Methods for determining coupling and stemming coefficients of underground explosions

Coupling and stemming coefficients are essential for predicting ground shock magnitude and damage zones from underground explosions, yet their variation with burial depth and dependence on media and explosion types remain insufficiently understood. Experimental and theoretical methods for determining these coefficients in concrete, rock, and soil under both chemical and nuclear explosions were systematically reviewed. Based on collected data from published tests, definitions of different coupling coefficients (energy coupling, ground shock parameter coupling, equivalent yield, and stemming coefficients) were clarified, and conversion relationships among them were derived using energy conservation and wave attenuation principles. The critical burial depth for full coupling was analyzed separately for peak quantities (e.g., peak stress, particle velocity) and integral quantities (e.g., impulse, surface vibration). Experimental results show that peak quantities reach full coupling at a depth approximately equal to the contained explosion cavity radius, which is much shallower than the critical depth for contained explosions. In contrast, impulse and ground motion require depths close to the contained explosion threshold. The coupling energy is proportional to the volume of the damaged zone, and the evolution of coupling coefficients with scaled depth of burial follows a Boltzmann function, requiring only two parameters to define the entire curve. For chemical explosions, the fully coupled equivalent yield coefficient (relative to contained explosions) in concrete, limestone, and soils was quantified, with stemming coefficients ranging from 1.4−1.8 in rocks and 2.4−2.6 in soils. It is concluded that different ground shock parameters exhibit distinct coupling behaviors, challenging the assumption of a universal coupling coefficient. The proposed empirical formulas provide conservative estimates for engineering design, while the underlying mechanisms of free-surface unloading require further quantitative investigation.