Probabilistic models of dynamic increase factor (DIF) for reinforced concrete structures: A Bayesian approach

Dade Lai, Fabrizio Nocera, Cristoforo Demartino, Yan Xiao, Paolo Gardoni

Research output: Contribution to journalArticlepeer-review


The response of structures under rapidly varying loads can be affected by strain rate sensitivity generally expressed using Dynamic Increase Factor (DIF). Current models for estimating the DIF in Reinforced Concrete (RC) structures are generally deterministic and have restricted applicability due to their dependence on limited experimental data resulting in bias. This paper overcomes these limitations by proposing three probabilistic models that quantify compressive and tensile concrete and steel DIF, accounting for the relevant uncertainties. The proposed models are based on existing deterministic models with the addition of probabilistic correction terms. Bayesian updating is employed to estimate the unknown model parameters using observational data from a large collection of experimental observations. The models incorporate model uncertainties stemming from assumed model form and (potential) missing variables through a model error term. The proposed probabilistic models are used to evaluate the reliability of RC structures under dynamic loads. As an illustration, the proposed probabilistic models are used to estimate the reliability of an example RC column under combined dynamic axial force and moment, and a RC column or beam under dynamic bending moments resulting in cracking. In the two examples, we consider the ACI 318-19 requirements for Ultimate Limit State (ULS) and Serviceability Limit States (SLS). In comparison to deterministic DIF models, the proposed probabilistic models yield enhanced predictive accuracy, presenting a practical and robust approach to assess the structural reliability under impact and blast loads.

Original languageEnglish (US)
Article number102430
JournalStructural Safety
StatePublished - May 2024


  • Bayesian updating
  • Dynamic increase factor
  • Impact and blast loads
  • Probabilistic models
  • RC structures

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Building and Construction
  • Safety, Risk, Reliability and Quality


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