An Improved Fick Model for Predicting Carbonation Depth of Concrete

Concrete carbonation can weaken its strength, cause the corrosion of steel reinforcement, and shorten its service life. Predicting the concrete carbonation depth is a critical aspect of assessing concrete durability. Currently, mathematical models for the concrete carbonation depth, exemplified by the Fick model, suffer from a low fitting accuracy and limited applicability due to the complexity and variability of concrete materials and service environments. In light of this, this work proposes an improved Fick model that incorporates a correction term to effectively enhance the curve fitting accuracy. The correction term in the improved model provides a reasonable adjustment for deviations in the development pattern of the concrete carbonation depth from the Fick model under different conditions, thereby broadening the applicability of the new model compared to the Fick model. Several sets of experimental data on the concrete carbonation depth are used to validate the universality and superiority of the new model. The results of the case studies indicate that the average prediction error and standard deviation of the new model are significantly smaller than those of the Fick model. For the first two examples, in most situations, the average prediction error and standard deviation of the new model are less than 50% of those of the Fick model, with the lowest average prediction error being only 4% and the lowest standard deviation being only 2% of the Fick model's respective values. For the third example, the new model demonstrates superior predictive capability for the later-stage concrete carbonation depth compared to the Fick model and the ANN model. Specifically, for the carbonation depth of the concrete on the 56th day, the relative error between the predicted value of the new model and the measured value is only 2%, which is much smaller than the 27% of the Fick model and the 12% of the ANN model. These results demonstrate the unique advantage of the proposed model in predicting the carbonation depth, especially when only a limited amount of experimental data are available.