The International Information Center for Geotechnical Engineers

Landslides: Slope stability, triggers, failure dynamics, and morphology

 Katherine Lowe

Department of Earth and Environmental Science
University of Michigan
CEE 544: Rock Mechanics
Professor: Dimitrios Zekkos

           This report provides a brief overview of the physics of landslides and overviews many types of landslides and triggers, with a focus on landslides triggered by earthquakes. I focus only on terrestrial landslides and do not consider subaqueous landslides.

Why Study Landslides?

            The economic and human losses related to landslides are significant. In the United States alone, 25 to 50 lives are lost each year due to landslides and repairs after landslides occur require 1 to 3 billion dollars to repair (National Academies, 2004). A harsh reminder of the devastating effects of landslides occurred in Oso, Washington in 2014 when a hillside collapsed, destroying a neighborhood and killing 43 people. However, the effects of an extensive landsliding event, such as one triggered by an earthquake dwarf the detrimental effect of a single landslide. Between 1968 and 2008, earthquake induced landslides were responsible for over 70,000 deaths (Marano, 2009). The landslides triggered by the 2008 Wenchuan earthquake alone were responsible for more than 20,000 of these fatalities (Chuan Tang, 2011).

            While some potential slides can be predicted and stabilized, the majority cannot. Widespread stabilization is not feasible, especially on a global scale. Instead, we rely on hazard mapping to identify vulnerable areas. Accurate hazard maps depend on knowledge of landslide dynamics, physical conditions, and forcings (such as increased precipitation or shaking from an earthquake). 


Slope Stability
Slope stability is dependent on the following:

  1. Material involved including:
    -Material properties (cohesion and the internal friction)
    -Fracture density and quality
    -Weathering of the material
  2. Geometry of material
  3. Slope angle
  4. Weight distribution
  5. Water content
  6. Vegetation
  7. External impulsive forces (such as earthquakes)

 

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.  

Factorofsafetydiagram

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. 


Triggers

            A landslide trigger decreases the factor of safety to less than one. When the factor of safety is less than one, driving forces are greater than resisting forces, and failure will occur. Triggers include both natural and human-caused events.  Human induced triggers include removal of the toe of the landslide through excavation, loading of the head of the landslide (addition of mass), and artificial vibration.  Natural triggers include toe removal through erosion, changes in water pressure, and earthquakes. Any of these potential triggers can also combine to cause failure (Waltham, 1994).

Water Pressure

            Increasing water levels is the most common trigger of landslides. Increased water pressure decreases the effective stress and the factor of safety of a slope. The Oso landslide in Washington was likely triggered by increased precipitation in the weeks before the slide occurred (Henn et al, 2015). Precipitation can also trigger landslides destabilized by a previous event such as an earthquake, as seen in the landslides triggered by a rainstorm after the Wenchuan earthquake (Tang et al, 2011).

Earthquake triggers

            Earthquakes cause failure in two different manners. The vibration from an earthquake can cause liquefaction in uniformly graded, fine-grained, sediments due to loss of effective stress.  Earthquakes can also increase the shear stress on a slope, decreasing the factor of safety to below one (De Blasio, 2011). According to Newmark analysis (Newmark, 1965), displacement and landsliding occurs when a critical acceleration is reached. The critical acceleration for failure can be calculated using the following equation:AccEqnwhere ac is the critical acceleration, g is acceleration due to gravity and alpha is local slope.

            Large, shallow earthquakes frequently trigger landslides. Work from Keefer (1984) suggests that an earthquake as small as a magnitude 4.0 can trigger failures. The smallest earthquakes (ML (Richter local magnitude) = 4.0) can trigger rock falls, rockslides, soil falls, and soil slides. The largest earthquakes (Ms (Richter surface wave magnitude) 6.5 can trigger rock and soil avalanches. The area affected by landsliding is also dependent on earthquake magnitude (see figure 2). As magnitude increases, the extent of landsliding increases. An example of the extensive area that can be effected by landsliding during an earthquake is shown in figure 3 below. Figure 3 shows the distribution of landslides from the magnitude 6.7 1994 Northridge earthquake. Around 10,000 km2 was effected by landsliding, matching predictions made by Keefer (see figure 2).

