Quantifying and addressing uncertainties in empirical vibration attenuation relationship for underground blast by re-sampling

Abstract

For efficient and timely execution of deep excavations, tunnelling or mining activities in rock, controlled blasting often becomes essential. For design of the controlled blasting operation, scaled distance regression analysis of trial blast data, namely, distance, charge weight, and peak particle velocity (PPV), is the regular industrial practice. Due to limited number of input data from trial blasts, and further due to variability of underlying media, multiple uncertainties creep into expressions thus developed. To account for these uncertainties in design of safe controlled blasting, therefore, 95 percent confidence expression obtained from trail blast data is generally preferred in industry. However, this approach lacks statistical quantification or treatment of the parameter uncertainty and there is no methodology suggested in literature, codes or standards to address this aspect. The present article proposes to estimate the parameter uncertainties in the empirical vibration attenuation relationship for underground blast using re-sampling approach. With blast data from literature, multiple samples are randomly selected and empirical parameters are evaluated for each set by least square principle. It is found that both empirical parameters in power form of expression (popular in industry) follow Normal distribution. Using the 95 percentile value for each parameter, the safe charges are calculated and thereafter are compared to the traditional industrial practice of employment of 95 percent confidence expression from trail blast data. Re-sampling approach yielded conservative charge weight for lower limiting values (PPV ≤ 15 mm/s) and efficient charge weights for higher limiting values (PPV ≥ 50 mm/s) of PPV.