This work is supported by the National Science Foundation’s Transforming Undergraduate Education in STEM program within the Directorate for Education and Human Resources (DUE-1245025).

sS = Shear Stress is the sum of all of the Driving Forces

sN = Normal Stress is only a part of the Resisting Forces Besides the normal stress (gravitational component),

the other components of the resisting force depend on the material’s shear strength:

Normal Stress: holding block in place

Shear Stress: pulling block down slope

W = FG

FN q

Besides the normal stress (gravitational component), the other components of the Resisting Force depend

on the material’s shear strength:Internal Friction (friction between material particles)

Cohesion(how well material sticks together)

Pore Pressure (degree of saturation in unconsolidated materials)

ANGLE OF REPOSE

What seems to be the relationship between angle of

repose and grain size?

The maximum angle possible between a non-cohesive material and a horizontal plane.

If a material is standing at the angle repose, which of the following is true?(a) shear strength > shear stress(b) shear strength < shear stress(c) shear strength = shear stress

ANGLE OF REPOSE

Freeman, Environmental Geology

In most sediments, angle of repose is ~30-45°

INTERNAL FRICTION

Rounded grains Angular grains Measured in the lab!

Discuss with a partner 2-3 factors that may influence internal friction.

COHESION

Non-cohesive granular material

Cohesive granular material

Measured in the lab!

COHESION

Materials αr Repose angle (°)

σr Cohesive index

Height heap (mm) Flow properties

Clay 71.7 2.3 53.2 Extremely poor

Polymer 33.7 0.1 14.6 Good

Lactose 56.4 1.4 27.9 Very poor

Metallic 43.8 0.2 17.9 Passable

Flour 66.4 2.1 48.4 Very poor

ROLE OF WATERSurface tension between grains increases cohesion

Pore Pressure:• Opposes Normal Force• Depends on degree of

saturation• Higher saturation,

reduces the normal (resisting) force)

DRIVING VS. RESISTING FORCES: REVIEW

Driving Forces: SHEAR STRESSA component of the gravitational force (dependent on mass) pulling the mass down a slope (FS = shear force)

Resisting Forces: SHEAR STRENGTH A component of the gravitational force (FN = normal force) AND forces related to material strength (cohesion, friction,

pore-pressure)

W = FG

Shear Strength: holding block in place FN

Shear Stress pulling block down slope

q

Driving Forces:Resisting ForcesFS

When Driving Forces > Resisting ForcesMass wasting occurs!

The block slides down the slope.

Shear Strength: holding block in place

Resisting Forces

When Driving Forces = Resisting ForcesThe block stays in place. This is the angle of

repose for a given material.

FN

FS Shear Stress pulling block down slope

Driving Forces:

THE SAFETY FACTOR!

The Safety Factor (SF) is the ratio of Resisting Forces to Driving Forces. Mathematically:

Driving ForcesResisting ForcesSF =

When SF > 1 THIS IS SAFE!When SF < 1 THIS IS UNSAFE!

FACTORS INFLUENCING DRIVING AND RESISTING FORCES

Let’s hear some of the things from your lists that increase the driving force or decrease the resisting force. We’ll make a list on the board.

Given what is on our list, what are some geologic processes that might play a role?

Given what is on our list, what are some anthropogenic processes that might play a role?

And thus, mass wasting potential (“The safety factor!”)

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