Figure 1: Simple slope slip section
The field of slope stability encompasses the analysis of static and dynamic stability of slopes of earth and rock-fill dams, slopes of other types of embankments, excavated slopes, and natural slopes in soil and soft rock.[1]
As seen in Figure 1, earthen slopes can develop a cut-spherical weakness zone. The probability of this happening can be calculated in advance using a simple 2-D circular analysis package.[2] A primary difficulty with analysis is locating the most-probable slip plane for any given situation.[3] Many landslides have only been analyzed after the fact.
It should be noted that real life failures in naturally deposited mixed soils are not necessarily circular, but prior to computers, it was far easier to analyse such a simplified geometry. Nevertheless, failures in 'pure' clay can be quite close to circular. Such slips often occur after a period of heavy rain, when the pore water pressure at the slip surface increases, reducing the effective normal stress and thus diminishing the restraining friction along the slip line. This is combined with increased soil weight due to the added groundwater. A 'shrinkage' crack (formed during prior dry weather) at the top of the slip may also fill with rain water, pushing the slip forward. At the other extreme, slab-shaped slips on hillsides can remove a layer of soil from the top of the underlying bedrock. Again, this is usually initiated by heavy rain, sometimes combined with increased loading from new buildings or removal of support at the toe (resulting from road widening or other construction work). Stability can thus be significantly improved by installing drainage paths to reduce the destabilising forces. Once the slip has occurred, however, a weakness along the slip circle remains, which may then recur at the next monsoon.
Slope stability issues can be seen with almost any walk down a ravine in an urban setting. An example is shown in Figure 2, where a river is eroding the toe of a slope, and there is a swimming pool near the top of the slope. If the toe is eroded too far, or the swimming pool begins to leak, the forces driving a slope failure will exceed those resisting failure, and a landslide will develop, possibly quite suddenly.
Analysis methods
Figure 2: Slope with eroding river and swimming pool
If the forces available to resist movement are greater than the forces driving movement, the slope is considered stable. A factor of safety is calculated by dividing the forces resisting movement by the forces driving movement. In earthquake-prone areas, the analysis is typically run for static conditions and pseudo-static conditions, where the seismic forces from an earthquake are assumed to add static loads to the analysis.
Method of slices
The method of slices is a method for analyzing the stability of a slope in two dimensions. The sliding mass above the failure surface is divided into a number of slices. The forces acting on each slice are obtained by considering the mechanical equilibrium for the slices.
Bishop's method
The Modified (or Simplified) Bishop's Method is a method for calculating the stability of slopes. It is an extension of the Method of Slices. By making some simplifying assumptions, the problem becomes statically determinate and suitable for hand calculations:
- forces on the sides of each slice are horizontal
The method has been shown to produce factor of safety values within a few percent of the "correct" values.
![F=\frac{\sum [\frac{c'+((W/b)-u)\tan\phi'}{\psi}]}{\sum[(W/b)\sin\alpha]}](http://upload.wikimedia.org/math/6/3/0/630e0547a2259a7adc824742d047dfee.png)
where
 - c' is the effective cohesion
- f' is the effective internal angle of friction
- b is the width of each slice, assuming that all slices have the same width
- W is the weight of each slice
- u is the water pressure at the base of each slice
Lorimer's method
Lorimer's Method is a technique for evaluating slope stability in cohesive soils. It differs from Bishop's Method in that it uses a clothoid slip surface in place of a circle. This mode of failure was determined experimentally to account for effects of particle cementation.
The method was developed in the 1930s by Gerhardt Lorimer (Dec 20, 1894-Oct 19, 1961), a student of geotechnical pioneer Karl Terzaghi.
See also
Notes
- ^ US Army Corps of Engineers Manual on Slope Stability
- ^ "Slope Stability Calculator". Retrieved on 2006-12-14.
- ^ Chugh, Ashok (2002), "A method for locating critical slip surfaces in slope stability analysis", NRC Research Press, <http://article.pubs.nrc-cnrc.gc.ca/ppv/RPViewDoc?_handler_=HandleInitialGet&journal=cgj&volume=39&calyLang=eng&articleFile=t02-042.pdf>
References
- Coduto, Donald P. (1998). Geotechnical Engineering: Principles and Practices. Prentice-Hall. ISBN 0-13-576380-0
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