A probabilistic analysis is applied to rock slope stability with an example case of a rock slope with translational potential failure mode. The capacity and the demand are represented as independent triangular random variables. The distribution of the factor of safety is found analytically and its reliability measures are evaluated, allowing for decisions to be taken in terms of risk and reliability. The same slope is examined in its limit state by applying the partial factors approach of Eurocode 7. The Eurocode design is compared to the traditional factor of safety and probability of failure.
Numerous uncertainties, arising from natural variability in space and time, experimental errors, imprecise information, insufficient knowledge, up-scaling, simplistic assumptions, etc., are pervasive in rock engineering. These are commonly taken into account, indirectly, in the traditional factor of safety design, where acceptable safety factors are selected through experience or regulation, depending on application and its importance (e.g. Priest & Brown 1983). Some drawbacks may be recognized in this approach (Yucemen et al. 1973). The same value of the safety factor is adopted (or imposed) for a particular type of application, regardless of the degree of uncertainty involved (Duncan 2000), the risk level associated with it, or the amount and quality of information available before and acquired during construction. The type of uncertainty is also relevant to rock engineering (Bedi & Harrison 2013) and its assessment essential for reliable design (Bagheri & Stille 2011). Limit States Design (LSD) in Eurocode 7 (CEN 2004) introduced several changes to the previous geotechnical design practice. Verification at the ultimate limit state requires that the design actions, increased to reflect a low probability of occurrence, be lower than the design resistances, which have been factored down to reflect prescribed (or intended) probabilities of being exceeded. The values of the partial factors of the characteristic actions and material parameters are largely associated to variability and other uncertainties and therefore the partial factors approach may be considered as a form of reliability based design, although for complex systems the relation of the partial factors to the intended failure probabilities may be somewhat difficult to observe. Calibration of the partial factor design equations has been primarily based on method a of Figure 1, where the relation between the various calibration methods considered by EN 1900 (CEN, 2002) is presented. There, the probabilistic calibration procedures are divided into Level II reliability and Level III probabilistic methods.