Seismic Rock Slope Failure Modes and Time-Dependent Displacements Using Single Block Methods

Abstract

Seismically induced rock slope failures have resulted in billions of dollars of economic damage and enormous loss of life throughout the world. Accurate prediction of the triggering and run out of these failures is elusive for a variety of reasons, including knowledge of the physical modes of failure. Simplified tools that are prevalent in soil slope engineering are relatively non-existent in rock slope engineering. Current state of art in rock slope engineering requires complex and computationally expensive numerical models to evaluate the seismic performance or rock slopes, which inhibits extensive evaluations to be conducted. This research explores the potential failure modes of an idealized rigid rock block and expands the modes typically considered to include not only sliding but also toppling (pure forward rotation), confined toppling (constrained forward toppling) and slumping (combined backward rotation and translation). The yield acceleration (or minimum inertial acceleration to cause block movement) for slumping, similar to toppling, is found to be lower than for pure translational sliding. These yield accelerations indicate the initial modes of rock block failure; however, they do not always predict the ultimate failure mode. To predict the final failure modes, the results of discrete element numerical analyses were compared to pseudo static yield acceleration to develop a seismic failure mode chart based on block geometry and interface friction. For co-seismic displacement predictions, simplified models predicting ultimate displacement of a mass under seismic conditions are limited to purely translating, sliding blocks (i.e.\ Newmark's sliding block method). This dissertation introduces additional non-linear, time-dependent models to predict ultimate displacement in toppling and slumping modes as well. Similarities of the dynamic response of rocking, toppling, and slumping systems are exposed and allow knowledge from the well-established literature of rocking blocks to be leveraged. The parameters of these non-linear models are combined such that mapping of more complex systems to these simple models can be performed. Important findings from these new methods are that the magnitude of seismically-induced displacement is dependent on the size and shape of the block (or failure mass) and the displacement dependent yield accelerations. In addition, by establishing a failure criteria for the different modes of failure, ground motion characteristics (mean period and intensity) can be used to predict the likelihood of failure. Design charts are developed to allow seismic toppling and slumping failures to be integrated into PBEE evaluations or real-time regional assessments.