Joint exploration of regional importance of possibilistic and probabilistic uncertainty in stability analysis

Stability analysis generally relies on the estimate of failure probability P. When information is scarce, incomplete, imprecise or vague, this estimate is imprecise. To represent epistemic uncertainty, possibility distributions have shown to be a more flexible tool than probability distributions. The joint propagation of possibilistic and probabilistic information can rely on more advanced techniques such as the classical random sampling of the cumulative probability distribution F and of the intervals from the possibility distributions π. The imprecise probability P is then associated with a random interval, which can be summarized by a pair of indicators bounding it. In the present paper, we propose a graphical tool to explore the sensitivity on these indicators. This is conducted by means of the contribution to sample probability of failure plot based on the ordering of the randomly generated levels of confidence associated with the quantiles of F and to the α-cuts of π. This presents several advantages: (1) the contribution of both types of uncertainty, aleatoric and epistemic, can be compared in a unique setting; (2) the analysis is conducted in a post-processing step, i.e. at no extra computational cost; (3) it allows highlighting the regions of the quantiles and of the nested intervals which contribute the most to the bounds of P. The method is applied on two case studies (a mine pillar and a steep slope stability analysis) to investigate the necessity for extra data acquisition on parameters whose imprecision can hardly be modelled by probabilities due to the scarcity of the available information (respectively the extraction ratio and the cliff geometry).