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Prediction of Near-Field Wave Attenuation Due to a Spherical Blast Source

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Abstract

Empirical and theoretical far-field attenuation relationships, which do not capture the near-field response, are most often used to predict the peak amplitude of blast wave. Jiang et al. (Vibration due to a buried explosive source. PhD Thesis, Curtin University, Western Australian School of Mines, 1993) present rigorous wave equations that simulates the near-field attenuation to a spherical blast source in damped and undamped media. However, the effect of loading frequency and velocity of the media have not yet been investigated. We perform a suite of axisymmetric, dynamic finite difference analyses to simulate the propagation of stress waves induced by spherical blast source and to quantify the near-field attenuation. A broad range of loading frequencies, wave velocities, and damping ratios are used in the simulations. The near-field effect is revealed to be proportional to the rise time of the impulse load and wave velocity. We propose an empirical additive function to the theoretical far-field attenuation curve to predict the near-field range and attenuation. The proposed curve is validated against measurements recorded in a test blast.

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References

  • AUTODYN A (2009) Interactive non-linear dynamic analysis software, version 12, user’s manual. SAS IP Inc

  • Blair DP (2003) A fast and efficient solution for wave radiation from a pressurised blasthole. Fragblast 7:205–230

    Article  Google Scholar 

  • Blair DP (2007) A comparison of Heelan and exact solutions for seismic radiation from a short cylindrical charge. Geophysics 72:E33–E41

    Article  Google Scholar 

  • Blair DP (2010) Seismic radiation from an explosive column. Geophysics 75:E55–E65

    Article  Google Scholar 

  • Blair DP (2015) Wall control blasting. In: Paper presented at the 11th international symposium on rock fragmentation by blasting, Sydney, pp 13–26

  • Blake F Jr (1952) Spherical wave propagation in solid media. J Acoust Soc Am 24:211–215

    Article  Google Scholar 

  • Chen S, Cai J, Zhao J, Zhou Y (2000) Discrete element modelling of an underground explosion in a jointed rock mass. Geotech Geol Eng 18:59–78

    Article  Google Scholar 

  • Cho SH, Kaneko K (2004) Influence of the applied pressure waveform on the dynamic fracture processes in rock. Int J Rock Mech Min 41:771–784

    Article  Google Scholar 

  • Deng XF, Zhu JB, Chen SG, Zhao ZY, Zhou YX, Zhao J (2014) Numerical study on tunnel damage subject to blast-induced shock wave in jointed rock masses. Tunn Undergr Space Technol 43:88–100

    Article  Google Scholar 

  • Dowding C (1984) Estimating earthquake damage from explosion testing of full-scale tunnels. Adv Tunn Technol Subsurf Use 4(3):113–117

    Google Scholar 

  • Dowding C (1996) Construction vibrations. Prentice Hall, Upper Saddle River, pp 41–60

    Google Scholar 

  • Duvall WI (1953) Strain-wave shapes in rock near explosions. Geophysics 18:310–323

    Article  Google Scholar 

  • Fan SC, Jiao YY, Zhao J (2004) On modelling of incident boundary for wave propagation in jointed rock masses using discrete element method. Comput Geotech 31:57–66

    Article  Google Scholar 

  • Hao H, Wu C, Zhou Y (2002) Numerical analysis of blast-induced stress waves in a rock mass with anisotropic continuum damage models part 1: equivalent material property approach. Rock Mech Rock Eng 35:79–94

    Article  Google Scholar 

  • Heelan PA (1953) Radiation from a cylindrical source of finite length. Geophysics 18:685–696

    Article  Google Scholar 

  • Hino K (1956) Fragmentation of rock through blasting and shock wave; theory of blasting. Quarterly of the Colorado School of Mines

  • ISO (2000) ISO 4866: mechanical vibration and shock—vibration of fixed structures—guidelines for the measurement of vibrations and evaluation of their effects on structures. International Organisation for Standardisation ISO, Geneva

    Google Scholar 

  • Itasca Consulting Group I (2011) Fast Lagrange analysis of continua, Version 7.0

