last lecture chemical weathering: main driver is acidic water when common rock forming minerals are...

Last Lecture• Chemical weathering: main driver is acidic water• 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 CO2, weathering can influence global climate

Sediment transport on hillslopesHillslope hydrology

Slope stability

Today’s lecture

What might the rate of these processes depend on?

Physical Weathering

• Two prevailing theories:

Physical Weathering

alpha

Quantifying Physical Weathering Rates

Cosmogenic Radionuclides:

neutron

CRNs produced in rock and soil• We know how fast• Can give age / erosion rate

Heimsath et al., 1999Coastal California

Heimsath et al. 2000SE Australia

Does soil production vary with soil depth?

Heimsath et al. 2001Oregon Coast Range

Wilkinson et al. 2005Blue Mountains, Australia

Does soil production vary with soil depth?

YES!

Evidence for both peaked and exponential soil production functions depending on where you are

Stability vs Instability

h

Wep

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 like

h

Wep

This is what the soil production function looks like

• 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 Disturbance

• 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:

Epdt

dh

Human Disturbance

• Take a very simple situation. You strip away all the soil, and then you manage to reduce the erosion rate to zero:

Epdt

dh

Time it takes soil to recover

0

• 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:

Epdt

dh


0

h

Wep

• 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:

h

Wedt

dh

1 h

eW

t


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?

Late Holocene (last 4ka) uplift/subsidence rates (mm/yr)

Late Holocene surface change

Shennan and Horton (2001), J. Quat Sci., 17, 511-526.

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 UK

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 UK

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?

Mobile Soil

Bedrock/Saprolite

Soil Production

Erosion

Soil Mantled Landscape: Soil Production > Erosion

It rains. What happens?

Infiltration rates

• Also:– Tropical rainforest in Australia: 1350 mm/hr– Oregon Coast Range 5400 mm/hr

Rain rate < infiltration capacity

All rain goes into soil

Shallow subsurface storm flow

Saturation overland flow

Rain rate > infiltration capacity: overland flow

SOF (and piping)

Partial areaand distributed

hydrologic models

Lyon et al. Hyd. Proc. 2004

Montgomery et al, WRR, 1997

Coos bay, Oregon

Patterns of saturation

Montgomery et al, WRR, 1997

Saturation in Vermont

Convergent and Divergent areas

What happens during a storm?Example storm hydrograph

Understanding saturation on hillslopes

• Important for hydrology

• Also for slope stability

Why are these the bits that are saturated?Water collects, but soil is thicker.Can we make predictions????

Predicting saturation

If you cant get this right, you’ve got no chance of predicting basin response to storms because of this


Also you won’t be able to predict this


or this (as we’ll see later in this lecture)

Darcy’s law• Rate of water coming from tube proportional to

change in height/distance

Darcy’s law• q = K(h/L)• K is just a constant of proportionality• q is the ‘Darcy velocity’

DarcyAssume that water in soil flows

parallel to the soil surface

The components of the Darcy equation

trigonometryq = K(h/L)

trigonometryq = K(h/L)h/L=?

Water fluxq = K(h/L)h/L=sin(q)

So q = K sin(q)

Darcy’s lawAssume that water in soil flows

parallel to the soil surface

Slope correctionBut we want to know flow of

water horizontally

Why? It is just more convenient.

trigonometry

Water flux, corrected

Some simple

box models:

It rains

Imagine this as a box

Some simple

box models:

It rains


Water comes inWater goes out

Some simple

box models:

It rains


Coming in:Rain

Going out:Overland flowEvaporation

Groundwater flowDeep flow

Nothing coming inFrom the right becauseIt is a drainage divide

Going in, coming out

• Coming in:p*LWhere p is precipitation rate and L is

length of box

• Going out:r*LWhere r is the return flow rate

Going in, coming out

• Going outet*LWhere et is

evapotranspiration rate

qSSF*dSSF

Where q is the Darcy velocity and d is the depth of shallow subsurface flow

What about in

3D?

3D

• You define where you want water to flow out

• Follow lines of steepest descent upslope

3D

• This gives you a contributing area, A

What about what goes out?

