Research of extreme – explosives

Postgraduate Study

Author: Barbara Štimac, mag.geol.

One of the main aims of the research, as a part of HRZZ project NEIDEMO, is to develop an improved model of nonideal detonation, based on Wood-Kirkwood’s theory and thermochemical code EXPLO5.

Detonation of explosive charge results in a detonation wave through explosive propagating with velocity up to 10 km/s, pressure up to 40 GPa and temperatures up to 6000 K, all in a timeframe of couple of nanoseconds. Due to this extremely short timeframe and high pressure, energy is transmitted from the detonation products to the unreacted part of explosive by motion. There are two generally accepted theories of detonation based on conservation laws and hydrodynamic theory: Chapman-Jouguet (CJ) theory that assumes instantaneous chemical reaction (meaning there is no chemical reaction zone) and Zeldovich-von Neumann-Doering (ZND) theory that takes into account the existence of a chemical reaction zone of defined width and duration (Figure 1). Explosives that behave in according to CJ theory are called “ideal explosives”.

However, detonation parameters of commercial explosives (so-called “nonideal explosives”) cannot be accurately predicted using CJ theory. Theoretically calculated detonation velocity and detonation pressure of commercial explosives are considerably higher than those experimentally obtained, and detonation velocity shows strong dependence on initial radius of explosive charge and confinement (Esen, 2004; Souers et al, 2004; Minchinton, 2015; Sućeska i ostali, 2019).


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Figure 1 Simplified illustration of CJ (upper) and ZND (lower) detonation theory

Main cause of nonideality of commercial explosives is relatively longer duration time of chemical reactions in the chemical reaction zone (order of microseconds) compared to duration time of chemical reaction of ideal explosives (order of nanoseconds). As a result of slower chemical reactions, nonideal detonation results in curved detonation front, non-linear dependence of detonation velocity to initial density of explosive, dependence of detonation parameters to initial radius of explosive charge and confinement, incomplete chemical reactions at CJ point, larger critical radius, that is the radius under which there is no possible stabile detonation (Figure 2).

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Figure 2 Simplified illustration of nonideal detonation

All this makes numerical modeling of nonideal explosives significantly harder, but not impossible. There are a couple of proposed theories for describing nonideal behaviour of commercial explosives, but most widely used is Wood-Kirkwood slightly divergent flow theory. This theory, supplemented with corresponding equations of state, reaction rate equations and model of radial expansion, forms a basis of most existing models of nonideal detonation (Figure 3).

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Figure 3. Sub-models in nonideal detonation model

Existing models of nonideal detonation have some key disadvantages, such as a certain degree of empirical or engineering approach, simple and not complete equations of state of detonation products, too simple or too complicated reaction rate models, lack of information on the structure of chemical reaction zone, etc. There is no doubt there is a need for improvement of nonideal detonation models.

Main focus of my research is to develop that improved model, based on Wood-Kirkwood’s theory and thermochemical code EXPLO5.  Improvement will be and are focused on improvements in reaction rate law and radial expansion model. This type of integrated model will be less dependent on empirical constant (thus more predictable) and will provide more information on chemical reaction zone than any so far existing model.


Esen, S. (2008) „A new non-ideal detonation code for evaluating the performance of commercial explosives“, Rock Mechanics and Rock Engineering, 41, str. 467–497.

Minchinton, A. (2015) „On the Influence of Fundamental Detonics on Blasting Practice“, u 11th Internation Symposium on Rock Fragmentation by Blasting, str. 41–54.

Souers, P. C. i ostali (2004) „The Effects of Containment on Detonation Velocity“, Propellants, Explosives, Pyrotechnics, 29(1), str. 19–26. doi: 10.1002/prep.200400028.

Sućeska, M. i ostali (2019) „Equation of State of Detonation Products Based on Exponential-6 Potential Model and Analytical Representation of the Excess Helmholtz Free Energy“, Propellants, Explosives, Pyrotechnics, 44(5). doi: 10.1002/prep.201800339.


Barbara Štimac, mag. ing. geol. is an assistant on a project at Department of Mining Engineering and Geotechnics, Faculty of Mining, Geology and Petroleum Engineering, University of Zagreb. She is a part of H2020 project (EXERTER), bilateral project with Leoben and HRZZ project (NEIDEMO). She is currently in final phase of completing his doctoral thesis Numerical modelling of non-ideal detonation of ANFO explosive implementing Wood-Kirkwood theory.  

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