Development of new comprehensive relations to assess rock fragmentation by blasting for different open pit mines using GEP algorithm and MLR procedure

The fragment size of blasted rocks considerably affects the mining costs and production efficiency. The larger amount of blasthole diameter (ϕh) indicates the larger blasting pattern parameters, such as spacing (S), burden (B), stemming (St), charge length (Le), bench height (K), and the larger the fragment size.  In this study, the influence of blasthole diameter, blastability index (BI), and powder factor (q) on the fragment size were investigated. First, the relation between each of X20, X50, and X80 with BI, ϕh, and q as the main critical parameters were analyzed by Table curve v.5.0 software to find better input variables with linear and nonlinear forms. Then, the results were analyzed by multivariable linear regression (MLR) procedure using SPSS v.25 software and gene expression programming (GEP) algorithm for prepared datasets of four open-pit mines in Iran. Relations between each of X20, X50, and X80 with the combination of adjusted BI, ϕh, and q were obtained by MLR procedure with good correlations of determination (R2) and less root mean square error (RMSE) values of (0.811, 1.4 cm), (0.874, 2.5 cm) and (0.832, 5.4 cm) respectively. Moreover, new models were developed to predict X20, X50, and X80 by the GEP algorithm with better correlations of R2 and RMSE values (0.860, 1.3 cm), (0.913, 2.49 cm), and (0.885, 5.6 cm) respectively and good agreement with actual field results. The developed GEP models can be used as new relations to estimate the fragment sizes of blasted rocks.