Development of a flyrock prediction model for open-pit mining based on an analogy with the Navier-Stokes equations

Blasting is the most commonly used method for rock fragmentation in open-pit mining. Its objective is to achieve an adequate particle size for subsequent stages; however, not all the energy is utilized, and some energy is transformed into undesirable effects. Among these effects, flyrock is one of the most hazardous, as it endangers the safety of personnel, machinery, and infrastructure. Over the years, numerous flyrock prediction models have been developed based on different blasting and ground parameters. In the present study, a new predictive model is proposed for the maximum distance reached by a rock fragment based on the velocity obtained using an analogy with the Navier–Stokes equations. The development of the model considered three fundamental stages of fragment projection: (ⅰ) detonation of the explosive, which produces pressure on the blasthole perimeter owing to gas expansion, (ⅱ) propagation of the kinetic energy transmitted through the rock mass until it reaches the propelled rock fragment, and (ⅲ) trajectory of the flyrock. The resulting model depends on rock parameters (rock density), explosive parameters (density and energy of the explosive), design parameters (charge length, blasthole diameter, and burden), and a site-specific constant K, which can be determined using multiple regression analysis of the measured field data. A model consistency comparison was developed using Monte Carlo simulations, evaluating 100,000 realizations, demonstrating its potential for use. Similarly, a sensitivity analysis was performed, which verified that the burden was the parameter with the greatest influence within the model, whereas rock density had the least impact. Finally, as a future line of work, its application is proposed in ground conditions under different scenarios to strengthen its use in defining safety zones during blasting and to deepen the physical understanding and meaning of parameter K, as its current interpretation still presents some degree of uncertainty.