Intro to Geomorphology (Geos 450/550)Lecture 9: hillslope processes • FT#4 preview• slope transport processes• Mohr-Coulomb slope stability criterion• HW#2 out on web site – due next week• read ch. 7 of Anderson2

North South

Erosion in hillslope&fluvial systems: two basic regimes

1. Weathering (detachment) limited• low weathering rates relative to high transport

rates• thin regolith or soil• slope landsliding• bedrock rivers (downcutting)

2. Transport limited• low transport rates relative to high weathering

rates• thick regolith or soil• slope creep, bioturbation, etc. (diffusive processes)• alluvial rivers (transporting or depositional)

Typical slopes of arid and humid environments

Slide courtesy of Mike Poulos

Classic arid slope

Hillslope transport processes

• creep: heave+gravity, diffusive, low-slope, high veg• continuous creep (solifluction), seasonal drainage• mass movements: gravity, weathering-limited• bioturbation: movement of animals and growth of plants,

coarse-grained• raindrop impact: diffusive, fine-grained• overland flow: semi-diffusive, low veg• rill wash: low veg (badlands)• solution: karst• piping: the movement of water and sediment in interconnected

networks of cracks in the near-surface. fine-grained, low- perm

• spring sapping: outflow of water at a spring where surface and water table meet. structural control

When and where do hillslopes “fail”?

Landslide hazard map – U.S.

slope angle = q

potential failure plane

Stability Index

for a buried water table at a vertical distance hw above the base of the soil layer (depth hs):

Stability Index = tf / t

C’ + tan f [1 – (rw/ rs)(hw/hs)] cos2 q=

where C’ = C/ rsghs = ratio of cohesion to weight of soil

sin q cos q

water table

hs hw

slope angle = q potential failure plane

x unit area on surface

block exerts:normal force per unit area on buried plane = rgx cos qshear force per unit area on buried plane = rgx sin q

rgx

r = densityg = gravitational accelerationh = depthx = thickness perpendicular to surface

force/area components

h

slope angle = q

potential failure plane

normal stress acting on plane = s = rgh cos2 qshear stress acting on plane = t = rgh sin q cos q

in terms of vertical thickness h,x = h cos qhence

s

t

r = densityg = gravitational accelerationh = depthx = thickness perpendicular to surface

Stress on buried plane parallel to infinite sloping surface

x

hs

slope angle = q

potential failure planeseff

t

Coulomb slope failure: effect of pore pressure

Coulomb failure:

t = tf = C + tan (f seff)

whereseff = effective normal stress = s – m = (rsghs – rwghw) cos2 qm = pore pressurers = wet soil density, rw = water densitytan f = coefficient of friction of the materialC = cohesion of material

water table

hw

h

slope angle = q = f

potential failure plane

s = normal stress acting on plane = rgh cos2 qt = shear stress acting on plane = rgh sin q cos q

st

angle of repose

For c = 0 and m = 0 (cohesionless material without pore pressure)

t = tf = s tan f

sin q cos q = cos2 q tan ftan q = tan f

q = f = angle of repose

h

slope angle = q

potential failure plane

Stability Index

In general, for c and m not = 0, one can compute the

“safety factor” or “Stability Index” = SI = tf / t

slope angle = q

potential failure plane

Stability Index

for a buried water table at a vertical distance hw above the base of the soil layer (depth hs):

Stability Index = tf / t

C’ + tan f [1 – (rw/ rs)(hw/hs)] cos2 q=

where C’ = C/ rsghs = ratio of cohesion to weight of soil

sin q cos q

water table

hs hw

slope angle = q

potential failure plane

predicting slope failure

Stability Index = tf / t

C’ + tan f [1 – (rw/ rs)(hw/hs)] cos2 q= sin q cos q

water table

hs hw

This is a basis for predicting slope instability by knowing the slope angle and water table. These can be estimated by knowing the topography. See SINMAP* manual for more discussion of this approach.

Cinder cones provide unusually well-constrained initial condition

Slide courtesy Craig Rasmussen

South Facing North Facing

~70 kyr

~300 kyr

~2,000 kyr

~70 kyr

~300 kyr

~2,000 kyrSlide courtesy Craig Rasmussen

Use both topo and soil variations with aspect to discriminate better among competing models

In water-limited environments:• Bioturbation is 1-2 orders of magnitude more

important that freeze-thaw-driven creep.• North-facing slopes have greater maximum

steepness.• Regolith is thicker on north-facing slopes but clay

clay accumulation more well developed on south-facing slopes (Rech, 2001; Rasmussen et al.)

• Modern biomass density is greater on north-facing slopes BUT paleo-biomass density was greater on south-facing slopes (glacial climates are 80% of Quaternary).

Blue – North facingRed – South facing

Soils more well developed (e.g. clay accum.) on south-facing slopes

Slide courtesy Craig Rasmussen

McGuire et al., in rev.

Biomass greater on north-facing slopes now, but what about the past?

McGuire et al., in rev.

Paleovegetation a key element of the story – South-facing slopes had greater biomass for 80% of Quaternary

Pelletier et al. (2013); McGuire et al. (2014) conceptual model

For water-limited environments and slopes (>2 km a.s.l. in warmer parts of western U.S., 1-2 km a.s.l. in colder parts):• Greater soil water availability on north-facing slopes

drives faster regolith production.• Greater biomass on south-facing slopes (during

glacial climates) increased colluvial transport rates compared with north-facing slopes, leading to lower max gradients on north-facing slopes over time.

• Greater biomass led to greater dust (clay, quartz) accumulation in soils on south-facing slopes.