Machine Learning Modeling and Prediction of Mechanical Strengths of Steel Fiber-Reinforced Concrete

Conventional concrete suffers from its inherently low tensile strength. To address this drawback, researchers propose steel fiber reinforced concrete (SFRC) as a novel material that significantly improves tensile properties and exhibits outstanding performance in cracking resistance, toughness, and durability. However, the incorporation of steel fibers makes the mechanical behavior of SFRC more complex. To ensure its safe application in structural engineering, an accurate prediction of its mechanical properties is essential.

Artificial intelligence technologies are widely applied to accurately evaluate the mechanical properties of concrete. However, the existing machine learning models for SFRC are typically trained on a limited number of samples (i.e., fewer than 300), which restricts their generalization capability. Moreover, these models often lack interpretability, undermining their credibility and limiting their practical application in engineering projects.

This study was to establish a database for the compressive and splitting tensile strengths of SFRC, develop corresponding machine learning prediction models, and evaluate their predictive performance. Furthermore, the interpretability of the models was analyzed. The findings of this study could offer some insights into the development of high-precision machine learning models for SFRC and their interpretability analysis, thereby promoting their application in engineering practices.

In this study, a total of 636 experimental data points on SFRC were collected from 24 independent studies to establish a comprehensive database, including 419 data points for compressive strength and 217 for splitting tensile strength. Each data entry contains a mix-related information such as the water-to-binder ratio, sand ratio, aggregate-to-binder ratio, maximum size of coarse aggregate, fiber shape factor, fiber aspect ratio, fiber volume fraction, and the corresponding compressive or splitting tensile strength.

Based on this database, five machine learning models (i.e., Random Forest (RF), Gradient Boosting Regression Tree (GBRT), Extreme Gradient Boosting (XGB), Light Gradient Boosting Machine (LGBM) and Bayesian Neural Network (BNN)) were proposed. The predictive performance of these models was evaluated using the coefficient of determination (R²), mean absolute percentage error (MAPE), and root mean square error (RMSE), in order to identify the most effective prediction model.

For the selected model, the SHAP (SHapley Additive exPlanations) method was employed to analyze the trends and contribution of each input parameter on the compressive and splitting tensile strengths of SFRC. In addition, the Partial Dependence Plot (PDP) and Individual Conditional Expectation (ICE) methods were also used to quantitatively investigate the variation patterns of predicted values with respect to individual input parameters.

All the models proposed demonstrate a great predictive performance. The R² for the test set ranges from 0.84 to 0.90, while for the training set it ranges from 0.80 to 0.90. A small difference between them (i.e., both being > 0.75) indicates a good predictive accuracy and a generalization ability.For the overall performance across R², MAPE and RMSE metrics, the LGBM model shows the optimum prediction performance.

The SHAP analysis reveals that the compressive and splitting tensile strengths of SFRC decrease with increasing water-to-binder ratio and aggregate-to-binder ratio, while the strengths both increase at a higher sand ratio and a greater fiber reinforcement factor. In addition, as the maximum size of coarse aggregate increases, the compressive strength decreases, whereas the splitting tensile strength increaseds. These results are consistent with the practical observations. Based on the mean absolute SHAP values, the input parameters influencing the compressive strength in a descending order are water-to-cement ratio, sand ratio, fiber reinforcement factor, aggregate-to-cement ratio, and maximum coarse aggregate size. For splitting tensile strength, the order is fiber reinforcement factor, sand ratio, water-to-binder ratio, aggregate-to-binder ratio, and maximum coarse aggregate size.

The influence and parameter importance rankings obtained through the PDP and ICE analysis are in a reasonable agreement with those derived from SHAP, further validating the interpretability and reliability of the model.

A large-scale database containing 636 data entries was established for the compressive and splitting tensile strengths of SFRC. Based on this database, five machine learning prediction models (i.e., RF, GBRT, XGB, LGBM and BNN) were proposed. All the models exhibited good predictive performance and generalization ability, significantly outperforming the existing prediction methods. Among them, the LGBM model showed the optimum overall performance. The SHAP, PDP and ICE techniques were employed to analyze the influence and importance of each input parameter on the compressive and splitting tensile strengths. Based on the variable contribution analysis, the main factors affecting the compressive strength were the water-to-cement ratio, sand ratio, fiber reinforcement factor, aggregate-to-cement ratio, and maximum coarse aggregate size. In contrast, the key determinants of splitting tensile strength were the fiber reinforcement coefficient, sand ratio and water-to-cement ratio.