Influence of Sample Size on the Bayesian Update of Statistical Hyperparameters of Concrete Compressive Strength

In structural reliability, the scatter of basic variables, as concrete compressive strength, can influence the failure probabilities and, therefore, the safety levels of new structural components or systems. The current Probabilistic Model Code, postulated by the Joint Committee of Structural Concrete, includes a statistical model for the description of concrete compressive strength by means of four hyperparameters (m, n, s and \(\nu\) ). Normal-Gamma or Lognormal-Gamma distributions are utilised as the conjugate prior distributions for updating the unknown mean and standard deviation of Normal or Lognormal distributions, respectively, describing the concrete compressive strength. This model was based on the preliminary work of Rackwitz conducted during the 1980’s, which considered the statistical investigations led by Rüsch during the 1960’s. A recent study suggests that some of these hyperparameters could be improved for more accurate safety assessments. However, the updating may depend on the way the concrete compressive strength values are assembled and, particularly, on the sample size configuration. An extensive database of experimental concrete compressive strength values of ready-mixed concretes is utilised to investigate the influence of the sample size on the updating of hyperparameters through Bayesian methods with prior information. The results suggest that an “optimal” sample size depends on the available data and how it is assembled and, therefore, for the updating, certain trade-offs are required. This investigation is relevant to fundament potential adjustments of the existing stochastic model and establish possible guidelines for practitioners to update the stochastic model of concrete strength when new experimental data becomes available.