Due to its geological origin, rock mass properties have an inherent variability which brings an uncertainty that should be considered in engineering modeling. This uncertainty is divided in both aleatory and epistemic. The aleatory uncertainty is usually accounted for by conventional probability techniques. However, this approach has restrictions when limited information on variables is available, which is the case in most rock engineering projects. Besides, probability theory cannot consider the epistemic uncertainty properly. On the other hand, in many rock mechanics problems, especially in mining, there are several sources of information at different stages of the project, which should be properly incorporated into the model to assist the decision-making process. Dempster-Shafer theory provides an alternative to deal with both epistemic and aleatory uncertainty, since it allocates probability mass to sets or intervals (Dempster-Shafer structure). Hence, reliability assessment in terms of intervals can be carried out under limited information. A key aspect of the Dempster- Shafer theory is the possibility of combining several pieces of evidence from different sources, considering even conflicting information. With this framework, this paper explores different combination rules for Dempster- Shafer structures, considering a key block problem in a slope from a sandstone mine located in Cundinamarca, Colombia, where information from different sources has been collected at different stages of the operation for 20 years, on both geomechanical and geometrical properties of rock joints.
Rock masses are natural materials subjected to a long history of stresses including tectonic load, earthquakes, glaciations, subsidence, tidal effects and gravity. In most cases, these stresses bring fracturing on the rock mass. The presence of fractures highly influences its mechanical response under perturbations. In hard rock masses, the geometry and locations of joints, along with slope geometry, define the kinematically controlled mechanisms of rock failures. Some mechanisms are very simple, like planar or wedge failure, in which one or two joint sets along with the slope face define the geometry of the rock failure. For more general problems, involving three or more joint sets, the block theory (Shi, 1985) arises as a powerful tool to identify potential unstable block for a given excavation geometry. Once defined the potentially unstable block geometry, the next step is to assess its stability. The limit equilibrium (LE) is suitable to calculate the stability of potentially unstable rock wedges. Besides, its formulation is straightforward and has a low computational cost, compared to numerical techniques like Finite Element Method or Discrete Elements.