Keywords: domino effect, industrial explosions accident, mechanical impact, tanks, projectile, penetration, perforation, risk, reliability, probabilistic methods.

The present paper deals with domino effect analysis for industrial facilities. An explosion or accident may generate various sets of projectiles. In their trajectory, they may impact on other existing facilities, such as tanks under high-pressure or other strategic components or installations. If the impacted targets fail, this may give rise to other sets of projectiles and so on. These potential series of accidents are known as the domino effect.

A probabilistic approach is developed by the authors. The probability of the domino effect occurring requires three main steps:

• Probabilistic modelling of the source term (the first set of projectiles): the probability of the first explosion occurrence and therefore number, masses, velocities, departure angles, geometrical form and dimensions, constitutive materials properties are described with probabilistic distributions [1,5,6,7,8].
• Probabilistic modelling of the target term (first set of impacted targets): number of impacting projectiles, velocities, incidence angles and energy at impact, constitutive materials and the dimensions of the impacted targets, projectiles penetration depths into the targets are also described with probabilistic distributions [4,7].
• Evaluation of the risks of second set of explosions that may take place in the impacted components [2,3,9,10,11].

Two-dimensional simulations are undertaken within this probabilistic framework:

• For the probabilistic description of the source term, the authors have collected existing models from the literature [1,5,6,7,8].
• The authors propose new models for the impact (the probability of impact which depends on the trajectory and geometry of both the target and projectile: ellipses, cylinders and planar plates, in a first step) and the penetration depth when there is impact. A simplified mechanical model is developed in the case of cylindrical rods impacting on rectangular plates, both are made of metal [10]. The estimated penetration depth into the target is compared with the experimental data (four sets of data) collected fromthe literature [2,3,9,10,11] with the following features: projectile mass ranging from 0.1g up to 250kg, projectile velocity ranging from 10 m/s up to 2100 m/s, projectiles diameters ranging from 1.5 mm up to 90 mm, target strength ranging from 300 MPa up to 1400 MPa and incidence angles ranging from 0^o up to 70^o.

Monte Carlo simulations were run in order to calculate the different probabilities: the probability of impact, the distribution of the penetration depth and the probability of the domino effect.

1

Baum M.R. "Failure of a horizontal pressure vessel containing a high temperature liquid: the velocity of end-cap and rocket missiles", Journal of Loss Prevention in the Process Industries, 12, 137-145, 1999. doi:10.1016/S0950-4230(98)00051-5

2

Bless S.J., Barber J.P., Bertke R.S. and Swift H.F. "Penetration mechanics of yawed rods", Int. J. Eng. Sci., 16 (11), 829-834, 1978. doi:10.1016/0020-7225(78)90068-X

3

Bukharev Y.I. and Zhukov V.I. "Model of the penetration of a metal barrier by a rod projectile with an angle of attack", Combustion, Explosion and Shock Waves, 31 (3), 104-109, 1995. doi:10.1007/BF00742683

4

Gubinelli G., Zanelli S. and Cozzani V. "A simplified model for the assessment of the impact probability of fragments", Journal of Hazardous Materials, A116, 175-187, 2004. doi:10.1016/j.jhazmat.2004.09.002

5

Hauptmanns U. "A procedure for analyzing the flight of missiles from explosions of cylindrical vessels", Journal of Loss Prevention in the Process Industries, 14, 395-402, 2001. doi:10.1016/S0950-4230(01)00011-0

6

Holden P.L. and Reeves A.B. "Fragment hazards form failures of pressurised liquefied gas vessels", Institution of Chemical Engineers Symposium Series, 93, 205-220, 1985.

7

INERIS "Les éclatements de réservoirs, Phénoménologie et modélisation des effets", Direction des Risques Accidentels, No Ineris-DRA-2004-46055, 2004.

8

INERIS "Calculs des effets mécaniques d'un BLEVE de citerne ferroviaire", Rapport d'étude, No Ineris-DRA-72293, 2005.

9

Lepareux M., Jamet Ph., Matheron Ph., Lieutenant J.L., Couilleaux J., Duboellee D. and Aguilar J. "Experimental and numerical studies of impacts on stainless steel plates subjected to rigid missiles at low velocity", Nuclear Engineering and Design, 115, 105-112, 1989. doi:10.1016/0029-5493(89)90263-X

10

Mebarki A., Nguyen Q.B., Mercier F., Ami Saada R., Meftah F., Reimeringer M. "A probabilistic model for the vulnerability of metal plates under the impact of cylindrical projectiles", Journal of Loss Prevention in the Process Industries, 2006 (in Press). doi:10.1016/j.jlp.2006.09.001

11

Neilson A.J. "Empirical equations for the perforation of mild steel plates", International Journal of Impact Engineering 3 (2), 137-142, 1985. doi:10.1016/0734-743X(85)90031-4

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