Authors: Baczynski, NRP
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Strength of most rock masses is anisotropic. This means that strength is often not uniform in all directions but depends on layering and structural fabric of the rocks. Three components of strength are rock mass, geological defects and intact rock or rock mass ‘bridges’ between defects. The Hoek–Brown criterion applies to those segments of failure path that are not co-aligned with dominant defect orientations. Conversely, the Hoek–Brown criterion is less representative where the failure path is co-aligned with such fabric. In the latter case, strength is better estimated by the Step-Path method. This approach requires slope face mapping data for several input parameters; drill core does not provide the necessary data. Conventional Step-Path methods use Monte–Carlo simulation of large numbers (> 10,000) of paths (Baczynski 2000). Any statistical model (normal, lognormal, exponential) can be considered for input parameters; many are lognormally distributed. A less rigorous Simplified Step-Path method is described in this paper. However, this approach has a limitation; statistical variability for all inputs is approximated by normal distributions. The Rosenblueth method of statistical moments, and Sampling Theory, are used to develop statistical strength models for any user-nominated Step-Path traverse length. Analysis is Excel spreadsheet based. Case study examples are presented. Step-Path computed strength may be 30 to 45% less than Hoek–Brown values. This strength reduction significantly decreases Factors of Safety and increases stability risks for rock slopes.

Keywords: jointed rock slopes, stability, failure path strength, simplified step-path, statistical approach, Monte-Carlo simulation, Rosenblueth Method of statistical moments, case studies   

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