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Mach stem due to an underground explosion near a rigid structure buried in soil

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Abstract

This paper presents recent results of an analysis of pressure distributions along the circumference of underground structures of various shapes due to a nearby buried explosion. The present study examines the effect of the standoff distance on the results and special attention is given to the soil medium equation of state characteristics and their effect on the Mach stem. It was found that for a short standoff distance and a steep growth of pressure beyond the full compaction point that characterizes dense soils, the envelope of the pressure distributions shows a maximum value, which is located at some distance away from the plane of symmetry rather than along it, as is the case for a distant explosion. This phenomenon causes the distortion of the frontal part of the explosive cavity. This effect is more pronounced for more dense soils that show a sharper pressure increase in the equation of state. It has been proven that these pressure distributions and associated shapes of the explosion cavities are caused by the Mach stem effect appearing in a soil medium with full locking.

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References

  1. Rakhmatulin, KhA, Dem’yanov, YuA: Strength Under High Transients Loads. Daniel Davey, New York (1966)

    Google Scholar 

  2. Smith, P.D., Hetherington, J.G.: Blast and Ballistic Loading of Structures. Butterworth Heinemann, Oxford (1994)

    Google Scholar 

  3. Bulson, P.S.: Explosive Loading of Engineering Structures. Spon Press, London (1997)

    Google Scholar 

  4. Luccioni, B., Ambrosini, D., Nurick, G., Snyman, I.: Craters produced by underground explosions. Comput. Struct. 87, 1366–1373 (2009)

    Article  Google Scholar 

  5. Wlodarczyk, E.: Reflection of a stationary shock wave from a rigid partition in a three-component medium. J. Tech. Phys. 23, 309–322 (1982)

    MathSciNet  MATH  Google Scholar 

  6. Wang, Zhongqi, Hao, Hong, Lu, Yong: A three-phase soil model for simulating stress wave propagation due to blast loading. Int. J. Numer. Anal. Methods Geomech. 28, 33–56 (2004)

    Article  MATH  Google Scholar 

  7. Lyakhov, G.M., Okhitin, V.N.: Plane waves in nonlinear viscous multicomponent media. J. Appl. Mech. Tech. Phys. 18, 241–248 (1977)

    Article  Google Scholar 

  8. Hurty, W.C., Rubinstein, M.F.: Dynamics of Structures. Prentice-Hall, London (1964)

    Google Scholar 

  9. Belytchko, T., Hughes, T.J.R.: Computational Methods for Transient Analysis. North-Holland, Amsterdam (1983)

  10. Zienkiewich, O.C.: The Finite Element Method. McGraw-Hill, London (1977)

    Google Scholar 

  11. Lewis, R.W., Pettess, P., Hinton, E.: Numerical Methods in Coupled Systems. Wiley, Chichester (1984)

    MATH  Google Scholar 

  12. Stevens, D.J., Krauthammer, T.: Combined finite difference/finite element analysis for soil structure interaction. In: Roesset J.M. (ed.) Dynamics of Structures, ASCE, pp. 485–496 (1987)

  13. Grujicic, M., Pandurandan, B., Cheeseman, B.A.: The effect of degree of saturation of sand on detonation phenomena associated with shallow-buried and ground-laid mines. Shock Vib. 13, 1–21 (2006)

    Article  Google Scholar 

  14. Feldgun, V.R., Kochetkov, A.V., Karinski, Y.S., Yankelevsky, D.Z.: Internal blast loading in a buried lined tunnel. Int. J. Impact Eng. 35, 172–183 (2008)

    Article  Google Scholar 

  15. Yankelevsky, D.Z., Karinski, Y.S., Feldgun, V.R.: Re-examinations of shock wave’s peak pressure attenuation in soils. Int. J. Impact Eng. 38, 864–881 (2011)

    Article  Google Scholar 

  16. Schwer, L.E., Murray, Y.D.: A three-invariant smoth cap model with mixed hardening. Int. J. Numer. Anal. Methods Geomech. 18, 657–688 (1994)

    Article  MATH  Google Scholar 

  17. Yankelevsky, D.Z., Feldgun, V.R., Karinski, Y.S.: Underground explosion of cylindrical charge near a buried wall. Int. J. Impact Eng. 35, 905–919 (2008)

    Article  Google Scholar 

  18. Bangash, M.Y.H.: Impact and Explosion. Analysis and Design. Spon Press/Blackwell Scientific Publications, London/Oxford (1993)

    Google Scholar 

  19. Lyakhov, G.M., Osadchenko, R.A., Polyakova, N.I.: Plane waves in nonhomogeneous media and their interaction with obstacles. J. Appl. Mech. Tech. Phys. 10, 559–566 (1969)

    Article  Google Scholar 

  20. Baylor, J.T.: Parameters affecting loads on buried structures subjected to localized blast effects. Final Report. Army Engineer Waterways Experiment Station Vicksburg MS Structures Lab (1992)

  21. Luccioni, B., Ambrosini, D., Steeve Chung Kim, Yuen, Nurick, G.: Effects of large and spread explosives loads. Int. J. Prot. Struct. 1, 319–344 (2010)

    Article  Google Scholar 

  22. Wilkins, M.L.: Fundamental methods in hydrodynamics. In: Alder, B., Fernbach, S., Rotenberg, M. (eds.) Calculation of Elastic–Plastic Flow. Methods in Computational Physics, vol. 3, pp. 211–263. Academic Press, New York (1964)

