Explosives and Blasting (화약ㆍ발파)

Korean Society of Explosives and Blasting Engineering (대한화약발파공학회)
권호 표지

[ $PFC^{3D}$ ] Modeling of Stress Wave Propagation Using The Hopkinson's Effect

$PFC^{3D}$ 상에서의 홉킨슨 효과를 이용한 응력파의 전파모델링

  • Published : 2005.09.01
Download PDF
⟨ Previous Next ⟩

Abstract

An explosion modeling technique was developed by using the spherical discrete element code, $PFC^{3D}$, which can be used to model the dynamic stress wave propagation phenomenon. The modeling technique is simply based on an idea that the explosion pressure should be applied to a $PFC^{3D}$ particle assembly not in the form of an external force (body force), but in the form of a contact force (surface force). The stress wave propagation modeling was conducted by simulating the experimental approach based on the Hopkinson's effect combined with the spatting phenomenon that had previously been developed to determine the dynamic tensile strength of Inada granite. As a result, the stress wave velocity obtained by the proposed modeling technique was 4167 m/s, which is merely $3\%$ lower than the actual wave velocity of 4300 m/s for an Inada granite.

본 연구에서는 $PFC^{3D}$상에서 공내입자들의 반경을 팽창/수축시키는 기법을 통해 공벽입자들에 접촉력의 형태로 폭발압력을 부여하는 폭원모델링을 기법을 소개하고, 제안된 기법을 이용하여 홉킨슨 효과 효과와 스폴링 현상을 응용하여 암석코어에 대한 응력파의 전파 및 반사과정을 기존의 외력을 적용함으로써 서로 비교하여 보았다. 암석코어는 직경 20m, 길이 200mm의 입자결합체로서 접촉결합을 이용하여 구성하였으며, 시료의 선단에 주기 0.050m$(50{\mu}s)$의 펄스형태의 폭발하중을 기존의 방법과 제안된 폭원모델링 기법을 이용하여 각기 입사시켰다. 해석결과 두 기법은 서로 유사한 결과를 보였으며, 입사압축파는 0.060ms$(60{\mu}s)$ 이후 시료의 후단에서 반사되어 반사인장파의 형태로 되돌아오면서 시료의 축방향과 직각방향으로 인장균열을 발생시켰다. 또한 시료 중을 전파하는 응력파의 속도는 4,167m/s로 계산되어 물리시료에 대한 측정치 4,300m/s와 $3\%$ 정도의 근소한 오차를 보였다.

Keywords

References

  1. Brinkmann, J. R, 1987, Separating Shock Wave and Gas Expansion Breakage Mechanisms, Proc. 2nd Int. Symp. on Rock Fragmentation by Blasting, W. L. Fourney and R D. Dick, Eds., Bethel, Connecticut, Society for Experimental Mechanics, pp. 6-15
  2. Brinkmann, J. R., 1990, An Experimental Study of the Effects of Shock and Gas Penetration in Blasting, Proc. 3rd Int. Symp. on Rock Fragmentation by Blasting
  3. Cho, S., 2003, Dynamic Fracture Process Analysis of Rock and Its Application to Fragmentation Control in Blasting, Ph.D. Thesis, Graduate School of Engineering, Hokkaido Univ., pp. 39-76
  4. Cundall, P. A., and O. D. L. Strack, 1979, A Discrete Numerical Model for Granular Assemblies, Geotechnique, Vol. 29, pp. 47-65 https://doi.org/10.1680/geot.1979.29.1.47
  5. Fourney, W. L., 1993, Mechanism of Rock Fragmentation by Blasting, Comprehensive Rock Engineering, Principles, Practice and Projects, J. A Hudson, Ed. Oxford, Pergamon Press, pp. 39-69
  6. Jung, W. J., Y. Ogata, Y. Wada, M. Seto, K. Katsuyama and T. Ogawa, 2001, Effects of Water Saturation and Strain Rate on the Tensile Strength of Rocks under Dynamic Load, Journal of Geotechnical Engineering, JSCE, No. 673, III-54, pp. 53-59
  7. Munjiza, A, D. R. J. Owen, N. Bicanic and J. R. Owen, 1994, On a Rational Approach to Rock Blasting, Computer Methods and Advances in Geomechanics, pp. 871-876, H. J. Siriwardane and M. M. Zaman, Eds., Rotterdam, Balkema
  8. Potyondy, D. O., and P. A Cundall, 1996, Modeling of Shock- and Gas-Driven Fractures Induced by a Blast Using Bonded Assemblies of Spherical Particles, Rock Fragmentation by Blasting, Balkema, Rotterdam, pp. 55-61
  9. Preece, D. S., B. J. Thorne, M. R. Baer and J. W. Swegle, 1994, Computer Simulation of Rock Blasting: A Summary of Work from 1987 through 1993, Sandia National Laboratories, Report No. SAND92-1027
  10. Sarracino. R. S., and J. R. Brinkmann, 1994, Modeling of Blasthole Liner Experiments, Computer Methods and Advances in Geomechanics, H. J. Siriwardane and M. M. Zaman, Eds., Rotterdam, Balkema, pp. 871-876
  11. Schatz, J. F., B. J. Zeigler, R. A. Bellman, J. M. Hanson, M. Christianson and R. D. Hart, 1987, Prediction and Interpretation of Multiple Radial Fracture Stimulations, Science Applications International Corporation (SAIC), Report to Gas Research Inst. (GRI), SAIC Report No. SAIC087/1056, GRI Report No. GRI-87/0199