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Environmental and Engineering Geoscience

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Simplified Dynamic Analysis of Vibration-Induced Rock Toppling

¹ Haneberg Geoscience, 10208 39^th Avenue SW, Seattle, WA 98146

The first 20% of the full text of this article appears below.

Introduction

This note describes a simplified approach to the preliminary assessment of rock toppling as the result of earthquakes, blasting, or other vibrations. The method is dynamic in the sense that it goes beyond pseudo-static or quasi-static analyses to incorporate information about vibration frequency in addition to acceleration magnitude. It is simplified in the sense that it assumes single-frequency shaking of a rectangular rock, and thus falls short of a complete dynamic analysis of an irregular three-dimensional rock with complicated basal geometry and a full spectrum of frequencies. The approach was originally motivated by a consulting project in which the possibility of blasting-induced rock toppling was raised by homeowners living near hillside construction sites. Calculations based upon the method show that high-frequency vibrations caused by typical blasting operations are unlikely to pose problems even if peak acceleration values are relatively high. Moderate to large earthquakes generating lower frequency vibrations might, however, topple some rocks at the same or lower accelerations.

Previously published analyses of rock toppling are divided between static kinematic or mechanistic formulations for single- or multiple-block toppling in the rock slope engineering literature (e.g., Norrish and Wyllie, 1996; West, 1996) and quasi-static to fully dynamic back-calculations used to infer past earthquake intensity in the seismology literature (e.g., Shi et al., 1996; Anderson and Brune, 1999; Anooshehpoor and Brune, 2002; Anooshehpoor et al., 2004; and O'Connell et al., 2007). Most recently, Crider (2008) incorporated toppling into a three-dimensional (3-D) quasi-static stochastic model simulating the degradation of fault scarps in jointed rock.

Although the method described in this note lacks the sophistication of the dynamic or multiple block analyses undertaken by others, it can be performed using geometric variables easily estimated in the field and such vibration information as horizontal acceleration and vibration frequency . . . [Full Text of this Article]