  23. Miller, G.H., Colella, P.: A high-order. Eulerian Godunov method for elastic–plastic flow in solids. J. Comput. Phys. 167, 131–176 (2001)

    Article  MATH  Google Scholar 

  24. LeVeque, R.J.: Finite Volume Methods for Hyperbolic Problems. Cambridge University Press, London (2002)

    Book  MATH  Google Scholar 

  25. Feldgun, V.R., Kochetkov, A.V., Karinski, Y.S., Yankelevsky, D.Z.: Blast response of a lined cavity in a porous saturated soil. Int. J. Impact Eng. 35, 953–966 (2008)

    Article  Google Scholar 

  26. Washizu, K.: Variational Methods in Elasticity and Plasticity, pp. 1–348. Pergamon Press, Oxford (1968)

    MATH  Google Scholar 

  27. Kim, M.K., Lim, Y.M., Rhee, J.W.: Dynamic analysis of layered half planes by coupled finite and boundary elelments. Eng. Struct. 22, 670–680 (2000)

    Article  Google Scholar 

  28. Karinski, Y.S., Feldgun, V.R., Yankelevsky, D.Z.: Explosion induced dynamic soil–structure interaction analysis with the coupled Godunov–variational difference approach. Int. J. Num. Methods Eng. 77, 829–854 (2009)

  29. Forestal, M.J., Lee, I.M., Jenrette, B.D., Setchell, R.E.: Gas-gun experiments to determine forces on penetrators into geological targets. Trans. ASME Ser. E J. Appl. Mech. 51, 602–607 (1984)

    Article  Google Scholar 

  30. Bragov, A.M., Grushevsky, G.M., Lomunov, A.K.: Use of the Kolsky method for confined tests of soft soils. Exp. Mech. 36, 237–242 (1996)

    Article  Google Scholar 

  31. Zukas, J.A.: Introduction to Hydrocodes. Studies in Applied Mechanics. Elsevier, New York (2004)

    Google Scholar 

  32. Lundborg, N.: Strength of rock-like materials. Int. J. Rock Mech. Min. Sci. 5, 427–454 (1968)

    Article  Google Scholar 

  33. Collins, G.S., Melosh, H.J., Ivanov, B.A.: Modeling damage and deformation in impact simulations. Meteorit. Planet. Sci. 39, 217–231 (2004)

    Article  Google Scholar 

  34. Collins, G.S., Melosh, H.J., Morgan, J.V., Warner, M.R.: Hydrocode simulations of Chicxulub crater collapse and peak-ring formation. Icarus 157, 24–33 (2002)

    Article  Google Scholar 

  35. Vovk, A.A., Luchko, I.A., Lyakhov, G.M., Plaksii, V.A., Remez, N.S.: Cylindrical blast waves in soils. J. Appl. Mech. Tech. Phys. 27, 571–576 (1986)

    Article  Google Scholar 

  36. Grigoryan, S.S., Lyakhov, G.M., Parshukov, P.A.: Spherical blast waves in soils inferred from stress and strain measurements. J. Appl. Mech. Tech. Phys. 18, 124–127 (1977)

    Article  Google Scholar 

  37. Bragov, A.M., Balandin, V.V., Lomunov, A.K., Filippov, A.R.: Determining the impact compressibility of soft soils from inversed test results. Tech. Phys. Lett. 32, 487–488 (2006)

    Article  Google Scholar 

  38. Resnyansky, A.D., Wildegger-Gaissmaier, A.E.: Hydrocode modeling of high-velocity jet penetration into sand. In: Proceedings of the 19 International Symposium on Ballistic, Interlaken, Switzerland, pp. 1561–1567 (2001)

  39. Vovk, A.A., Mikhalyuk, A.V.: Dimensions of cavities caused by blasting in soils near an obstacle. J. Min. Sci. 16, 117–122 (1980)

    Google Scholar 

  40. Courant, R., Friedrichs, K.O.: Supersonic Flow and Shock Waves. Interscience Publishers, New York (1967)

    Google Scholar 

  41. Balagansky, I.A., Hokamoto, K., Manikandan, P., Matrosov, A.D., Stadnichenko, I.A., Miyoshi, H., Bataev, I.A., Bataev, A.A.: Mach stem formation in explosion systems, which include high modulus elastic elements. J. Appl. Phys. 110, 123516-1–123516-7 (2011)

    Article  Google Scholar 

  42. Chock, J.M.K., Kapania, R.K.: Review of two methods for calculating explosive air blast. Shock Vib. Digest 33, 91–102 (2001)

    Article  Google Scholar 

  43. Karinski, Y.S., Feldgun, V.R., Yankelevsky, D.Z.: Shock waves interaction with a single inclusion buried in soil. Int. J. Impact Eng. 45, 60–73 (2012)

    Article  Google Scholar 

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Acknowledgments

The authors extend their appreciation to Dr. Len Schwer, with whom they had stimulatory discussions at earlier stages of this study. This work was supported by a joint grant from the Centre for Absorption in Science of the Ministry of Immigrant Absorption and the Committee for Planning and Budgeting of the Council for Higher Education under the framework of the KAMEA Program.

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Correspondence to Y. S. Karinski.

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Communicated by H. Kleine.

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Karinski, Y.S., Feldgun, V.R., Racah, E. et al. Mach stem due to an underground explosion near a rigid structure buried in soil. Shock Waves 25, 63–76 (2015). https://doi.org/10.1007/s00193-014-0544-1

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  • DOI: https://doi.org/10.1007/s00193-014-0544-1

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