Physical and mathematical analysis of the multistage blast rock fragmentation process

D.V. Moldovan, K.N. Yastrebova, V.I. Chernobai
Empress Catherine II Saint Petersburg Mining University, Saint Petersburg, Russian Federation
Russian Mining Industry №4S/ 2026 p. 217-222

Abstract: The article examines dynamics of the transition from high intensity shock action caused by detonation of the explosive to the quasi-static expansion of the cavity formed by the explosion products. The main focus is placed on the formation mechanisms of the damage zone, i.e. creation of the blast cavity, fragmentation, and crack initiation. The study looks closely at the key role of acoustic matching at the explosive–rock interface through the wave impedance concept, as well as development of the compression wave within the rock mass. The presented physical and mathematical tools create a scientific foundation for optimizing blasting technologies. Targeted selection of the explosive type, charge design, and blasting system based on analyzing wave and strength processes makes it possible to increase the energy efficiency of the blast, control the particle size distribution in the muck pile, and minimize negative impacts, e.g. seismic effects, over-crushing).

Keywords: blast fragmentation of rocks, detonation, wave impedance, shock wave, compression wave, blast cavity, fragmentation zone, crack initiation zone, explosion product pressure, quasi-static loading, dynamic loading, JWL state equation

For citation: Moldovan D.V., Yastrebova K.N., Chernobai V.I. Physical and mathematical analysis of the multistage blast rock fragmentation process. Russian Mining Industry. 2026;(4S):217–222. (In Russ.) https://doi.org/10.30686/1609-9192-2026-4S-217-222

Article info

Received: 20.06.2026

Revised: 29.07.2026

Accepted: 18.08.2026

Information about the authors

Dmitriy V. Moldovan – Cand. Sci. (Eng.), Associate Professor, Department of Blasting Engineering, Empress Catherine II Saint Petersburg Mining University, Saint Petersburg, Russian Federation; https://orcid.org/0000-0003-2227-6625; e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Karina N. Yastrebova – Cand. Sci. (Eng.), Researcher, Laboratory of Physical-Mechanical Properties and Rock Destruction, Scientific Center of Geomechanics and Mining Production Problems, Empress Catherine II Saint Petersburg Mining University, Saint Petersburg, Russian Federation

Vladimir I. Chernobai – Cand. Sci. (Eng.), Associate Professor, Department of Blasting Engineering, Empress Catherine II Saint Petersburg Mining University, Saint Petersburg, Russian Federation; https://orcid.org/0000-0002-6858-8854

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