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<p>Accurate estimation of the shear capacity of steel fiber reinforced concrete (SFRC) beams without stirrups remains challenging because the response is governed by strongly coupled geometric, material, and reinforcement parameters, while conventional empirical formulations often have limited generalizability across different test conditions. To address this issue, this study proposes a hybrid framework integrating finite element modeling (FEM), machine learning (ML), and gene expression programming (GEP) for shear capacity prediction of SFRC beams without transverse reinforcement. An experimental database was compiled from published studies and used, together with FEM-based information, to train and evaluate several ML models, including GEP, AdaBoost, gradient boosting, stochastic gradient descent, Gaussian process regression (GPR), and support vector machines. Among the examined models, GPR achieved the best overall predictive performance, showing the highest coefficient of determination and the lowest error metrics. SHAP and partial dependence analyses further indicated that effective depth and beam width were the most influential positive predictors, whereas increasing shear span-to-effective depth ratio reduced the predicted shear capacity; nonlinear effects of reinforcement ratio and fiber factor were also observed. In addition, FEM and GEP predictions showed close agreement within the investigated range, with differences of less than 2% for the examined cases. These results demonstrate that the proposed framework can provide accurate and interpretable shear capacity prediction for SFRC beams without stirrups and may offer practical support for structural assessment and design.</p>

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Physics guided explainable machine learning for shear capacity prediction of steel fiber reinforced concrete beams without stirrups

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月28日

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  • Muhammad Zia Ul Haq,
  • Yue Jia

摘要

Accurate estimation of the shear capacity of steel fiber reinforced concrete (SFRC) beams without stirrups remains challenging because the response is governed by strongly coupled geometric, material, and reinforcement parameters, while conventional empirical formulations often have limited generalizability across different test conditions. To address this issue, this study proposes a hybrid framework integrating finite element modeling (FEM), machine learning (ML), and gene expression programming (GEP) for shear capacity prediction of SFRC beams without transverse reinforcement. An experimental database was compiled from published studies and used, together with FEM-based information, to train and evaluate several ML models, including GEP, AdaBoost, gradient boosting, stochastic gradient descent, Gaussian process regression (GPR), and support vector machines. Among the examined models, GPR achieved the best overall predictive performance, showing the highest coefficient of determination and the lowest error metrics. SHAP and partial dependence analyses further indicated that effective depth and beam width were the most influential positive predictors, whereas increasing shear span-to-effective depth ratio reduced the predicted shear capacity; nonlinear effects of reinforcement ratio and fiber factor were also observed. In addition, FEM and GEP predictions showed close agreement within the investigated range, with differences of less than 2% for the examined cases. These results demonstrate that the proposed framework can provide accurate and interpretable shear capacity prediction for SFRC beams without stirrups and may offer practical support for structural assessment and design.