Reliability assessment of wedge failure in rock slopes by the random sets theory

In many cases, rock mass slope stability is controlled by discontinuities, which determine the most likely mechanism of failure, depending on joints and slope geometry. Among these mechanisms, the wedge failure is one of the most common ways of failure in rock slopes. The stability of the rock wedge is controlled by: joint sets dip and dip direction, slope geometry and direction, external forces (including water pressure and earthquake) and rock and joints mechanical properties. However, due to the geological origin of rock masses, these inputs are uncertain. Thus, the stability assessment method has to be capable of coping with this uncertainty. Random sets arise as a powerful tool to deal with uncertainty, even when limited information of inputs is available. With this framework, this work presents a reliability assessment of wedge stability in rock slopes by random sets, considering the joints geometry and strength parameters as random uncertain variables.