A new geometrical-statistical algorithm for predicting two-dimensional distribution of rock fragments caused by blasting

• 4 techniques of geometric-statistical models in prediction the rock fragments distribution are modeled.
• The geometric-statistical models compared with rock fragmentation in Midouk copper mine.
• The proposed model generates 2D models for given d50 and uniformity index, accurately.
• The proposed model could be used in modeling of small-scaled joints’ roughness.
• The proposed model could be used in modeling 3D of rock fragmentation distribution.

Four techniques, namely Voronoi, orthogonal, randomized fracture and an innovative geometric-statistical algorithm are modeled and the results are compared with the size distribution from image analysis of the field data from rock fragmentation by blasting. The results show that the proposed algorithm has higher ability in accurate prediction of real size distribution compared to image analysis. The coefficient of correlation and mean square error of prediction obtained through the algorithm were 0.9991 and 1.726, respectively. Since all these algorithms use statistical logics, 25 outputs of the models were recorded and compared. These results show that the proposed model has the greatest variance and estimates the mean size of distribution data more accurately. Also the uniformity index of proposed algorithm shows the average variance while it keeps the non-uniformity as comes from the real data. Other models show more uniform predictions. It could be concluded that the proposed model has the ability to be used in 3D modeling of rock fragmentation by blasting.