Physics-based probabilistic demand model and reliability analysis for reinforced concrete beams under blast loads

This paper proposes a general physics-based probabilistic demand model for the reliability analysis of reinforced concrete (RC) beams under blast loading. The formulation of the proposed demand model builds on a computationally convenient representation of the governing physical laws from structural dynamics and adds a correction term and a model error. Specifically, the proposed demand model starts with predictions from a generalized single-degree-of-freedom (SDOF) representation of the RC beam, derived from the conservation law of energy; the correction term removes the implicit bias and improves the accuracy of the model, and the model error captures the remaining uncertainty in model predictions. Unknown model parameters are included in the correction term and the model error. Once formulated, the probabilistic model is calibrated with data from experimental tests or high-fidelity computational models. The inclusion of the governing physical laws in the proposed model avoids a strong dependence of the model on the specific data used for the model calibration. The paper uses Bayesian inference that combines predictions from the generalized SDOF representation with experimental data and any prior information to estimate the unknown model parameters. The paper then uses the proposed demand model in a formulation to estimate the reliability of RC beams under blast loading. Finally, the paper illustrates the novel contributions by estimating the reliability of an RC beam under blast loading for three damage levels. As part of the reliability analyses, the paper also identifies the dominant sources of uncertainty in estimating the failure probability.