.Slide20
Late Holocene surface change
Fastest rate of soil production measured ->0.1-0.2 mm/yr)
We shouldn’t expect the same background erosion rates all over the UKSlide21
So
Fastest rate of soil production measured ->0.1-0.2 mm/yr)We shouldn’t expect the same background erosion rates all over the UKSlide22Slide23
Soil mantled landscape
Bedrock landscape
Relative balance between erosion and production of soil
http://static.panoramio.com/photos/original/147837.jpg
Transport limited
Weathering limited
Weathering can make sediment available for transport: then what?Slide24
Mobile Soil
Bedrock/Saprolite
Soil Production
Erosion
Soil Mantled Landscape:
Soil Production > ErosionSlide25
It rains. What happens?Slide26
Infiltration rates
Also:Tropical rainforest in Australia: 1350 mm/hrOregon Coast Range 5400 mm/hrSlide27
Rain rate < infiltration capacitySlide28
All rain goes into soilSlide29
Shallow subsurface storm flowSlide30
Saturation overland flowSlide31
Rain rate > infiltration capacity: overland flowSlide32
SOF (and piping)Slide33
Partial area
and distributed hydrologic models
Lyon et al. Hyd. Proc. 2004Slide34
Montgomery et al, WRR, 1997
Coos bay, OregonSlide35
Patterns of saturation
Montgomery et al, WRR, 1997 Slide36
Saturation in VermontSlide37
Convergent and Divergent areasSlide38
What happens during a storm?
Example storm hydrographSlide39
Understanding saturation on
hillslopesImportant for hydrologyAlso for slope stability
Why are these the bits that are saturated?
Water collects, but soil is thicker.
Can we make predictions????Slide40
Predicting saturation
If you cant get this right, you’ve got no chance of predicting basin response to storms because of thisSlide41
Predicting saturation
Also you won’t be able to predict thisSlide42
Predicting saturation
or this (as we’ll see later in this lecture)Slide43
Darcy’s law
Rate of water coming from tube proportional to change in height/distanceSlide44
Darcy’s law
q = K(h/L)K is just a constant of proportionalityq is the ‘Darcy velocity’Slide45
Darcy
Assume that water in soil flows parallel to the soil surfaceSlide46
The components of the Darcy equationSlide47
trigonometry
q = K(
h/L)Slide48
trigonometry
q = K(
h/L)
h/L=?Slide49
Water flux
q = K(
h/L)
h/L=sin(
q
)
So q = K sin(
q
)Slide50
Darcy’s law
Assume that water in soil flows parallel to the soil surfaceSlide51
Slope correction
But we want to know flow of water horizontally
Why? It is just more convenient
.
Slide52
trigonometrySlide53
Water flux, correctedSlide54
Some simple box models:
It rains
Imagine this as a boxSlide55
Some simple box models:
It rains
Imagine this as a boxSlide56
Some simple box models:
It rains
Imagine this as a box
Water comes in
Water goes outSlide57
Some simple box models:
It rains
Imagine this as a box
Coming in:
Rain
Going out:
Overland flow
Evaporation
Groundwater flow
Deep flow
Nothing coming in
From the right because
It is a drainage divideSlide58
Going in, coming out
Coming in:p*LWhere p is precipitation rate and L is length of boxGoing out:r*L
Where r is the return flow rate Slide59
Going in, coming out
Going outet*LWhere et is evapotranspiration rateqSSF
*dSSFWhere q is the Darcy velocity and d is the depth of shallow subsurface flowSlide60
What about in 3D?Slide61
3D
You define where you want water to flow outFollow lines of steepest descent upslopeSlide62
3D
This gives you a contributing area, ASlide63
What about what goes out?
