Prediction of Rock Fragmentation by Blasting Using Symbolic Regression and Explainable Artificial Intelligence

This study applies SR within an XAI framework to develop interpretable, white-box models for predicting P50 in rock fragmentation by blasting. The dataset comprised 221 observational subsets from 63 blasts across 16 quarries and 23 lithological units in northwestern Türkiye. Repeated PySR searches yielded four equation families of varying complexity. The best-performing model, incorporating ρ, σc, D50, q, and VoD, achieved a high R2 and low error metrics on the independent test set. This model significantly outperformed the empirical formulations and closely matched the predictive performance of black-box machine learning tools, while retaining a fully explicit and verifiable mathematical structure. Equations derived from the FDM produced more consistent predictions across the broad range of operational and geological conditions in the database. In contrast, equations derived from the LWM subset—constrained by recommended parameter ranges—performed well within their calibration domain but showed greater sensitivity to extrapolation. The turning points in the model responses were consistent with rock mechanics and blasting principles; however, they are interpreted as testable hypotheses requiring independent validation rather than confirmed physical thresholds. Overall, the study demonstrates the ability of SR to transform complex field observations into transparent empirical relationships between blasting parameters, rock mass properties, and fragmentation outcomes. Nonetheless, these equations remain candidate relationships derived from the present dataset and require independent validation before practical implementation.