Volume going out is: qSSF*dSSF*b

qSSF

Okay, lets do things in volumes per time

• Coming in:p*AWhere p is precipitation rate and L is

length of box

• Going out:r*AWhere r is the return flow rate

Okay, lets do things in volumes per time• Going outet*AWhere et is evapotranspiration rate

qSSF*b*dSSF

Where q is the Darcy velocity and d is the depth of shallow subsurface flow

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*dSSF

This 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-r


w*A = qSSF*b*dSSF

Okay, 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 flow

w*A = qSSF*b*dSSF

But wait! We know qSSF = K*sin(q)*cos(q)


q = K(h/L)h/L=sin(q)

So q = K sin(q)

Implications

Can solve for the depth of water at a given supply rate in the soil

bK

wAdw )cos()sin(

Implications

How much water can a hillslope transport before overland flow occurs?

Max water supply rate is:

A

bKdw soil )cos()sin(max

How much water can a hillslope transport before overland flow occurs?

Increase K Increase w

Increase dsoil

Increase w

Increase q Increase w (up to a point)

Increase A Decrease w

wmax = K*sin(q)*cos(q)*b*dSoil/A

Some numbersA/b (in metres)

– divergent slope ~1-10– Planar slope ~10-200– Convergent slope ~100-100,000

• Soil thickness: 0-3m

• K in cm/hr– Silt: 0.01– Sand: 40

Result: prediction of saturation during a

rainstorm

So why did we go to all that trouble?

Creep vs. Overland flowZone 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.

Landslides and Debris Flows

Why do landslides occur?

Resolution of forces acting on a slope

W

N

t

S

a

W: weight of materialN: normal force acting perpendicular to slope t: shear force acting parallel to slopeS: 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

Landslides

Force balanceStart by looking at W

ForcesW = g*rs*L*ds

Driving and resisting forces

Shear tries to get the block to slide downhill

This is resisted by friction

Stresses:Force divided by area

Stresses

Shear:

Resisting stress

• Friction resists sliding• The friction is a function of the effective

normal stress• R = seff*tan(f)• tan(f) is the friction slope

Resisting stress

• Effective normal stress: buoyant weight of the soil mass– Wbuoyant = Wsoil –Wwater

seff = cos(q)*(Wsoil-Wwater)

So, balance the forces:

• At the limit of stability, friction and cohesion just balance shear stress:

t = 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

So, balance the forces:

FS = (Cr + seff*tan(f))/t

or

The depth of water in soil at the failure point is equal to:

)sin()cos(

)tan()(cos)( 2

ss

wwssr

dg

ddgCFS

)tan()(cos

)cos()sin()tan()(cos2

2

w

ssssrw g

dgdgCd

Rainfall rate for failure

Can solve for the depth of water at a given supply rate in the soil

bK

wAdw )cos()sin(

)tan()(cos

)cos()sin()tan()(cos2

2

w

ssssrw g

dgdgCd

Rainfall rate for failureThis is the supply rate at failure

Now you can get a good idea of how much rain you need to get one of these:

)tan(

)sin()tan()cos()cos()tan(

w

ssr

Ag

dgCKbw

But wait…

Supply rate that fills soil:

wA

bKds )cos()sin(

Must be larger than the supply rate to cause failure

)tan(

)sin()tan()cos()cos()tan(

w

ssr

Ag

dgCKbw

A few typical values

Typical root cohesion: 500-15000N/m2

Typical tan(f): 0.8rw = 1000 kg/m3

rs = 1500-1900 kg/m3

• K in cm/hr– Silt: 0.01– Sand: 40

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 dw = ds)

)sin(

)tan()cos()(

)sin()cos(

s

ws

ss

r

dg

CFS

So this can be applied all over the landscape

There is tension between the amount of water available and the steepness of the hillslope

Conclusions• 4 runoff mechanisms• Slope stability: depends

on gradient, amount of water, cohesion, and soil thickness

• You 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

http://eps.berkeley.edu/development/view_person.php?uid=1164&page=81

last lecture chemical weathering: main driver is acidic water when common rock forming minerals are...

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