A Hybrid CNN–PINN–NSGA-II Framework for Physics-Consistent Surrogate Modeling of Reinforced Concrete Beams Incorporating Waste Fired Clay

This paper presents a physics-consistent hybrid surrogate framework for simulating the mechanical behavior of reinforced concrete beams that utilize waste fired clay (WFC) as a partial substitute for cement. The main contribution is the integration of empirically observed deformation behavior with physics-informed learning to produce an interpretable, mechanically valid surrogate model. Full-field surface deformation fields were measured using Digital Image Correlation (DIC) under monotonic loading and processed through a convolutional neural network (CNN) to extract deformation- and crack-sensitive features. These features were integrated with experimentally measured stress–strain data within a Physics-Informed Neural Network (PINN) in which equilibrium and conditional constitutive monotonicity constraints were enforced through the loss function. A Non-Dominated Sorting Genetic Algorithm II (NSGA-II) was utilized as a downstream parametric exploration tool to examine trade-offs among maximum load capacity, material cost, and embodied CO2 inside a constrained mixture-design space. Model interpretability was assessed by SHapley Additive exPlanations (SHAP), indicating that deformation-driven kinematic factors predominantly influence stress prediction, whereas WFC content and reinforcement parameters have a secondary, mixture-level impact. The resulting framework achieves enhanced predictive accuracy (R2 = 0.969) relative to its individual components and operates as an offline, physics-calibrated surrogate rather than a real-time digital twin, providing a reliable and interpretable basis for structural assessment and sustainability-oriented design evaluation of WFC-modified reinforced concrete beams.