Physics-guided probabilistic deep learning for modeling the cracking process of corroded reinforced concrete

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The process of corrosion cracking in reinforced concrete is important for understanding the durability evolution behavior of reinforced concrete. However, most of the proposed models in the literature are based on differential equations, which are computationally expensive when solved using traditional numerical methods, and they do not provide uncertainty quantification of the predicted results. In this study, a physics-guided probabilistic deep learning framework integrating Bayesian inference and physics-informed neural network (PINN) is proposed for modeling corrosion-induced cracking in reinforced concrete. Unlike existing PINN-based approaches that yield only deterministic predictions, the proposed framework embeds the governing physical equations directly into the Bayesian neural network training process, simultaneously enforcing physical consistency and quantifying prediction uncertainty. The Mean Absolute Percentage Error ( MAPE ) for the corrosion expansion force and radial displacement of the steel-bar concrete contact surface were 0.58% and 4.6%, respectively, demonstrating high prediction accuracy. The quantified uncertainty bounds provide engineers with reliable confidence intervals for the predicted corrosion expansion force and radial displacement, supporting structural inspection decision-making and risk-based maintenance planning. Finally, the effects of various parameters on modeling performance and stability were systematically investigated, offering practical guidance for model configuration in similar physics-informed probabilistic learning tasks.