Deterministic and Probabilistic Block Theory Analyses Comparison for an Open Pit Mine Rock Slope in USA


A new formulation is given to conduct a probabilistic block theory analysis. A new computer code (PBTAC) is developed to perform both deterministic and probabilistic block theory analysis. The variability of the discontinuity orientation and shear strength is incorporated in the probabilistic block theory analysis. Discontinuity orientation is treated as a bivariate random variable including the correlation that exists between the dip angle and dip direction. PBTAC code was applied to perform both deterministic and probabilistic block theory analyses for a part of an open pit mine in USA. Needed geological and geotechnical data for the analyses were obtained from field and laboratory investigations. The variability of the discontinuity orientations resulted in important differences between the probabilistic and deterministic block theory analyses results. The results confirmed that the design value selected for the Maximum Safe Slope Angle (MSSA) for a particular region in the open pit mine based on the deterministic block theory analysis can be on the un-conservative side. In summary, the results showed clearly the superiority of probabilistic block theory analysis over the deterministic block theory analysis in obtaining additional important information with respect to designing rock slopes. The calculated values agree very well with the existing almost stable bench face angles reported by a major mining company which cooperated with this study.

Meeting Name

49th US Rock Mechanics / Geomechanics Symposium (2015: Jun. 28-Jul. 1, San Francisco, CA)


Mining Engineering


The work was partially funded by the Centers for Disease Control and Prevention (Contract No. 200-2011-39886), National Basic Research Program of China (973 Program; No. 2010CB732005) and the National Natural Science Foundation Project of China (No. 51079093).

Keywords and Phrases

Rock mechanics; Rocks, Block theory; Calculated values; Computer codes; Design value; Geotechnical data; Laboratory investigations; Mining companies; Slope angles, Open pit mining

International Standard Book Number (ISBN)


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Article - Conference proceedings

Document Version


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© 2015 American Rock Mechanics Association (ARMA), All rights reserved.

Publication Date

01 Jul 2015

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