Estimation of Critical Distances for Electronic Detonators Using a Physics-Based Model

Prior estimation of the distance at which detonation pressure reaches a critical threshold is relevant for defining borehole separations and reducing the risk of damage to electronic detonators in underground mining. Empirical attenuation relationships require site-specific calibration through instrumentation, limiting their application at preliminary design stages. A physics-based formulation is proposed that integrates detonation pressure, explosive–rock impedance matching, and equivalent rock mass stiffness to estimate transmitted pressure and critical distance. Attenuation is represented by an exponent defined from the relative dynamic demand, expressed as the ratio between the initially transmitted pressure and the equivalent deformation modulus. The model was evaluated using experimental data from El Teniente, Chuquicamata Underground, and Pucobre. Across five experimental conditions, the estimates yielded a mean absolute relative error of 8.43% and a root mean square error of 0.101 m. The results show that critical distance depends on the interaction among explosive properties, impedance contrast, and rock mass stiffness, rather than exclusively on rock mass rating. The formulation provides a tool for preliminary estimation of safety separations, although broader experimental validation is required to establish its general applicability.