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.


The ultimate slopes of an open pit mine are generally excavated to the steepest possible angles because the economic consequences of the excavation angles are significant. For large scale open pits, changes in slope angle by approximately 2–3 degrees may correspond to a large amount of dollars in project value. However, steeper slope angles result in higher probabilities of slope failure. Therefore, it is critical to calculate the maximum safe slope angles (MSSA) and also to estimate probabilities of slope failure with respect to different cut slope dip angles.

The open pit mine slope stability is one of the geotechnical subjects dominated by variability and uncertainty because the slopes are composed of natural heterogeneous materials containing a large number of discontinuities. In discontinuous hard rock masses, the variability and uncertainty of rock slope stability analyses mainly arise from discontinuity geometry and discontinuity strength. Application of probabilistic analysis has provided an objective tool to quantify and model variability and uncertainty [1-2]. The first two types of probabilistic analyses to rock slope stability have been applied using either kinematic or limit equilibrium analysis [3-7].

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