Fig2

Figure 2: The relation between earthquake magnitude and the area affected by landslides. Figure is from Keefer (1984). 


NR ls
Figure 3: An example of the distribution of earthquake triggered landslides after the 1994 Northridge earthquake. Landslides (Harp and Jibson, 1996) are blue polygons and active quaternary faults (USGS and CGS, 2006) are the red lines.


Modeling the effects of an earthquake on a hillslope

            There have been many attempts to model the effects an earthquake has on a slope to assess the likelihood of failure in a given event. Jibson (2011) overviewed three of the methods used, pseudostatic analysis, stress-deformation analysis, and the Newmark sliding block analysis. 
Pseudostatic Analysis
            Pseudostatic analysis assumes that the shaking from the earthquake can be represented as a permanent body force applied to a slope.  The factor of safety is calculated using the equation below: 
FS2
W is the weight per unit slope, alpha is the slope angle, phi is the internal angle of friction, and k is the pseudostatic coefficient. The pseudostatic coefficient is the horizontal ground acceleration divided by acceleration due to gravity. Any ground acceleration that causes the factor of safety to decrease below one will trigger failure according to this analysis.  The diagram from Jibson (2011) below shows a force diagram used in pseudostatic analysis.

FS1
The representation of an earthquake as a single, continuous force on a slope is not accurate. Using the pseudostatic method to predict slope stability is often conservative, but in special cases where pore pressure will build up or shear strength will be lost during shaking, the analysis is unconservative. Essentially, pseudostatic analysis is a very basic analysis, and does not give any information about what occurs after the slope is no longer in equilibrium. However, due to its ease of use, and low cost, it can serve as a simple index of stability. 

Stress-Deformation analysis
            Stress-deformation analysis uses finite-element modeling methods to model the response of a slope to a stress. It uses a mesh and calculates the deformation of each node in response to the modeled stress. Quality of the model is determined by the quality of input data. High quality and high-density data are needed for the model to be accurate, and if the data is good enough, stress-deformation modeling will give the most accurate depiction of what occurs during shaking.  However, as acquiring the necessary data needed is very expensive, stress-deformation analysis is typically only used for critical slopes and structures.

Newmark analysis
            Newmark analysis models landslides as a rigid block on an inclined plane. The critical acceleration is the acceleration needed to overcome basal resistance. To determine the displacement of a block, the acceleration record from an earthquake greater than the critical acceleration is integrated to produce a velocity-time function, which is then integrated to produce an estimate of the displacement. The interpretation of the displacement varies. Typically, a threshold displacement is assumed, such as 5 or 10 cm.  Any displacements that exceed the threshold are predicted to fail.
            Newmark displacement assumes that the landslide experiences no internal deformation and moves as a rigid block during the entire failure. It also assumes that the critical acceleration remains constant and there are no dynamic pore pressure effects. Analyses of both laboratory models and earthquake-induced landslides have confirmed that Newmark analysis is fairly accurate when slope geometry, soil and rock properties, and acceleration are known.

            The stress-deformation analysis provides the most information about behavior, but is also the most expensive and work intensive technique, making it infeasible for widespread analysis. Newmark analysis bridges the gap between the two methods, being both inexpensive and providing better information than pseudostatic analysis. (Jibson, 2011)


Types of Landslides
            The mode of failure depends on the material type, the structure of the material (bedding, joints, and the orientation of these planes of weakness), and the slope. Different modes of failure can also combine in complex failures. Rocks tend to fail along pre-existing planes of weakness such as joints or bedding planes. Soils tend to fail in rotational slides along the radius of the sphere with the lowest factor of safety. They can also fail along planes of weakness, such as the interface between rock and soil. 

