# Model for Assessment of the Areas of Exposure due to Scattering of Window Glass Fragments in Case of Explosions

Annotation:

One of the secondary damaging factors of explosions at the explosion and fire hazardous production facilities is the fragmentation field. However, the calculations currently being performed to assess the damaging effect of window glass fragments are limited, as a rule, to two-dimensional simplified models.

The purpose of the article is to describe the mathematical model of fragments scattering as secondary damaging factors, to perform the numerical calculation, and to determine the area of fragments scattering in 3D space at the given parameters.

To achieve this goal, the mathematical model of window glass fragments scattering under the influence of the air shock wave is proposed. The model is based on the regularities of the distribution and dissipation of energy, which the fragments initially receive when a shock wave is exposed to the window opening due to explosion. Further calculations are carried out by solving the system of differential equations describing the fragment movement in projections in three directions of its motion.

Numerical solution of the system of differential equations with the given initial conditions is obtained by integrating the system of ordinary differential equations using the Runge — Kutta formula of the 4th and 5th order. When modeling, the system of equations is represented in the form of the vector function. In this case, the following is set: the vector of initial conditions, the time interval, on which it is required to find a solution, and, also the additional options. Numerical calculation ends at the moment when the calculated fragment reaches the ground.

Thus, the calculations performed according to the proposed mathematical model allow to substantiate the range, altitude and flight time of glass fragments in case of explosions. In future, the software implementation will allow in an expeditious manner to make assessment and forecast calculations for analyzing possible technogenic factors and their consequences, which in turn will help the timely development of relevant regulations on assessment of the facilities safety, performance of civil engineering defense measures, and also accelerate the development of an industrial safety declaration.

References:
1. Lisanov M.V., Zhukov I.S., Bazaliy R.V. Criteria for Buildings and Structures Blast Resistance at Hazardous Production Facilities. Bezopasnost Truda v Promyshlennosti = Occupational Safety in Industry. 2019. № 5. pp. 40–46. (In Russ.).
2. Rybakov A.V., Zamana K.Yu. The model for assessment of the zone of possible damage from the scattering of the equipment fragments in case of emergencies of the technogenic nature at fire and explosion hazardous facilities. Nauchnye i obrazovatelnye problemy grazhdanskoy zashchity = Scientific and educational problems of civil defence. 2015. № 4. 56–64. (In Russ.).
3. Willey R.J., Murphy J., Baulch A. The explosion in Tianjin, China, August 12, 2015. Process Safety Progress. 2015. Vol. 34. Iss. 3. pp. 312.
4. Li Z., Zhang X., Shi Y., Xu Q. Experimental Studies on Mitigating Local Damage and Fragments of Unreinforced Masonry Wall under Close-in Explosions. Journal of Performance of Constructed Facilities. 2019. Vol. 33. Iss. 2.
5. Wang X., Remotigue M., Arnoldus Q., Janus M., Luke E., Thompson D., Weed R. High-fidelity simulations of blast loadings in urban environments using an overset meshing strategy. Shock Waves. 2017. Vol. 27. Iss. 3. pp. 409–422. DOI: 10.1007/s00193-016-0680-x
6. Zinovev V.E., Plotnikova E.S., Gonchar A.E. Assessment of the consequences of accidental explosions of fuel-air mixtures in the oil, oil products underground tanks. Nauka i tekhnologii truboprovodnogo transporta nefti i nefteproduktov = Science & Technologies: Oil and Oil Products Pipeline Transportation. 2014. № 4 (16). pp. 74–83. (In Russ.).
7. STO Gazprom 2-2.3-351—2009. Guidelines on conducting risk analysis for hazardous production facilities of OAO Gazprom gas transmission enterprises. Available at: http://www.sra-russia.ru/upload/iblock/cfa/cfa0d60f4cec7857c61e5e2a99e77441.pdf (accessed: September 23, 2019). (In Russ.).
8. Rybakov A.V. Calculation of the resistance of building structures to baric pressure influence in case of accidents involving compressed natural gas. Information technology: monography. Khimki: FGBOU VPO «Akademiya grazhdanskoy zashchity MChS Rossii», 2014. 139 p. (In Russ.).
9. Sha S., Chen Z., Jiang X. Influences of obstacle geometries on shock wave attenuation. Shock Waves. 2014. Vol. 24. Iss. 6. pp. 573–582.
10. Sedov L.I. Continuum mechanics. In 2 volumes. Vol. 2. Moscow: Nauka, 1970. 568 p. (In Russ.).
11. Kalitkin N.N., Koryakin P.V. Numerical methods: guide. In 2 books. Book 2: Methods of the mathematical physics. Moscow: Izdatelskiy tsentr «Akademiya», 2013. 304 p. (In Russ.).
12. Bakhvalov N.S., Zhidkov N.P., Kobelkov G.M Numerical methods. Moscow: Binom. Laboratoriya znaniy, 2015. 639 p. (In Russ.).
13. Garoma H., Kabeto M.J. Numerical Solution of Fourth Order Ordinary Differential Equations Using Fifth Order Runge Kutta Method. Asian Journal of Science and Technology. 2017. Vol. 08. Iss. 02. pp. 4332–4339.
DOI: 10.24000/0409-2961-2019-12-19-23
Year: 2019
Issue num: December
Keywords : mathematical model explosion fragments scattering area of exposure Runge-Kutta method
Authors: