Reliability Assessment of FRP-RC Columns Using AK-MCS with a Piecewise Two-Branch Approach
Abstract
Slender concrete columns reinforced with fiber-reinforced polymer (FRP) bars fail at medium to high axial load levels either by concrete crushing or by loss of stability, while the tensile strains in the reinforcement remain far below the rupture strain. Each non-linear finite element (FE) analysis yields only the capacity of the governing failure mode, and the governing mode changes over a broad zone in which both capacities are nearly equal. Both characteristics conflict with active-learning Kriging-assisted Monte Carlo simulation (AK-MCS), which assumes a single, smooth limit-state function. This paper proposes a piecewise, two-branch AK-MCS framework in which each failure mode is represented by its own Kriging model, trained only on the FE analyses in which that mode governs, and the governing prediction is the minimum of both. Safeguards against data starvation keep rarely governing branches usable. After convergence, additional FE analyses are placed based on a leave-one-out calibration check and on the width of the confidence interval on the reliability index. A design-point search on the surrogate and importance sampling at the design points provide the reliability index even where direct Monte Carlo simulation finds no failure. For an FRP-reinforced concrete column example with mixed failure, 79% and 62% of the training points lie near the mode boundary. The reliability index from the design-point search agrees with the Monte Carlo estimate to within 0.05, and an FE analysis at the design point confirms the surrogate to within 0.6%.
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BibTeX
@misc{goldack2026reliability,
title = {{Reliability Assessment of FRP-RC Columns Using AK-MCS with a Piecewise Two-Branch Approach}},
author = {Arndt Goldack and Richard Koehler and Ahmed Usama Syed},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34472},
eprint = {2610.34472},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34472},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Reliability Assessment of FRP-RC Columns Using AK-MCS with a Piecewise Two-Branch Approach
AU - Arndt Goldack
AU - Richard Koehler
AU - Ahmed Usama Syed
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34472
UR - https://arxiv.org/abs/2610.34472
AB - Slender concrete columns reinforced with fiber-reinforced polymer (FRP) bars fail at medium to high axial load levels either by concrete crushing or by loss of stability, while the tensile strains in the reinforcement remain far below the rupture strain. Each non-linear finite element (FE) analysis yields only the capacity of the governing failure mode, and the governing mode changes over a broad zone in which both capacities are nearly equal. Both characteristics conflict with active-learning Kriging-assisted Monte Carlo simulation (AK-MCS), which assumes a single, smooth limit-state function. This paper proposes a piecewise, two-branch AK-MCS framework in which each failure mode is represented by its own Kriging model, trained only on the FE analyses in which that mode governs, and the governing prediction is the minimum of both. Safeguards against data starvation keep rarely governing branches usable. After convergence, additional FE analyses are placed based on a leave-one-out calibration check and on the width of the confidence interval on the reliability index. A design-point search on the surrogate and importance sampling at the design points provide the reliability index even where direct Monte Carlo simulation finds no failure. For an FRP-reinforced concrete column example with mixed failure, 79% and 62% of the training points lie near the mode boundary. The reliability index from the design-point search agrees with the Monte Carlo estimate to within 0.05, and an FE analysis at the design point confirms the surrogate to within 0.6%.
ER -