Mechanics of Slope Stability

Definition of Factor of Safety

Slope stability is  controlled by 2 main factors: the driving and the resisting forces. The driving forces tend to destabilize a slope, leading to landslide phenomena, and are typically associated with the triggering causes of the landslides (the weight of the ground and the additional loads) (see Introduction to Slope Stability). The impact of gravitational forces is significant, and thus, driving forces highly depend on the inclination of the slope, the unit weight of the ground and the slope height.

Contrary, the forces that resist slope instability are referred to as resisting forces. They depend on the shear strength of the soil/rock materials, the discontinuity planes between two ground layers, as well as any additional forces that can act in favor of the stabilization of the slope (e.g., a buttress at the lower section of the slope).

The Factor of Safety (FoS or FS) is defined as the ratio between the aforementioned two components, as:

If the FoS is less than 1, a landslide occurs since the driving forces exceed the resistance forces. When FoS is slightly higher than 1 (e.g., 1.30), the slope is stable but a small disturbance (e.g., an earthquake) may temporarily increase the driving forces (or reduce the resistance forces) and lead to landsliding. Finally, when the FoS is high enough (typically more than 2), an instability is less likely to occur.

How landslides occur with respect to FoS

Once the concept of FoS has been defined, it is important to assess a slope failure in terms of FoS reduction. A stable slope has, by default, an FoS greater than 1. However, with time, there are certain processes or events (weathering, rainfalls, earthquakes, etc.) that tend to destabilize a slope, reducing temporarily or permanently the FoS of the slope. At some point, one of those factors will result in reducing the FoS to less than one and subsequently, the landslide occurs. The latter factor is considered the trigger of the landslide, even though its impact may be less significant with respect to others. Once the landslide occurs, the slope eventually reaches a new equilibrium with a new FoS and a similar procedure begins.

A schematic of the aforementioned process is given in Figure 1. In this example, the FoS of a slope is steadily reduced due to weathering, with subsequent events causing temporal reductions  (precipitation, earthquake, toe erosion). The slope eventually fails given the persisting weathering processes, with a rainfall incident being the trigger factor.

Types of Slope Stability Methods

To assess the stability of a slope, typically a Slope Stability Analysis is performed. Slope stability analysis is widely used in soil mechanics and geotechnical engineering through many techniques such as empirical approaches (ex., Q-slope, SMR), limit equilibrium methods, finite element or finite difference methods or discrete element analysis.

The most widely used, practical approach for both 2-dimensional and 3-dimensional slope stability analysis is the Limit Equilibrium Method (LEM). The LEM method is assessing the stability of a slope by computing its FoS. Therefore, LEM differs from kinematic analyses since it investigates whether the slope will fail or not but it cannot predict the magnitude or the velocity of landslide deformations. It is an adequate method for most slope stability problems but it may be insufficient in certain cases (e.g., in progressive failures, liquefaction or creep) in which more advanced numerical techniques are required.

To employ the LEM, the following procedure is followed:

1. Definition of the failure surface
2. Derivation of driving and resistance forces
3. Calculation of the Factor of Safety

In this space, the slope stability methods that will be discussed utilize the LEM. The methods that consider the equilibrium of an entire soil mass consist of the Single Free-Body Procedures. On the contrary, methods that divide the soil mass into finite vertical columns, with each column being analyzed separately, are referred to as Methods of Slices.

References

Craig, R.F. (2004). Craig's Soil Mechanics (7th ed.). CRC Press. doi.org/10.4324/9780203494103

Murthy, V. N. S. (2003). Geotechnical engineering: Principles and practices of soil mechanics and foundation engineering. New York: Marcel Dekke

Samtani, N.C, Nowatzki, E.A. (2006). Soils and Foundations Reference Manual Volume 1. U.S. Department of Transportation, Federal Highway Administration, Washington, D.C. 20590

WG/WLI, 1994. A suggested method for reporting landslide causes. Bull. Int. Assoc. Eng. Geol. 50 (1), 71e74.