Physics-Constrained Neural Network Deep Learning Model for Predicting Residual Flexural Strengths of Steel Fibre Reinforced Concrete: A Multi-Study Generalisation Framework

Accurate prediction of residual flexural strengths is essential for the structural design and performance assessment of steel fibre reinforced concrete (SFRC). While machine learning models have recently demonstrated strong predictive capability, most of the existing approaches rely on heuristic feature selection, unconstrained architectures, and random validation splits that may overestimate generalisation capacity. This study proposes a Hard-Constrained Physics-Informed Neural Network (PCNN) for predicting the residual flexural strengths fR1–fR4 of steel fibre reinforced concrete (SFRC). Non-negativity, monotonic dependence on the reinforcement index, and bounded sequential evolution across crack mouth opening displacement (CMOD) stages are enforced architecturally through custom layers, guaranteeing mechanical admissibility by construction. The model was trained and validated on 235 original beam specimens from 18 experimental groups (expanded to 860 via controlled integer replication) using GroupKFold by Study cross-validation to eliminate data leakage. PCNN achieves fR1 MAE = 1.256 MPa and R2 = 0.606 across held-out experimental campaigns, competitive with Ridge Regression (MAE = 1.144, R2 = 0.688). Monotonicity audits show a 0% violation rate for PCNN versus 7.3% and 10.2% for Random Forest and GBDT, respectively. PCNN is the only model in the comparison that guarantees physical admissibility for all possible input configurations. The results demonstrate that embedding mechanical principles directly into neural network architecture enhances robustness and interpretability without compromising accuracy. The proposed Physics-Informed Neural Networks framework provides a transferable methodology for physics-guided machine learning in structural materials modelling.