Bayesian parameter and joint probability distribution estimation for a hysteretic constitutive model of reinforcing steel

Matias Birrell, Rodrigo Astroza, Rodrigo Carreno, Jose Restrepo, Gerardo Araya-Letelier

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


With the structural design paradigm shift since the early 2000′s from the traditional approach to performance-based design (PBD), there has been a growing need for reliable nonlinear finite element (FE) models that can accurately predict the response of structures when subjected to extreme loads, such as earthquakes. In the case of reinforced concrete (RC) structures, a proper representation of the hysteretic nonlinear behavior of reinforcing steel becomes crucial in order to carry out nonlinear time history analyses. The Giuffrè-Menegotto-Pinto (GMP) uniaxial steel constitutive law has been widely used by researchers and practitioners to model reinforcing steel bars. Despite the widespread in its implementation, a limited number of studies have proposed well-calibrated parameter values for this model. In addition, low identifiability of its governing parameters and the high cost of generating reliable experimental data have prevented a thorough probabilistic characterization of the GMP model parameters. Usually, only default parameter values from the early development of the model tend to be used. This paper uses experimental data from cyclic tests conducted on 36 reinforcing steel coupons manufactured in accordance to ASTM A615 and A706 Grade 60 reinforcing steel and proposes a joint probability density function (PDF) for the most influential parameters of the GMP material model. First, a local sensitivity analysis (LSA) is conducted to provide insight into the influence of each parameter in the model response. Also, global sensitivity analysis (GSA) is used to have a deep understanding of the composition of the variability in the model response due to parameter uncertainty and the level of interactions among parameters. The Bayesian approach is combined with the information obtained from GSA and LSA as input, to estimate model parameters and quantify the estimation uncertainties and propagate them to the material stress response. Uncertainty in model predictions obtained with the proposed PDF is assessed, and the impact of considering parameter correlations on the material response is investigated.
Original languageAmerican English
Article number102062
JournalStructural Safety
StatePublished - May 2021

Bibliographical note

Publisher Copyright:
© 2020 Elsevier Ltd


  • Bayesian estimation
  • Constitutive material model
  • Reinforcing steel
  • Sensitivity analysis


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