Bayesian statistical framework to construct probabilistic models for the elastic modulus of concrete

The commonly used Pauw's formula to predict elastic modulus of concrete is very general and does not address the complexity of modem concretes, such as high-strength concrete, use of different types of aggregates and admixtures, etc. This paper develops a statistical framework to construct probabilistic models for the elastic modulus of concrete and evaluates the influence of different aggregate types, based on a large number of experimental data. The proposed framework to construct probabilistic models expands upon Pauw's formula and properly accounts for both aleatory and epistemic uncertainties. Bayesian updating is used to assess the unknown model parameters based on experimental data. A Bayesian stepwise deletion process is used to identify important explanatory functions and construct parsimonious models. As an application, the approach is used to develop a probabilistic model for concretes made using crushed limestone and crushed quartz schist coarse aggregates.