Quantification of the Uncertainty of Shear Strength Models Using Bayesian Inference

Abstract

Different analytical models exist to predict the shear strength of reinforced concrete members. Generally, each of these shear strength models consists of a formulation based on certain underlying theory and fitted model coefficients. The model fitting parameters are usually established from the comparison with test data. Hence, the predictive value of a shear strength model depends, to some extent, on the quality and representativeness of the used test data.

This work investigates the predictive capability of several shear strength models for reinforced concrete beams without shear reinforcement. Particular attention is given to the application domain of relatively low reinforced and high depth concrete beams where limited shear test data is available. The predictive capability of the models for this area of interest is analyzed with Bayesian Inference. This probabilistic technique calculates the posterior distributions of uncertain parameters, given a set of measured test data and some prior knowledge.

The predictive capability of each shear strength model is quantified by means of a calculated model uncertainty. Furthermore, the influence of the uncertainty in model parameter values on the calculated model uncertainties is evaluated. Bayesian Inference is also used to estimate the model evidences conditionally on the used data.