  • Jiang J (1993) Vibration due to a buried explosive source. PhD Thesis, Curtin University, Western Australian School of Mines, pp 198

  • Jiang J, Blair D, Baird G (1995) Dynamic response of an elastic and viscoelastic full-space to a spherical source. Int J Numer Anal Met 19:181–193

    Article  Google Scholar 

  • Jiang J, Blaird G, Bair D (1998) Polarization and amplitude attributes of reflected plane and spherical waves. Geophys J Int 132:577–583

    Article  Google Scholar 

  • Kim DS, Lee JS (2000) Propagation and attenuation characteristics of various ground vibrations. Soil Dyn Earthq Eng 19:115–126

    Article  Google Scholar 

  • Konya CJ, Walter EJ (1991) Rock blasting and overbreak control. National Highway Institute 5

  • Kuhlemeyer RL, Lysmer J (1973) Finite element method accuracy for wave propagation problems. J Soil Mech Found Div 99(Tech Rpt)

  • Lee E, Hornig H, Kury J (1968) Adiabatic expansion of high explosive detonation products. California University, Lawrence Radiation Lab, Livermore

    Book  Google Scholar 

  • Liu Q, Tidman P (1995) Estimation of the dynamic pressure around a fully loaded blast hole. Canmet Mrl Experimental Mine

  • Lysmer J, Kuhlemeyer R (1969) Finite element model for infinite media. J Eng Mech Div ASCE 95:859–877

    Google Scholar 

  • Ma G, An X (2008) Numerical simulation of blasting-induced rock fractures. Int J Rock Mech Min 45:966–975

    Article  Google Scholar 

  • Ma G, Hao H, Zhou Y (1998) Modeling of wave propagation induced by underground explosion. Comput Geotech 22:283–303

    Article  Google Scholar 

  • Meredith J, Toksöz M, Cheng C (1993) Secondary shear waves from source boreholes. Geophys Prospect 41:287–312

    Article  Google Scholar 

  • Meyer M (1964) On spherical near fields and far fields in elastic and visco-elastic solids. J Mech Phys Solid 12:77–110

    Article  Google Scholar 

  • Nelson JT, Saurenman H (1983) State-of-the-art review: prediction and control of groundborne noise and vibration from rail transit trains

  • Ning Y, Yang J, An X, Ma G (2011) Modelling rock fracturing and blast-induced rock mass failure via advanced discretisation within the discontinuous deformation analysis framework. Comput Geotech 38:40–49

    Article  Google Scholar 

  • Saharan MR, Mitri H (2008) Numerical procedure for dynamic simulation of discrete fractures due to blasting. Rock Mech Rock Eng 41:641–670

    Article  Google Scholar 

  • Siskind DE (2005) Vibrations from blasting. Intern. Society of Explosives Engineers

  • Starfield AM, Pugliese JM (1968) Compression waves generated in rock by cylindrical explosive charges: a comparison between a computer model and field measurements. Int J Rock Mech Min 5:65–77

    Article  Google Scholar 

  • Trivino LF, Mohanty B, Munjiza A (2009) A seismic radiation patterns from cylindrical explosive charges by combined analytical and combined finite-discrete element methods. In: Paper presented at the 9th international symposium on rock fragmentation by blasting, Granada, pp 415-426

  • Tubman KM, Cheng C, Toksoez MN (1984) Synthetic full waveform acoustic logs in cased boreholes. Geophysics 49:1051–1059

    Article  Google Scholar 

  • Wiss J (1981) Construction vibrations: state-of-the-art. J Geotech Eng Div 107:167–181

    Google Scholar 

  • Yilmaz O, Unlu T (2013) Three dimensional numerical rock damage analysis under blasting load. Tunn Undergr Space Technol 38:266–278

    Article  Google Scholar 

Download references

Acknowledgements

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT, and Future Planning (NRF-2015R1A2A2A01006129).

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Correspondence to Duhee Park.

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Ahn, JK., Park, D. Prediction of Near-Field Wave Attenuation Due to a Spherical Blast Source. Rock Mech Rock Eng 50, 3085–3099 (2017). https://doi.org/10.1007/s00603-017-1274-3

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