A Method for Reconstruction of Size Distributions from 3D Drone Image Analysis: A Case Study

This paper describes a novel procedure to assess fragmentation from automatic analysis of 3D photogrammetric models with a commercial software. The muckpiles from 12 blasts were photographed with a conventional drone to build 3D photogrammetric models; the flights were made with a relatively constant ground sampling distance (GSD) of 6.2 sd 0.92 mm (mean and standard deviation, respectively). A comparison with already published mass-based size distributions from 11 of these blasts, shows a good performance of automatic 3D-fragmentation measurements in the coarse range (P >= 60%), while deviations between mass-based and 3D model fragmentation analysis grow towards the central-fines range. As a solution, the Swebrec function is fitted to the reliable part of the size distributions, well above the GSD, and then is extended towards the fines, down to a percentage passing of 5-10%. The suitable fitting range is obtained iteratively from the mass-based fragmentation data; the lower fragment size considered is independent of the model's resolution (i.e. GSD) with mean of 357 mm (equivalent to a passing in the range 66-86%, and well above the GSD of our models). The resulting distributions match properly mass-based size distributions with relative errors in percentile sizes of 15.5 sd 3.4%, and they can be represented with the simplest form of the fragmentation-energy-fan. As a guideline for reconstruction of size distributions and fines assessment when mass-based data is not available, the lower-fitting limit of 357 mm yields reasonable results (mean errors in pass in the range 5-36%) for the present case. The errors are limited enough to keep a sound description of the variation of fragmentation with change in blast design. 3D photogrammetric models are obtained from UAV flights over the muckpiles to assess fragmentation from blasting with a commercial software.The coarse fraction is reasonably well estimated through automatic analysis of 3D muckpile models.To correct deviations in the central-fines range, the Swebrec function is fitted to the coarse range (passings generally above 70%) and extrapolated to passing of 5-10%.The smaller fragment size considered for the fit is estimated for each blast from sieving data and it is independent of the model's resolution; the mean of these sizes (357 mm) procures a proper fines assessment for the present case.The reconstructed image-based size distributions match properly mass-based size distributions and are sensitive to changes in the powder factor in line with fragmentation-energy-fan principles.