Estimation of upper bounds to rock slopes by analysis of existing slope data wall stability in the South Roberts Pitt - an example of the use of previous slopes
Authors: McMahon B K 
Published: April 2018

This report applies a method developed by Shuk to the investigation of existing rock slope data. The study is incomplete. It is presented in this form in the hope of drawing additional data and explanations from other workers. The rock slopes studied tend to
confirm Shuk's observation that data from existing rock slopes form straight lines on log-log graphs when the slope height is plotted against the slope "length". The term "length" is defined by Shuk to be the horizontal component of the slope on a log-log plot, and this definition has been retained
throughout this compilation of papers. However, it is also shown that Shuk's procedure for estimation of probability of failure by regression analysis of existing slopes is likely to yield trivial results unless all slopes analyzed are known to be close to limiting equilibrium. This emphasizes
Shuk's requirements that the sample must be carefully defined and bounded if this procedure is to be used. It does raise concern that the requirements may be too restrictive for the procedure to be widely applied in practice. Of the data studied, only the slopes in shale are known to be close to
limiting equilibrium. The remainder are conservative to an unknown degree. However, it was assumed that the steepest existing slopes in any category would approach the upper limit for stable slopes in that category. A first attempt at drawing upper bounds for various broadly defined rock mass
categories. The proposed "upper bounds" are straight lines which, when extrapolated, converge at a point equivalent to a slope angle of 8° at a slope height of 10,000 ft. If they are confirmed and more precisely defined by further study, such upper bounds may provide a criterion for design of
rock slopes in stable orientations with respect to the geologic structure. Design of slopes with orientations that are critical with respect to structure should be based on analysis of the fractures. Theoretical curves derived from the Mohr failure criteria are a poor fit to most of the empirical
data. Shale slopes fit a straight line or a Mohr-Coulomb curve equally well. Besides the poor fit, the deduced values of the Mohr strength parameters are unexpectedly low and appear inconsistent with published values based on laboratory tests. Possible explanations are either that: (a) steepness is
limited by surface failures due to processes such as ravelling, over-toppling and exfoliation of small surface blocks and not by the strength of the underlying rock mass; (h) strength of the underlying rock mass is subject to a "power failure law" from which it is tentatively deduced that slope
height would bear an exponential relationship to a slope length; or (c) information for slopes in rocks other than shale merely represents accidental variation of slopes which could all be much steeper. It would follow from the first explanation that open pit slopes with stable orientations could be
excavated to very steep angles using surface reinforcement such as rock bolts. The second explanation would imply that very high rock slopes may need to be designed at slope angles less than residual angles of friction determined in the laboratory. The third explanation assumes that the rather
impressive fit of the data is due to coincidence.