Rock Failures
            Rockfall
                        Occurs on steep slopes (greater than 40 degrees)
                        Individual boulders or disrupted rock masses
                        Most abundant failure during earthquakes
                        Often from slopes that were borderline stable under non-seismic conditions
                        Mostly in heavily jointed or weakly cemented rocks

            Rock slides
                        Failure along a pre-existing discontinuity
                        Similar material to rockfalls

            Rock Avalanches
                        Disintegrated landslide that can travel hundreds km per hour across low slopes
                        Typically occur when there is a large amount of kinetic energy in the slide                        
                        
(falling 
from a height)

            Rock Slumps
                        Similar to soil slumps (deep seated slides in very weak rocks)

Soil Failures
            Compared to rocks, soils are more isotropic, and do not commonly have dominant weak layers. Instead of failing along a pre-existing plane of weakness, soils often fail along a sub-spherical shell where the lowest factor of safety occurs.

            Soil falls
                        Similar to rockfall, but material involved is soil

            Disrupted soil slides
                        Disintegrate during movement
                        Most slide on basal shear surfaces at contact between bedrock and soil, some
                        slide 
on boundaries between different soil layers

            Soil Avalanches
                        Similar to disrupted soil slides, but faster moving and more disrupted

            Soil Slumps
                        Curved basal shear surface, deep seated

            Soil block slide
                        Movement along a planar surface, often deep seated

            Rapid soil flows
                        Streams of soil grains that flow in a fluid-like manner at high velocities

            Debris flows
                        Debris flows are a mixture of sediment and water. They are typically fast
                        moving 
and pose a serious hazard due to their speed, transport of large
                        
boulders, and variable viscosity. 


Failure
            The physics of landslides during failure depend on the type of landslide. Coherent blocks behave differently from disrupted, incoherent slides, and saturated slides behave differently from dry slides.  This section briefly overviews the effect of water on landslide dynamics, focusing on debris flows, and the failure process of rock avalanches.

Effects of water on landslide dynamics

            Landslides that have high water contents behave as Non-Newtonian fluids and have little to no shear strength (this includes mudflows). Behavior depends on the amount of water present, as water decreases the shear strength. Materials with low water contents will behave in a brittle fashion; increasing the water content progressively results in ductile, then plastic, then fluid like behavior. Because of the effects of water on debris flows, the mechanics of the flow are in between that of fluid dynamics and that of soil dynamics.

            Modeling the dynamics of debris flows is difficult due to the interaction between particles in water and the interaction of the debris flow with its channel. Simple experiments on the effect of shear rate on the shear strength of water-clay mixtures show shear thickening behavior. Unlike water, which shows a linear relationship between shear stress and strain rate, and does not show an increase in shear strength with increasing strain rates, the shear strength of clay-water mixtures increases non-linearly with strain rate. Increasing clay content also increases the shear strength of the mixture. 

Fig 3
Figure 4: The dependence of shear strength on shear rate for clay-water mixtures. Each line is labeled with the percent clay. Figure is from De Blasio (2011).  

           The flow behavior of a mudflow is modeled as a Bingham fluid. Bingham fluid flow consists of a basal shearing layer with velocity increasing until the boundary with an upper plug layer is reached. The upper plug layer moves at the same velocity as the top of the shearing layer. Figure 5 shows Bingham fluid flow on a slope. Channel morphology also controls the flow behavior, with decreasing channel volume increasing velocity, and increasing channel volume decreasing velocity.

Fig 4

Figure 5: Bingham fluid flow on a slope. Figure is from De Blasio (2011). 

 Rock Avalanches
            Rock avalanches, also known as sturtzstroms, are the largest failure events on the planet.  They originate as a gravitational failure of a plane or wedge (in many cases likely triggered by an earthquake) that disintegrates into a fragmented mass. Possible mechanisms of disintegration include impact with the ground surface, particle impacts, and bending of the slab beyond the tensile strength of the rock. The disintegrated mass then travels rapidly across long distances, with run-outs that are much greater than any other types of failure. The mechanism for transport across long distances is debated. Some have argued that a layer of compressed air supports the slide and provides a lubricated layer for sliding (Shreve, 1959) while others argue that acoustic fluidization may sustain fluid-like flow for long distance travel (Collins and Melosh, 2003).

saidmareh-landslide
Figure 6: Satellite image of the Saidmarreh landslide in Iran. This sturtzstrom occurred about 10,000 years ago, and was likely triggered by an earthquake. About 20 cubic kilometers of material were transported up to 14 km from the source. Image from Geology.com.

