Bayesian inference for calibration and validation of uniaxial reinforcing steel models

Abstract

With ever-advancing structural design and evaluation techniques becoming available for structural engineers, the required level of knowledge about nonlinear material behavior in civil structures has increased accordingly over recent years. In the context of finite element (FE) modeling, constitutive material models play a crucial role in the computation of the structural response. Although significant research has focused on characterizing the stress–strain relationship in reinforcing steel, most of these efforts have considered experimental response data from monotonic tests. In this paper, results from experimental cyclic tests conducted on 36 reinforcing steel coupons obtained from three major manufacturers encompassing two widely used steel grades are employed to gain a deep understanding of the relationship between model formulation and response, for three well-known hysteretic reinforcing steel one-dimensional constitutive stress–strain relationships. Initially, the three models are briefly described. Then, a local sensitivity analysis (LSA) is performed to provide an insight on the influence of each model parameter in model response, followed by a global sensitivity analysis (GSA) performed to further understand the composition of response variability due to parameter uncertainty. Model calibration is then carried out in a probabilistic manner, using the Bayesian estimation (BE) framework through the use of Markov Chain Monte Carlo (MCMC), and informed by LSA and GSA results. Parameter estimation results for each model are discussed, with an emphasis on the level of accuracy of predictions achieved with estimated sets of parameters in each case. The amount of information extracted about each parameter during calibration is assessed, leading to a performance comparison between the three constitutive laws under study.