Geol 33 Environmental Geomorphology

J Bret Bennington

Mass Wasting Processes

Translational Landslides

Assuming a soil or rock cover over a failure plane where the failure plane is parallel to the slope, the forces at play in maintaining the stability of the soil / rock mass can be calculated.

Properties of the soil / rock mass:

1. thickness normal to failure plane = vertical thickness H x cos q (angle between failure plane and horizontal).
2. unit weight = density x g (9.8 m/sec²) x thickness (H x cos q)
3. internal friction angle f (determined experimentally) - this is a measure of the internal friction between grains within a mass of material. It can be approximated as the tangent of the angle of repose of the material under consideration. The angle of internal friction is affected by size, shape, and surface roughness of the grains, the density of packing, and the moisture content of the material.
4. cohesion (c) = tendency for mass to adhere to the failure plane

Gravity is the force trying to move the mass downslope. It is also the force that is holding the mass to the slope. Thus, both the tangent force and the normal force are related to the weight of the mass and the slope angle:

Weight = unit weight x thickness

Normal force = weight x cos q

Tangent force = weight x sin q

Note: Force is mass x acceleration (F=ma) and has units of Newtons or kN.

To determine if a slope is stable the Factor of Safety (F.S.) can be calculated. This is the ratio of the Resisting Stress to the Driving Stress.

The driving stress is simply the tangental force of gravity trying to move the mass downhill. The resisting stress is the sum of the cohesion + normal force x friction angle. If water is saturating the material then a pore pressure must also be introduced. Pore pressure will work to reduce the resisting stress by reducing the normal force.

F.S. = Resisting Stress / Driving Stress

Pore pressure is proportional to hydraulic head, which is the elevation of the water table above the failure plane. Thus, m can be calculated as:

where H_w is the height of the water table above the failure plane.

If there is no saturation and therefore no pore pressure, then the m term drops out.

If the factor of safety is less than unity, then failure is imminent. The higher the F.S. value, the less likely it is that the slope will fail.

Translational Landslide with a Cut Slope

A = H-Z / sin y_p

More complicated failure scenarios can be analyzed using the same principles. For example, the following equations apply to a slope cut at an angle y_f where the sliding plane is parallel to the cut (as when strike is parallel to a highway) and has a dip toward the cut at angley_p. Furthermore, let us assume that there is a vertical fracture creating a free-standing block and that the vertical fracture is filled with pore water, as is the sliding plane.

The F.S. equation is still F.S. = resisting force / driving force, but now there are more forces to consider:

The three forces involved (W, V, and U) can be solved using trigonometry:

Rotational Landslides

Rotational landslides can by analyzed using a balance of rotational moments.

Driving moment (M_d) = W x A

Resisting moment (M_r) = shear force (L x Shear strength of soil) x R

F.S. = L x S x R / W x A

Note: moments are forces x distance = work and have unit of Newton-meters.

From this it can be seen that a landslide could be triggered by anything that might decrease L (excavation at the base of the hill) or S (saturation of the soil) or increase W (adding additional material to the top of the hillslope).

Rotational slumps can be analyzed using the method of slices.

In this method a cross section of the slope in question is drafted and subdivided into a series of slices that can be analyzed independently and then summed together to estimate the factor of safety. Different possible failure arcs can be analyzed to find the most likely surface of slumping (the arc with the lowest F.S. value).