The removal of sediment around bridge abutments and piers due to the erosive action of flowing water (i.e. scouring) is of the greatest concern to society. Currently it has been estimated that scour produced by rivers and streams causes about 60% of the total amount of bridge failures. Underestimating this natural process can seriously threaten the overall safety of the infrastructure. Several factors may affect the scour depth at bridge piers: flow intensity and sediment grading, flow depth, nature and occurrence of floods, side wall effects, sediment size, geometry and inclination of piers, etc. The depth of the scour hole in the sand adjacent to the bridge foundations can be estimated using theoretical models with hydraulic parameters. However, the uncertainty associated with the parameters involved in the evaluation (e.g. flow characteristics, debris, structural and geotechnical factors, etc.) makes it almost impossible to adopt a deterministic approach for the reliability analysis. Therefore, in order to properly assess the structural safety, both aleatory variability (i.e. due to randomness) and epistemic uncertainty (i.e. due to limited data and knowledge) must be considered. A fuzzyprobabilistic approach can take some of those uncertainties into account. This paper proposes an original method for modelling the debris action in river bridges. Based on fuzzy-random theory, both the aleatory variability related to the particle accumulation size and the epistemic uncertainty characterising fluvial hydraulics equations can be successfully modelled.