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Landslides: Slope stability, triggers, failure dynamics, and morphology - Modeling the effects of an earthquake on a hillslope

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)

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