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Rock Mechanics Analyses: Upon reviewing data from the vibration study, and learning that <br />equipment generated vibrations operating at distances farther than 300 feet from the Rollins <br />Sandstone would create very low intensity motions at relatively high frequencies averaging <br />more than 35 Hz and less than 13 Hz, it was reasonably concluded that there is no need to <br />study the structural condition of the rock bluff because impacts of normal weathering <br />effects, temperature changes and perched hydrostatic water pressure in vertical joints within <br />the bluff are much more likely to trigger rock falls that will certainly occur at some future <br />time, whether mining occurs or not. It is well documented in scores of technical papers and <br />geotechnical references that rock falls are commonly triggered by perched hydrostatic water <br />in vertical joints or cracks. In perspective, at an expected maximum particle velocity of 0.05 <br />in/s, the theoretical peak pressure exerted by compressive vibration waves at a velocity of <br />8,000 ft/s, in sandstone with an average density of 143.5 ]b/ft , and a modulus of elasticity of <br />6.5 x 106 psi, would be around 3.41 psi [0.05 / (8,000 x 12) x 6.5 x 106]. Perched water with <br />a height of 25 feet creates a static pressure of 10.38 psi, which is three times greater than the <br />peak theoretical pressure created by the expected peak vibrations. <br />Gregory D. Lazear Letter -April 11, 2006: <br />In this letter Mr. Lazear creates a hypothetical case whereby it assumed that a normal <br />acceleration of 0.165g is required to keep a block of rock in place. A sinusoidal motion <br />calculation is then used to predict acceleration, which is then doubled because differential <br />acceleration of the block and main rock bluff are assumed. This whole argument whereby <br />static forces like gravity are compared to dynamic forces is not appropriate and will almost <br />always lead one to false conclusions regarding the stability of rock slopes exposed to low <br />intensity vibrations. <br />A very good reference describing the fallacy of these calculations is explicitly explained in <br />"Explosive Engineering, Construction Vibrations, and Geotechnology" authored by Lewis <br />L. Oriard. I quote from Page 125: <br />Several basic concepts about stability analysis are attractive in their mathematical con- <br />venience and have found their way into contracts, specifications, even regulations. The most <br />common are those known as pseudostatic methods of analysis, based on the assumption that <br />even dynamic forces such as blasting can be equated to static forces like gravity if we <br />include a mod~ing factor (as opposed to dynamic forces like seismic waves). In some <br />cases, the modifying factor has not even been included. The acceleration of the dynamic <br />force (such as blasting) is either predicted or measured, then assumed to be applied to the <br />slope as a continuing or steady horizontal acceleration. Unfortunately, this concept is <br />physically inaccurate and leads to a false conclusion of slope failure in many situations <br />which are quite safe. It is not appropriate to apply acceleration as a criterion for a wide <br />range of frequencies, and certainly not as a static force. <br />REVEY Associates, Inc. Page 4 of 13 4/19/06 <br /> <br />