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Probabilistic durability design of concrete exposed to CO2-rich environments with a physics-guided machine learning framework
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DOI：10.1016/j.cscm.2026.e06398.png)
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Abstract
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Carbonation-induced steel depassivation in concrete is a time-dependent problem involving uncertainties of materials and environment. Most existing studies on concrete carbonation remain limited to deterministic prediction, which cannot be adopted for reliability-based durability design. This study proposed a physics-guided probabilistic machine learning framework that linked carbonation depth prediction, uncertainty quantification, and full-probabilistic durability design together. A dual-branch neural architecture was developed to predict the effective initial carbonation depth d0 and carbonation rate k, and carbonation depth was determined through an empirical evolution law. Three probabilistic models, including heteroscedastic Gaussian neural network, mixture density network, and artificial neural network with Monte Carlo dropout, were evaluated over 50 repeated random train-test splits. The physics-guided mixture density network achieved the best overall performance, exhibiting high prediction accuracy, reliable interval estimation, and physically reasonable long-term extrapolation. Following, this model was refined through feature ablation and validated using an independent external dataset. Finally, the predictive distribution was coupled with Monte Carlo simulation to propagate input and model uncertainties based on the carbonation-induced limit state function. Overall, the proposed framework provides a practical tool for performance-based durability design of concrete structures exposed to CO2-rich environments by translating probabilistic carbonation prediction into quantitative failure probability assessment, reliability index evaluation, and minimum cover depth determination.
Keywords:
Physics-guided neural network
Carbonation
Probabilistic modeling
Reliability
Durability design
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