Mechanics-Informed Symbolic Regression for Shear Strength Prediction of Reinforced Concrete Deep Beams

Introduction: Accurate prediction of shear strength in reinforced concrete deep beams (RCDBs) remains challenging due to nonlinear interactions between geometry, reinforcement detailing, and concrete strength. Provisions in design standards such as Eurocode 2 and ACI 318-19 have been found to be overly conservative, with the mean predicted-to-actual strength ratios of 3.05 and 2.83, respectively, recorded on the 810-specimen database used herein.

Methods: This study proposes a mechanics-informed symbolic regression framework using only dimensionless variables – including the shear span-to-depth ratio, a geometric strut-width ratio, and effective reinforcement indices normalising steel contributions by concrete strength. The experimental database was partitioned via stratified splitting into training (70%, n=567), validation (10%, n=81), and testing (20%, n=162) subsets. Six dimensionless parameters were employed in PySR. To prevent overfitting, equation selection from the Pareto front was based on hold-out validation loss combining mean absolute percentage error (MAPE) with a soft negativity penalty, followed by a 5-fold stability assessment. The discovered equation was benchmarked against Chetchotisak’s MIST and Megahed’s SR-STM models.

Results: The discovered equation achieved R²=0.952, MAPE=14.45%, and a mean prediction ratio μ=0.997 on the unseen test set, indicating virtually unbiased predictions. The model reduced RMSE by 12.6% compared with the best benchmark (MIST: 149.2 vs. 170.7 kN) and achieved a 90th-percentile absolute percentage error of 29.8% versus 34.8% for MIST. Compared with Megahed's SR-STM, which attained R²=0.608 and MAPE=42.0%, the proposed model reduced prediction error by a factor of 2.9. Monotonicity assessment yielded zero violations across all feature perturbations (0/3402), confirming full consistency with expected structural behaviour. Subgroup analysis demonstrated robust performance across shear span-to-depth ratios (R²=0.871–0.973).

Conclusion: The proposed equation provides an interpretable, compact alternative for predicting RCDB shear strength, combining high accuracy (R²=0.952), negligible bias (μ=0.997), and complete compliance with structural mechanics. Future work should incorporate reliability analysis and propose partial safety factors for code adoption.