Explainable machine learning for shear capacity prediction of reinforced concrete deep beams

Abstract

The shear capacity prediction of reinforced concrete (RC) deep beams remains a challenging issue in design of concrete structures. Although the code-based strut-and-tie method is widely accepted, it is often time-consuming for routine design applications, while existing empirical equations are unable to fully capture the highly nonlinear interactions among material properties, geometric characteristics, and reinforcement variables. To address this limitation, this study proposes an explainable machine learning framework for predicting the shear capacity of RC deep beams. A comprehensive database of 419 experimentally tested specimens was compiled from the literature, and eight supervised machine learning models were developed with hyperparameters optimized using the Optuna framework. Comparative analysis showed that the optimized Gradient Boosting Decision Tree (GBDT) model achieved the best predictive performance, with a test coefficient of determination (R2) of 0.93. A synthetic Gaussian input-perturbation study was conducted to assess the numerical sensitivity of the models under progressively disturbed inputs. To interpret the black-box behavior of the model, Shapley Additive Explanations (SHAP) and three-dimensional Partial Dependence Plots (3D-PDPs) were employed. The resulting feature-response patterns were broadly consistent with established deep-beam behavior, particularly the positive effect of concrete compressive strength and the negative influence of the shear-span-to-depth ratio, along with important nonlinear interactions among key variables. Finally, a user-friendly graphical user interface integrating the optimized GBDT model was developed to provide rapid and interpretable shear-capacity estimation for practical engineering applications.