Proposing Novel Symbolic Regression-Based Equations for Predicting the Shear Capacity of Polypropylene-Fiber-Reinforced Concrete (PFRC) Beams Without Transverse Reinforcement

Predicting the shear strength of polypropylene and macro-synthetic fiber-reinforced concrete (PFRC) beams remains challenging because many available formulations were originally developed for conventional reinforced concrete or steel-fiber-reinforced concrete. This study develops practical and explicit symbolic equations for estimating the shear strength of PFRC beams without transverse reinforcement. A dedicated database comprising 98 shear-critical PFRC beam specimens was assembled using clearly defined inclusion and exclusion criteria. Seven predictors representing beam geometry, concrete strength, longitudinal reinforcement, and fiber properties were employed. Gene Expression Programming (GEP) and Multi-Expression Programming (MEP) were used to derive explicit mathematical equations, which were evaluated using a hold-out testing subset and compared under consistent data conditions with six benchmark machine learning algorithms and twenty existing shear strength formulations. Unlike previous studies that generally focused on individual prediction approaches or specific classes of fiber-reinforced concrete, the present study combines a PFRC-specific database, two explicit symbolic regression methods, comprehensive benchmarking, and SHAP-based model interpretation within a unified framework. The proposed MEP equation achieved the best testing performance, with a coefficient of determination (R2) of 0.976 and a root-mean-square error (RMSE) of 15.75 kN. The corresponding mean absolute percentage error (MAPE) and coefficient of variation (COV) were 10.55% and 0.143, respectively. The GEP equation also demonstrated satisfactory predictive performance, with an R2 of 0.965 and a MAPE of 18.16%. Among the benchmark machine learning algorithms, CatBoost achieved the best testing performance, with an R2 of 0.968, but was outperformed by the MEP equation. The MEP equation also improved the highest R2 among the twenty existing formulations from 0.883 to 0.976 and reduced the lowest MAPE among the existing formulations from 25.81% to 10.55%. Shapley additive explanations (SHAP) analysis indicated that beam width, shear span-to-effective depth ratio, and effective depth were the most influential variables governing the predictions of the MEP equation. Within the limits of the assembled database, the proposed MEP equation provides an accurate, transparent, and directly applicable approach for estimating the shear strength of PFRC beams without transverse reinforcement.