Accurate prediction of concrete carbonation depth is essential for durability assessment and service-life prediction of reinforced concrete structures, as well as for evaluating the CO₂ uptake capacity of cement-based materials. Concrete carbonation is affected by material composition, mix proportions, curing conditions, and the exposure environment, and these factors exhibit complex nonlinear coupling effects. Traditional empirical models are generally based on simplified assumptions and limited variables, making it difficult to fully describe the carbonation process. Machine learning (ML) models can capture nonlinear relationships from large datasets and achieve high prediction accuracy, but they usually lack explicit analytical expressions. To balance prediction accuracy, model simplicity, and interpretability, this study proposes an interpretable ML-based framework for constructing an explicit prediction formula for concrete carbonation depth.

A natural carbonation database shared by Marani et al. was used in this study. After data cleaning and feature processing, a database containing 35 input features, 2077 carbonation-depth data points, and 709 concrete mixtures was obtained. Decision tree (DT), random forest (RF), XGBoost (XGB), and CatBoost (CB) models were established for carbonation depth prediction. Considering the skewed distribution of carbonation depth, log1p transformation was applied to the target variable. The data were divided by concrete mixture group to avoid data leakage. SHAP analysis was then used to rank feature importance and guide feature selection. Based on the optimal CB model, the relationships between input variables and their SHAP contributions were fitted, and the additive SHAP contribution terms were further transformed into a multiplicative explicit prediction formula.

The carbonation depth data showed an obvious skewed distribution, and log1p transformation improved model training stability and test-set prediction performance. By comparing different ML algorithms and feature sets, the CB model based on log1p transformation and the FS2 feature set showed the best overall performance. The root mean square error (RMSE) values of the training and test sets were 0.55 mm and 1.14 mm, respectively, and the corresponding coefficient of determination (R²) values were 0.98 and 0.93. These results indicated that the model could accurately predict natural carbonation depth and effectively capture the nonlinear relationship between input variables and carbonation depth. In the final FS2-CB model, SHAP analysis showed that W/CaO, carbonation time, and carbonation environment were the three most important variables affecting the prediction of carbonation depth. Among them, W/CaO showed the highest feature importance, indicating that it was a key combined variable influencing model prediction. Based on the SHAP dependence relationships, variable contribution functions were fitted, thereby enabling transformation from a black-box model to an explicit prediction formula (PF).

The PF model achieved an RMSE of 2.28 mm on the test set, which was approximately 47.2% lower than that of F4, the best-performing formula model on the same test set. This indicated that the PF model had higher prediction accuracy than traditional formula models on the original dataset. On the external dataset, the PF model achieved an RMSE of 4.48 mm, which was 11.6% lower than that of the ML model (5.07 mm), and also lower than those of formula models F1-F3, which ranged from 5.91 mm to 8.52 mm. These results showed that although the PF model was less accurate than the optimal ML model on the original full dataset, it combined relatively high prediction accuracy, an explicit mathematical expression, and better cross-source generalization ability, indicating its potential for engineering application.

This study proposes an interpretable machine learning-based method for concrete carbonation depth prediction and explicit formula extraction. Through literature database processing, feature selection, machine learning modeling, and SHAP contribution function fitting, a high-accuracy black-box model is transformed into an interpretable formula model. The CB model with log1p transformation and the FS2 feature set achieves the best prediction performance. In the final FS2-CB model, SHAP analysis shows that W/CaO, carbonation time, and carbonation environment are the dominant variables controlling carbonation depth, indicating that concrete carbonation is mainly governed by pore transport conditions, carbonation buffering capacity, exposure time, and environmental effects. The constructed PF model shows higher accuracy than traditional formula models and better cross-source generalization performance than the ML model on the external dataset. Overall, the proposed method improves model simplicity and interpretability while maintaining relatively high prediction accuracy, providing a useful reference for explicit model construction in concrete carbonation depth prediction and other performance prediction tasks of cement-based materials.