Parameter estimation and uncertainty quantification of a fiber-reinforced concrete model by means of a multi-level Bayesian approach

The paper presents a procedure for the stochastic calibration of a cracked hinge model on the basis of an extensive experimental campaign performed on a large group of nominally identical fiber-reinforced specimens. The calibration is carried out in a multi-level Bayesian framework that allows to quantify and separate several uncertainty contributions affecting model parameters. Indeed, the variability in the experimental response for nominally identical specimens due to the material heterogeneity represents a significant uncertainty contribution as well as model error. The former can be quantified at the hyper-parameter level of the multi-level framework. The presented results highlight the good agreement of the numerical predictions with the experimental data and the superior performance of the multi-level framework compared to that of the classical single-level framework. We also perform analyses to explore the impact of the prior parameter model conditioned on hyper-parameters and assess the minimum number of specimen datasets needed to quantify the inherent variability of model parameters.