Multivariate Scaling Approach for Laboratory Scaled Rock Blasting

Rock blasting is an inherently difficult field to quantify independent & dependent variables and the specifics of how the energy interacts with the material for a number of reasons. Independent variables such as geology are innumerable and stochastic, thus, on a laboratory and full-scale basis these variables are assumed to be homogenous across the desired rock boundary. Dependent variables are difficult to quantify in the laboratory based on the specific aspect of the fracture mechanisms that caused the fracturing. The same variables are difficult to quantify in the field because of the shear amount of material being blasted. The energy interactions with the material are difficult to quantify due to the rate of the reaction and the lack of quantification of independent variables. The second main issue with laboratory scaled rock blasting is the nature of the small form-factor explosives required for use in a scaled setting. These explosives that are utilized, traditionally PETN detonating cord, have a greater ratio of potential energy converted to shock energy rather than gas energy when compared to traditional field explosives, such as emulsion or ANFO. Research over the past decades has indicated that gas pressure has the greatest contribution to rock blasting performance, such as fragmentation and material throw. The factor of varying ratios of energy production has not been discussed in any of the reviewed publications. Publications discuss dimensionless scaling, dynamic similitude, and length-based scaling, however, none of these scaling methods discuss the ratio of energy production. The main focus will be correlation of energy production ratio of shock versus gas to dependent variables. This paper analyzes previous publications within rock blasting and related field as they pertain to scaling procedures and will highlight the similarities and differences in the various publications and detail the observed omitted variables that possibly lead to skewed data.