Pseudo-static failure modes and yield accelerations in rock slopes

Earthquake-induced landslide databases indicate that failure modes, observed in the field following earthquakes, include sliding, toppling, and slumping. Methods based on simplified, discrete, single block models are limited to rectangular blocks on a plane or wedge blocks that restrict the potential failure modes to sliding or toppling. This paper expands the geometry assumptions so that additional failure modes will be kinematically admissible. A simple, yet broadly applicable, two-dimensional (2D) single block framework is introduced that does not restrict the geometry to orthogonal fracture sets. This framework allows for the slumping failure mode to naturally occur and can identify a new failure mode, confined toppling. Using simple failure mode charts, this framework can be easily applied to a wide range of analysis and design applications. In addition to the identification of new failure modes, seismic yield acceleration equations are presented for all four modes of failure: sliding, toppling, slumping, and confined toppling. The equations for slumping and confined toppling are derived for the first time. Although the model may be simple in its formulation and implementation, it is quite powerful, allowing for significant implications to be developed. Complex shaped blocks can be easily evaluated knowing just their centers of mass and contact points with supporting fractures. The failure mode of a discrete rock block is shown to be independent of the primary fracture inclination on which the block rests upon and the scale of the block itself. Seismic failure modes are demonstrated to be different from those induced by static forces alone and can even change modes depending on the amount of displacement during the ground motion. In addition, it is shown that the characteristics of an earthquake ground motion acting on these blocks in combination with geometric variability can influence the abundance of failure types observed in the field. Finally, an example mode and yield acceleration evaluation of Alaskan rock slope is presented.