## 1 Introduction
A large number of equations of state have been devised to describe the behavior of gaseous explosion products, and they can be divided into two main groups: (1) equations of state that include the chemical composition of gaseous explosion products (the Becker-Nedostup equation, the Abel equation, the Berthelot equation, the Becker-Kistiakowsky-Wilson equation); (2) equations of state that do not include the chemical composition of the explosion products but describe them as an average (the theta equation of state, Landau-Stanyukovich equation of state, Jones-Wilkins-Lee equation of state). In practice, the first group of equations of state are able to predict the detonation characteristics of, as a rule, gaseous explosive mixtures and, less often, condensed explosives. Equations of state in the second group can be used to solve problems applicable to mining. The Jones-Wilkins-Lee equation of state, which is widely used in the scientific literature [15; 16; 17; 18; 19; 20], has six empirical (adjustable) constants. On the one hand, this provides for a good description of the behavior of gaseous explosion products, but the resulting combinations of empirical constants are not precisely determinable, and it is always possible to choose another set of constants that will describe the behavior of gaseous explosion products in addition to the first set. This equation is effective for describing well-characterized high-brisance explosives (trotyl, hexogen, ten), but for industrial explosives, an equation of state that does not require an additional basis for its application is more practical. This approach is presented in this work and has been previously described [21]. The main premise of the applied equation of state (1) is as follows: in the zone of the chemical reaction, the condensed explosive is in a highly compressed state; the atoms or molecules of the explosive are in oscillatory motion, rather than thermal motion, and the repulsive forces determine the pressure magnitude. To describe such a system, methods of statistical physics for expressing Helmholtz energy are applied. Further gaseous explosion products appear at the Chapman-Jouguet point, contributing to the magnitude of the detonation pressure (namely, reducing it) because there is a volume of molecules that cannot be compressed. Then, it defines the pressure at the Chapman-Jouguet point, which is the initial pressure for the polytropic expansion of gaseous explosion products. The next important objective of this research is to determine the parameters on the wall of an explosion cavity. At present, when designing blasting operations in open-pit mines, the shock wave parameters in the rock are not calculated. The main approach to determining these parameters for drilling and blasting operations and choosing the applicable explosive is based on the empirical ratio of the required amount of explosive to the volume of rock moved in space. This approach does not consider physical processes of transmitting the detonation pressure into the rock; therefore, it is necessary to study these physical processes to assess the expediency of using an explosive and to prepare the initial data for calculating the parameters of drilling and blasting operations based on the propagation of shock waves. Many scientists use acoustic approximation to determine the pressure on the explosion cavity wall [21]:  
\[P_{f}=\frac{\rho_{m}\cdot C_{p}}{\rho_{m}\cdot C_{p}+\rho_{vv}\cdot D}P_{d},\]  
where \(P_{d}\) is the pressure of detonation products at the Chapman-Jouguet point, \(\rho_{m}\) is the density of the rock, \(C_{p}\) is the velocity of a longitudinal wave, \(\rho_{vv}\) is the density of the explosive, and \(D\) is the velocity of detonation. In the framework of the acoustic approach, it is initially assumed that the shock wave has a small amplitude that appears at a relatively large equilibrium pressure, and it is also assumed that the shock wave propagates with the local velocity of sound.