## Abstract

A general framework for analyzing the failure probability of concrete specimens with the mean strength sampled from a large database is presented. The framework explicitly takes into account the level of uncertainty of the existing strength database involving different concretes tested in different labs. This uncertainty strongly influences the probability distribution of the nominal strength of each structure. The energetic (nonstatistical) size effect on structural strength is also incorporated into the analysis. The proposed framework is demonstrated by analyzing the reliability of reinforced concrete beams against diagonal shear failure. The analysis considers four different levels of uncertainty of the mean strength database, with coefficients of variation 5%, 10%, 25%, and 40%. It is shown that the overall failure probability strongly depends on the structure size, and that this size effect is also influenced by the uncertainty level of the database. In addition, an approximate solution procedure is developed for calculating the failure probability in the spirit of the first-order reliability method. Compared to the existing procedure, the proposed model is shown to yield a more realistic estimate of the structural failure risk and to lead to an analytical solution of the safety factor that can be used for reliability-based structural design.

Original language | English (US) |
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Article number | 04020038 |

Journal | Journal of Engineering Mechanics |

Volume | 146 |

Issue number | 6 |

DOIs | |

State | Published - Jun 1 2020 |

### Bibliographical note

Funding Information:J.-L. Le acknowledges partial financial support from National Science Foundation (NSF) Grant No. CMMI-1361868 to the University of Minnesota. Z. P. Bažant acknowledges partial financial support from Army Research Office (ARO) Grant No. W911NF-19-1-0039 to Northwestern University. Thanks are due to Wen Luo, doctoral candidate at Northwestern University, for valuable comments.

Publisher Copyright:

© 2020 American Society of Civil Engineers.