Data-driven formulation of steel fiber pull-out force in cementitious composites using genetic programming

This study aims to develop a data-driven approach for predicting and formulating the pull-out force of steel fibers in cementitious composites using a genetic programming variant, gene expression programming (GEP). A comprehensive dataset of 437 experimental data was collected from previous studies, including key variables such as embedment length, fiber inclination angle, tensile strength of fibers, aspect ratio, loading rate, water-to-cement ratio, compressive strength of matrix, and fiber geometry. The GEP model developed in this study demonstrated notable accuracy in predicting pull-out force, with an R² of 0.93. Model performance was evaluated using multiple statistical criteria, confirming its satisfactory predictive ability. Furthermore, a k-fold cross-validation was performed, and the results confirmed the model's robustness and capability for generalizing to new data. Sensitivity analysis using SHAP interpretation revealed that the fibers' tensile strength and the embedment length are the most influential factors affecting the pull-out force. The GEP method was adopted for its ability to generate accurate and interpretable mathematical formulas. Accordingly, a mathematical formula for the pull-out force is proposed, providing an efficient and interpretable tool for future studies. Overall, the GEP approach can significantly reduce reliance on costly and time-consuming experimental procedures while ensuring reliable performance predictions and practical formulations.