Bayesian Prediction of Elastic Modulus of Concrete

The Bayesian updating rule is used to assess the American Concrete Institute (ACI) model relating the elastic modulus of concrete to its compressive strength. Uncertainties inherent to the modeling process are identified. A likelihood function for the assessment of the model is derived assuming statistical independence between observations. This function is subsequently modified to account for model-induced correlation. It is shown that the correlation effectively reduces the amount of information contained in the data. The likelihood model is used with data available from literature and new data acquired at the University of California, Berkeley, for a specific concrete mix to compute the posterior statistics of the model parameters and to derive a predictive model for the elastic modulus of concrete. The presented approach is unique as it accounts for all sources of model uncertainty, deals with the important issue of model-induced correlation, and shows how Bayesian updating can be used to derive an improved predictive model for a specific concrete mix. Use of the proposed approach in performance-based codified design is discussed.