Morphology and mapping
            Failures that involve the transport of material, such as slides and flows, have three distinct parts, the source region, the run out region, and the deposition area. The source region is characterized by erosion, the run out region can be both erosional and depositional, and the deposition area is characterized by the deposition of the rock or sediment. The morphology of the depositional area is dependent on the type of failure. Disrupted failures can produce inverse grading, and compression ridges may appear when velocity in the center of the slide was greater than that on the sides of the slide. In cases where the slide moved as a coherent block, the block will be found in the depositional area with some internal deformation.

            While distinguishing between the distinct failure parts in the field may be relatively simple, doing so for large scale mapping using aerial photography is difficult. Many landslide inventories have problems with landslide amalgamation, and do not differentiate between source areas and deposition. Accurate and complete landslide inventories are needed to train hazard models (See Coseismic landslide hazard mapping methodologies-Von Voigtlander). Incorporating the physics of landslide failure and transport will improve mapping of source areas and improve predictions of where landslides will occur and what they will impact.

References

Collins, G. S. (2003). Acoustic fluidization and the extraordinary mobility of sturzstroms. Journal of Geophysical Research, 108(B10), 2473–14. doi:10.1029/2003JB002465

De Blasio, F. V. (2011). Introduction to the Physics of Landslides. Dordrecht: Springer Netherlands. doi:10.1007/978-94-007-1122-8

Harp, E.L., Jibson, R.W., 1996, Landslides triggered by the 1994 Northridge, California, earthquake, U.S. Geological Survey Open-File Report 95-213.

Henn, B., Cao, Q., Lettenmaier, D. P., Magirl, C. S., Mass, C., Bower, J. B., et al. (2015). Hydroclimatic Conditions Preceding the March 2014 Oso Landslide. Journal of Hydrometeorology, 150312130204000–18. doi:10.1175/JHM-D-15-0008.1

Jibson, R.W., Harp, E.L., Keefer, D.K., and Wilson, R.C., 1994a, Landslides triggered by the 17 January 1994 Northridge, California earthquake: Earthquakes and Volcanoes, U.S. Geological Survey, v. 25, no. 1.

Keefer, D. K. (1984). Landslides caused by earthquakes. Geological Society of America Bulletin, 95(4), 406. doi:10.1130/0016-7606(1984)95<406:LCBE>2.0.CO;2

Jon W. Koloski, Sigmund D. Schwarz, and Donald W. Tubbs, Geotechnical Properties of Geologic Materials, Engineering Geology in Washington, Volume 1, Washington Division of Geology and Earth Resources Bulletin 78, 1989

Marano, K. D., Wald, D. J., & Allen, T. I. (2009). Global earthquake casualties due to secondary effects: a quantitative analysis for improving rapid loss analyses. Natural Hazards, 52(2), 319–328. doi:10.1007/s11069-009-9372-5

Newmark, N., 1965, Effect of earthquakes on dams and embankment. The Rankine lecture: Geotechnique, v. 15, no. 2.

Partnerships for Reducing Landslide Risk: Assessment of the National Landslide Hazards Mitigation Strategy. Washington, D.C.: National Academies, 2004. Print.

Shreve, Ronald Lee (1959) Geology and mechanics of the Blackhawk landslide, Lucerne Valley, California. Dissertation (Ph.D.), California Institute of Technology.

Tang, C., Zhu, J., Qi, X., & Ding, J. (2011). Landslides induced by the Wenchuan earthquake and the subsequent strong rainfall event: A case study in the Beichuan area of China. Engineering Geology, 122(1-2), 22–33. doi:10.1016/j.enggeo.2011.03.013

"The Saidmarreh Landslide." : One of the World's Largest Slides. N.p., n.d. Web. 01 Apr. 2015.

Waltham, T. (1994). Foundations of Engineering Geology (3rd ed., pp. 1–105). London.

U.S. Geological Survey and California Geological Survey, 2006, Quaternary fault and fold database for the United States, accessed Nov. 12, 2014, from USGS web site: http//earthquakes.usgs.gov/regional/qfaults/.

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