Reliability analysis of FRP-confined concrete at ultimate using conjugate search direction method

Behrooz Keshtegar, Aliakbar Gholampour, Togay Ozbakkaloglu, Shun Peng Zhu, Nguyen Thoi Trung

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)
19 Downloads (Pure)


In this paper compressive strength and ultimate strain results in the current database of fiber-reinforced polymer (FRP)-confined concrete are used to determine the reliability of their design space. The Lognormal, Normal, Frechet, Gumbel, andWeibull distributions are selected to evaluate the probabilistic characteristics of six FRP material categories. Following this, safety levels of the database are determined based on a probabilistic model. An iterative reliability method is developed with conjugate search direction for evaluating the reliability. The results show that Lognormal and Gumbel distributions provide best probability distribution for model errors of strength and strain enhancement ratios. The developed conjugate reliability method provides improved robustness over the existing reliability methods owing to its faster convergence to stable results. The results reveal that the part of the database containing normal strength concrete (NSC) heavily confined (i.e., actual confinement ratio (flu,a/f'co) 0.5) by low and normal modulus carbon fibers (i.e., fiber elastic modulus (Ef) ≤ 260 GPa) and moderately confined (i.e., 0.3 ≤ flu,a/f'co ≤ 0.5) by aramid fibers exhibits a very high safety level. The segments of the database with a low and moderate safety level have been identified as i) NSC moderately and heavily confined by higher modulus glass fibers (i.e., Ef 60 GPa), ii) high strength concrete (HSC) moderately and heavily confined (i.e., flu,a/f'co 0.3) by glass fibers, iii) HSC lightly confined (i.e., flu,a/f'co ≤ 0.2) by carbon fibers, and iv) HSC lightly confined by aramid fibers. Additional experimental studies are required on these segments of the database before they can be used reliably for design and modeling purposes.

Original languageEnglish
Article number707
Number of pages18
Issue number3
Publication statusPublished - 1 Mar 2020
Externally publishedYes

Bibliographical note

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (


  • Fiber-reinforced polymer (FRP)
  • FRP-confined concrete
  • Model error
  • Reliability analysis
  • Safety level


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