Volume going out is: q
SSF*dSSF*b
q
SSFSlide64
Okay, lets do things in volumes per time
Coming in:p*AWhere p is precipitation rate and L is length of boxGoing out:r*A
Where r is the return flow rate Slide65
Okay, lets do things in volumes per time
Going outet*AWhere et is evapotranspiration rateqSSF*b*dSSFWhere q is the Darcy velocity and d is the depth of shallow subsurface flowSlide66
If there is no change in the amount of water in the box, what goes in must come out
p*A=et*A+r*A+ qSSF*b*dSSFThis is a bit ugly. Lets name something the water supply, call it ‘w’, and let it be equal to the precipitation minus the evapotranspiration and return flow: w = p-et-rSlide67
If there is no change in the amount of water in the box, what goes in must come out
w*A = qSSF*b*dSSFOkay, all this equation says is that the water supplied to the hillslope must equal the water leaving the hillslope from Horton overland flow and shallow subsurface flowSlide68
w*A = q
SSF*b*dSSFBut wait! We know qSSF = K*sin(q)*cos(q)
If there is no change in the amount of water in the box, what goes in must come out
q = K(
h/L)
h/L=sin(
q
)
So q = K sin(
q
)Slide69
Implications
Can solve for the depth of water at a given supply rate in the soilSlide70
Implications
How much water can a hillslope transport before overland flow occurs?
Max water supply rate is:Slide71
How much water can a hillslope transport before overland flow occurs?
Increase K
Increase w
Increase d
soil
Increase w
Increase
q
Increase w (up to a point)
Increase A
Decrease w
w
max
=
K*sin(
q
)*cos(
q
)
*b*
d
Soil
/ASlide72
Some numbers
A/b (in metres)divergent slope ~1-10Planar slope ~10-200Convergent slope ~100-100,000Soil thickness: 0-3m
K in cm/hrSilt: 0.01Sand: 40Slide73
Result: prediction of saturation during a rainstormSlide74
So why did we go to all that trouble?Slide75
Creep vs. Overland flow
Zone where creep dominates
(Convex)
Zone where overland flow dominates
(Concave)
Exfiltration and overland flow
Creep processes lead to hillslopes with different curvature than overland flow. Slide76
Landslides and Debris FlowsSlide77
Why do landslides occur?Slide78
Resolution of forces acting on a slope
W
N
t
S
a
W
: weight of material
N
: normal force acting perpendicular to slope
t
: shear force acting parallel to slope
S
: shear strength (resistance to shear)
a
: slope angle
Friction/shear strength depends on the normal force!
Pore water reduces both normal force and frictional resistance to sliding
LandslidesSlide79
Force balance
Start by looking at WSlide80
Forces
W = g*r
s*L*dsSlide81
Driving and resisting forces
Shear tries to get the block to slide downhill
This is resisted by frictionSlide82
Stresses:
Force divided by areaSlide83
Stresses
Shear:
Slide84
Resisting stress
Friction resists slidingThe friction is a function of the effective normal stressR = seff*tan(f)tan(f) is the friction slopeSlide85
Resisting stress
Effective normal stress: buoyant weight of the soil massWbuoyant = Wsoil –Wwaterseff = cos(q)*(Wsoil
-Wwater)Slide86
So, balance the forces:
At the limit of stability, friction and cohesion just balance shear stress:= Cr + seff*tan(f)
There is something called the ‘factor of safety’. It is the ratio between resisting forces and forces compelling the soil to move downslope:FS = (Cr + seff*tan(f))/
t
Slide87
So, balance the forces:
FS = (Cr + seff*tan(f))/t
orThe depth of water in soil at the failure point is equal to:Slide88
Rainfall rate for failure
Can solve for the depth of water at a given supply rate in the soilSlide89
Rainfall rate for failure
This is the supply rate at failure
Now you can get a good idea of how much rain you need to get one of these:Slide90
But wait…
Supply rate that fills soil:
Must be larger than the supply rate to cause failureSlide91
A few typical values
Typical root cohesion: 500-15000N/m2Typical tan(f): 0.8rw = 1000 kg/m3rs
= 1500-1900 kg/m3 K in cm/hrSilt: 0.01Sand: 40Slide92
Can the hillslope fail at all?
If the slope is still stabile once it fills with water, it won’t fail at all. This is the equation for the factor of safety if the soil is saturated (that is d
w = ds) Slide93
So this can be applied all over the landscapeSlide94
There is tension between the amount of water available and the steepness of the hillslopeSlide95
Conclusions
4 runoff mechanismsSlope stability: depends on gradient, amount of water, cohesion, and soil thicknessYou should familiarize yourself with the stability equations (we use them in practicals!
Reading:
Get it here:
http://eps.berkeley.edu/development/view_person.php?uid=1164&page=81