# Landslides: Slope stability, triggers, failure dynamics, and morphology - Slope Stability

**Slope Stability**Slope stability is dependent on the following:

- Material involved including:

-Material properties (cohesion and the internal friction)

-Fracture density and quality

-Weathering of the material - Geometry of material
- Slope angle
- Weight distribution
- Water content
- Vegetation
- External impulsive forces (such as earthquakes)

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** Factor of Safety** The factor of safety of a slope describes the stability of the slope and is a ratio of the resisting forces to driving forces. A factor of safety greater than one indicates a stable slope. There are multiple methods for calculating the factor of safety of a slope. The calculation of the safety of a sliding block on a plane (a layered slide with preferential failure along pre-existing weaknesses) is shown below in figure 1. This calculation takes into account slope angle, friction, cohesion, and water content. Increasing water content and slope angle decreases the factor of safety. Increasing friction and cohesion increases the strength and therefore increases the factor of safety. The sliding plane calculation of the factor of safety cannot be applied to homogenous soils where there is no preferential weak layer for failure. The failure surface in homogenous soils is sub-spherical, resulting in a rotational slide.

Figure 1: Factor of safety calculation. Figure from Marin Clark (personal communication).

Material properties control the strength of a rock or soil and are an important control on the type of failure. The intrinsic strength of a rock or soil comes from cohesive strength and the internal friction. Cohesion is the resistance force per unit area, and is measured in Pascals. In fine-grained soils, cohesion is a result of electrostatic bonds between clay and silt particles and is on the order of a few KPa. Sands and gravels are effectively cohesion-less. Rock has much greater cohesion due to interlocking particles and cement. Cohesion values for rock may be 1000s of times larger than those of soils (De Blasio, 2011). The internal friction of a soil or rock is due to the frictional forces between grains, and is often represented as the internal angle of friction, Φ. The internal angle of friction depends on grain size and grain properties, and can range from 0 to 45. Sandy soils and gravels generally have a friction angle between 30 and 40 degrees, while clayey soils tend to have a friction angle up to about 35 degrees. These values are generalizations and do not apply to all soils in these catagories (Koloski et al, 1989).

The cohesion and internal angle of friction can be determined for small samples in the lab using a tri-axial compression test or a uniaxial compression test (among others). Small-scale tests can also be used to measure the strength of individual discontinuities. However, these small-scale tests do not take into account the large-scale heterogeneities encountered in the field, such as variable weathering, fractures, jointing, and bedding. Large-scale heterogeneities often control the initiation and location of failure. Multiple failure criterions to evaluate the stability of a slope accounting for large-scale discontinuities have been developed. All require careful study of a field site, and are difficult to apply broadly.

The above factor of safety calculation does not take into account the geometry of the slope, the distribution of weight, or the vegetation. Geometry of a slope includes the strike and dip of the potential failure planes (bedding, joints, etc) and the orientation of the failure planes with respect to the slope. Discontinuities that "daylight" and are dipping at a lower angle than the slope angle are capable of failure along the weakness plane. Planes that are steeper than the slope slope angle will not slide, though they may undergo toppling failure.

Changes in the center of gravity of a potential failure can trigger failure or serve to stabilize a slope. Adding weight to the top of a potential failure will decrease stability while adding weight to the base of the same potential failure can increase stability. The role that weight distribution plays is also dependent on geometry of the slope. Vegetation generally serves to stabilize a slope; the roots of plants serve as anchors, and vegetation decreases the water content of a slope. However, vegetation also adds weight to a potential slide, and can decrease stability. All of these factors must be evaluated for each potential slide, and considered when analyzing a slide that has already occurred.