Stability analyses of geotechnical structures in rock are traditionally performed using deterministic methods. In Europe, Eurocode7, introduced in the beginning of the 21st century, adopts limit state design and semi-probabilistic methods, using partial factors for the design of geotechnical structures. Meanwhile, reliability-based design, using probabilistic methods, is becoming more common in practical cases. The paper considers an intentionally simple case study―the analysis of a slope in a rock mass with one discontinuity, considered in a discrete way, forming a rock block to be stabilised by anchors―to compare the results obtained with the different methods. The objective is to calculate the force applied by the anchors so that the ultimate limit states of sliding of the rock block is verified. Deterministic-based design optimization considering both the traditional global safety factor approach and the partial factor approach following the Eurocode 7 are first applied. A reliability-based design optimization procedure―which takes geometrical and mechanical properties of the discontinuities as random variables―is then used, and the results are compared to the former ones. A discussion is presented concerning the consistency of the obtained results.
Stability analyses of geotechnical structures in rock are traditionally performed with deterministic methods, using global factors of safety (FoS). The FoS values are mainly based on experience and differ from case to case, depending on the data uncertainty and on the acceptable risk of failure [1].
In Europe, the structural Eurocodes (EN 199x) for design of buildings and civil engineering works were introduced in the beginning of the 21st century and brought structural reliability concepts to the design of geotechnical structures. EN 1990 (Eurocode: Basis of structural design) [2] is the main Eurocode, with which all other Eurocodes comply, and EN 1997 (Eurocode 7: Geotechnical design) [3] deals with the design of geotechnical structures. The suite of Eurocodes is currently undergoing a process of evolution to a second generation and a major feature of the revision of Eurocode 7 is to consider soil and rock on an equal basis. Hence, it also applies to the design of geotechnical structures in rock masses. Eurocode 7 adopts limit state design using a semi-probabilistic approach, where uncertainties are considered implicitly by the specification of characteristic values of random variables (actions, effect of actions, resistances, and ground properties) and partial factors applied to those variables.
