A Modified Curve Model for Predicting the Chloride Diffusion Coefficient of Concrete

Chloride ion erosion is the dominant factor causing durability degradation of reinforced concrete structures. Accurate prediction of the time-varying chloride diffusion coefficient is essential for long-term structural durability evaluation. Traditional empirical models, including the power function model (PFM) and the inverse-square-root model (ISRM), often exhibit insufficient fitting accuracy and poor extrapolation stability, while back-propagation neural networks (BPNNs) tend to produce severe overfitting and oscillating prediction curves despite high in-sample fitting performance. To overcome these limitations, this study develops a new hypothetical modified curve model (MCM) by combining power and hyperbolic functions to comprehensively describe the time-dependent attenuation of chloride diffusion in concrete. Four groups of experimental datasets with different material compositions and curing ages were adopted for model validation. The results show that the proposed MCM outperforms other comparative models in overall performance for the conditions examined. For Case 1, the MCM reduces the mean fitting error by 24.67% and 35.16% compared with the PFM and ISRM, and achieves a low extrapolation error of 12.9% at 150 d. For Case 2, the MCM maintains a stable prediction error of 16.5%, which is significantly lower than the 48.2% and 66.4% of the PFM and ISRM. For Case 3 and Case 4, the MCM achieves high coefficients of determination of 0.9943 and 0.9815, with ultra-low extrapolation errors of only 7.2% and 0.2%, respectively. In contrast, although the BPNN achieves high fitting accuracy in some cases, its fitted curves fluctuate irregularly, and its extrapolation prediction accuracy is much lower than that of the MCM. Within the valid time range of the model, the MCM exhibits stable generalizability and superior comprehensive performance, which provides a reliable method for predicting the long-term chloride diffusion behavior of concrete.