Computational simulation of shock wave generated by the detonation of explosives for civil use

When conducting a research concerning the propagation of a shock wave generated by the detonation of civil use explosives, the first thing that comes to mind should be if the detonation process takes place in an obstacle-free field, or the area has obstacles such as rocks, metals structures, wood etc, obstacles that can and will influence the final results, the shock wave curve being obturated by it. On one hand, the paper presents the experimental results obtained after the detonation of a freely suspended load, placed at 0.5m above a concrete surface. On the other hand, it compares the values of explosion pressure as shock wave, measured on 4 sensors linearly disposed at the same elevation to the ground, at a distance of 2,3,4 respectively 6 meters from the explosive charge. These values are determined through computerized simulation, using ANSYS AUTODYN software, by virtually reproducing the real scenario. Following the two experiments (real and virtual), one can conclude that computerized simulation proves to be a very useful instrument in an a priori evaluation of hazardous situations/utility of peak values for shock wave, by allowing the user to develop prevention measures/optimization of the analysed processes and also in further investigations


Introduction
The shock wave that appears after the detonation of an explosive material can be characterized in coordinated quantity explosive (W) -distance (R) from the following measurable parameters: maximum pressure (overpressure) and dynamic pressure, incident and reflected pressure, incident and reflected pulse, the arrival time of the wave front, the speed of the wave front, etc. [1] The coordinates of the explosive quantity -distance (WR) are linked by a relation, also called the Hopkinson-Cranz scaling law: Or equivalent R =ZxW 1/3 (2) in which: -R is the distance from the place of the explosion and to the place where the respective parameter is measured (e.g. maximum pressure).
-W coordinate represents the amount of TNT equivalent (Tri-Nitro-Toluene) of the explosive material, which was used in detonation. The equivalence relation between the mass of an explosive material -M exp and the reference mass TNT -M TNT is based on the thermal energy ratio (E d exp and E d TNT ) released by the combustion reaction when detonating explosive materials, as follows: The shock wave produced by an explosion may have a spherical geometry, if the explosion occurred in the air at a considerable distance from the surface of the soil and a hemispherical geometry, if the explosion occurred on the surface of the soil or in its immediate vicinity [2]. In case of shock waves with hemispherical geometry, a wave front reflected by the surface of the ground also appears, besides the incident wave front. Also, the reflection of the shock waves can also occur at the interface between the air and the exterior or interior rigid surfaces of some civil constructions (e.g. walls, monuments, etc.). At a certain distance from the blast site, shock wave has the general profile shown in Figure 1. In which: P max is the maximum value of the pressure (overpressure) that is reached in an extremely short time and then descends until it reaches the reference P o value of atmospheric pressure As it can be seen in figure 1 besides the positive phase, the shock wave profile also has a negative phase in which the pressure value decreases below that of the atmospheric pressure to a minimum value, P min [3]. The duration of the positive phase is noted with t d , t a , being the time when the shock wave front reaches that point and which also includes the duration of the detonation process. The duration of the negative phase is noted by t n .
Between the 60s and 80s Charles Kingery and Gerald Bulmash carried out a series of experiments in which they measured the mentioned parameters, using quantities from under 1Kg and up to 400 tons of TNT. The results of the measurements were fitted with polynomial functions that became a benchmark in the evaluation of the effects produced by a shock wave in relation to the explosive mass and the distance at which the evaluation is made. In coordinates (WR), the experiments were performed for a range of variation of Z between 0.05 and 40 [4]. For the shock wave with spherical symmetry the characteristic parameters can be determined using the polynomial expression: where: P is the logarithm based on parameter 10 (e.g. pressure, impulse), C 0,1,2...n are constant and: U = K 0 + ln (K 1 xZ), where K 0,1 are constant.
Knowing the maximum values for the air pressure wave is important for the preliminary evaluation of the effects of an explosion with detonation (by energetic relation to the TNT equivalent) on the structures and on the people, the limits being known in the literature, but also by the investigations conducted by the INCD INSEMEX for elucidating the causes of industrial or domestic explosions. In these cases, computer simulations, previously calibrated on physical models, become very useful tools for assessing the damage, for approximating with a high degree of accuracy the energetic value of the explosion, going in the opposite direction and finally getting to express quantitatively the combustible substance that was involved in the investigated explosions.

Methods used 2.1 Experiments in open field for the air pressure wave in the INSEMEX Polygon
In order to carry out research on the propagation of the pressure wave when detonating explosive charges, an experimental assembly was performed as follows:  a flat concrete surface in open field, without obstacles, was selected;  4 pressure sensors were cascaded (two KISTLER systems were used to measure the explosion pressure, so that on the bayonet type sensors cylindrical sensors were placed, both systems using IEPE sensors and LabAmp type amplifiers 5165A4) at the following distances from the explosive charge at 0.5m above the concrete surface [5]: pressure sensor sp1 at 2m; pressure sensor sp2 at 3m; pressure sensor sp3 at 4m; pressure sensor 4 at 6m; metal support for suspending the explosive charge; a mass of 280 g equivalent TNT was used as an explosive charge [6]

Virtual simulation of the experiment
Through numerical simulations, the propagation of the shock wave with hemispherical geometry was modeled for an amount of 280 g TNT. The modeling was done in 2D axial symmetry, the actual space of simulation being a solid angle with the tip in the centre of detonation of the load considered spherical. [7]

. The results of the real tests -experiments in the INSEMEX Polygon
The results on the pressure curves for each distance and for 280 g of TNT equivalent explosive are as follows:

Virtual simulation results
The numerical simulations modeled the shock wave propagation, the results being as follows: The maximum values for explosion pressure recorded at gauge # 1, # 2, # 3, # 4 for 280g TNT, transformed into mbar, as well as the wave front velocities are in the following table:

Exemplary use of the PHANTOM high-speed camera
Visualization of the air pressure wave (observe the undistorted circular contour next to the sp2 pressure sensor) by using the BOS (background oriented Schlieren) effect, applied on fast shooting at 10,000 fps.

Interpreting the results and discussions
Comparing the results of the real tests in the INSEMEX polygon with those of the computer simulation ANSYS AUTODYN shows a good correlation of them, thus validating the used models.   Probable complete destruction of the building. 99% deaths in the exposed population as a result of the direct effects of the explosion. Overpressure (mbar) Effects 350 The ear drum rupture limit 700 Limit for lung damage 1000 Up to 50% rupture of the eardrum to the exposed population 1800 1% mortality 2100 10% mortality 2600 50% mortality 3000 90% mortality 3500 99% mortality

Conclusions
The data presented in the paper show that computer simulations allow the user to obtain the maximum explosion pressures, for various configurations (quantities of explosive materials, distances), to be used in preliminary evaluations of dangerous situations, respectively for estimating the characteristics of the substances involved in the investigation of post-factum explosions.
For the results of the overpressure of detonating a mass of 280g TNT it is estimated that this explosion could cause lung damage for persons less than 3m away, or punctured ear drum to people caught less than 6m away, at the same time being able to estimate the deterioration of unreinforced buildings.