The downhill movement of soil and loose unconsolidated sediments is due to the force of gravity and is resisted by friction. The forces of gravity and friction are in balance at the angle of repose which is the maximum slope angle that unconsolidated materials can maintain. At angles steeper than the angle of repose friction is not sufficient to counter gravity and mass wasting occurs. At angles less than the angle of repose gravity cannot overcome friction and sediments may accumulate to form steeper slopes.
Water plays an important role in mass wasting. Dry sediments, other than clays, have no cohesion. Damp sediments are cohesive because water coats the sedimentary grains and holds them together with its surface tension (surface tension is the result of the dipolar nature of water). The angle of repose increases (think of a sand castle). In saturated sediments all the pore spaces are filled with water. The weight of water in the interconnected pores exerts pressure. Pore water pressure acts to counter the weight of grain-on-grain contact. The friction between the grains is thereby decreased and so is the angle of repose, possibly resulting in mass wasting.
The two basic classes of mass wasting are flows and slides. In flows, the material behaves as a fluid. Soil creep, earthflows, and mudflows are examples. In slides, the material behaves as a rigid solid that detaches along a basal surface. Slumps and landslides are examples.
Steady soaking rains, undercutting slopes for road building and house sites, and removal of vegetation by fires, etc may induce mass wasting.
Consider the case pictured below of a block on an inclined plane. The block is attracted straight downward (toward the center of the Earth) by the force of gravity (fg). In the case of the inclined plane, a certain amount of the gravitational force is applied perpendicular to the plane (fn, normal force) and a certain amount is applied parallel to the plane (fs, shear force). The normal force acts to increase friction and stick the block to the plane. The shear force acts to pull the block down the plane.
See also notes on vectors.
That component of shear force and normal force derived from the downward gravitational force are dependent on the angle of slope.
Equation 1: (shear force) = (force of gravity) x (sin (slope angle))
Equation 2: (normal force) = (force of gravity) x (cos (slope angle))
In English Units the force of gravity is simply the weight of an object in pounds. In most problems we are interested in the force acting over a given area of the plane (like pounds per square inch). This is called the stress.
Equation 3: Stress = Force / Area
The shear and normal stresses are therefore simply the shear and normal forces divided by the area of contact between the block and the inclined plane.
Since the area between the block and the inclined plane are the same when considering both the shear and normal stress, the ratio of the shear to normal stresses is the same as the ratio of the shear to normal forces.
Now for the really important stuff relating the shear stress, cohesion (do they stick together even with no forces applied?), normal stress, and friction. Notice in the equations below how the normal stress works hand in hand with friction.
At the angle of repose:
Equation 4: (shear stress) = (cohesion) + (coefficient of friction) x (normal stress)
in cohesionless substances:
Equation 5: (shear stress) = (coefficient of friction) x (normal stress)
or restated:
Equation 6: (coefficient of friction) = (shear stress) / (normal stress)
The coefficient of friction is related to the friction between particles and depends on the characteristics of the material (e.g., is it rough or smooth, rounded or blocky):
Equation 7: (coefficient of friction) = tan (angle of internal friction)
and in the case of unconsolidated materials:
Equation 8: (angle of internal friction) = (angle of repose) = inverse tan ((shear stress) / (normal stress))
(see Chapters 4 and 6 in the textbook [Rahn] for further explanations)