Probabilistic Prediction of Oversized Rock Fragments in Bench Blasting Using Gaussian Process Regression: A Comparative Study with Empirical and Multivariate Regression Analysis Models

Oversized rock fragments (boulders) produced during bench blasting adversely affect the efficiency of mining downstream processes such as loading, hauling, and crushing, thus leading to regularly requiring costly secondary breakage and the use of mechanized rock breakers. This study presents a probabilistic framework for forecasting boulder size in surface mining operations by employing Gaussian Process Regression (GPR), benchmarked against the Kuznetsov–Cunningham–Ouchterlony (KCO) empirical fragmentation model and a Multivariate Regression Analysis (MVRA) equation. The research study has analyzed blasting datasets, comprising Geological Strength Index (GSI), number of holes (NH), hole depth (HD), maximum charge per delay (MCPD), total explosive mass (TEM), and boulder size determined by Split-Desktop image analysis. Eight Gaussian Process Regression kernels—squared exponential, rational quadratic, matern with ν = 3/2, and matern with ν = 5/2, both with and without automatic relevance determination (ARD)—were assessed. The GPR model with the ARD matern 3/2 kernel attained superior validation performance of R2 = 0.9016 and RMSE = 4.2482, outperforming the KCO and MVRA models, which displayed significant prediction errors for boulder size. In addition, the sensitivity analysis results demonstrated that GSI and HD were the most influential parameters on boulder size, followed by NH, MCPD, and TEM, accordingly. The findings indicate that GPR, especially when employing ARD matern kernels, precisely estimates the boulder size, and thus can serve as a viable method for optimizing blast design and facilitate efficient boulder management in surface mining operations.