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Some Dynamic Characteristics of Rocks

  • Werner Goldsmith
  • Carl F. Austin
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)

Abstract

The literature in the field of dynamic behavior of rock materials is relatively sparse and incomplete. Details and even raw data on pulse propagation and internal structural response of rock to the passage of a transient of more than negligible amplitude is virtually non-existent, particularly under controlled conditions. The present investigation consists of a study of the transmission and decay of pulses produced both by impact and explosive loading in a rock classified as a diorite. The samples were chosen and prepared with sufficient care and tested under identical conditions so that reproducibility of results comparable to that expected in metallic systems was obtained, indicating that the concept of non-reproducibility in geologic materials is not well founded.

Ballistically-suspended Hopkinson bars of diorite of 3/4-inch diameter and approximately 22 inches long were subjected to longitudinal impact by spherical and flat-ended projectiles of hardened steel at an initial velocity of about 3300 in/sec. Strain gages attaches to the specimens at various stations permitted a recording of the shape and velocity of propagation of the resultant wave. Similar experiments were performed on an aluminum alloy bar of identical size in order to assess the magnitude of the dispersion resulting from the three-dimensional character of the rod. The nature of the transformation of the pulse during passage permits an assessment of the validity of various models proposed for geologic substances in the field of seismology. A further detailed study of the internal response of the samples to such pulse passage was accomplished by means of microscopy and static tests, which correlated very well with the dynamic results. The average propagation velocity of a pulse generated by a contact explosion in a rectangular block of diorite was also determined.

Keywords

Plutonic Rock Seismological Society Dynamic Tensile Strength Mine Report China Lake 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliography

  1. [1]
    Ewing, W. M., W. S. Jardetzky and F. Press: Elastic Waves in Layered Media, New York: McGraw-Hill Book Co. 1957.MATHGoogle Scholar
  2. [2]
    Brekhovsikh, L. A.: Waves in Layered Media, New York: Academic Press 1960.Google Scholar
  3. [3]
    Sharpe, J. A.: The Production of Elastic Waves by Explosion Pressure, Geophysics 7, 144, 311 (1942).ADSCrossRefGoogle Scholar
  4. [4]
    Blake, F. G., Jr.: Spherical Wave Propagation in Solid Media, J. Acoust. Soc. Amer. 24, 211 (1952).ADSCrossRefGoogle Scholar
  5. [5]
    Selberg, H. L.: Transient Compression Waves from Spherical and Cylindrical Cavities, Arkiv för Fysik 5, 97 (1952).MathSciNetMATHGoogle Scholar
  6. [6]
    Obert, L., and W. I. Duvall: Generation and Propagation of Strain Waves in Rock, Part 1, U.S. Bureau of Mines Report of Investigations 4683, 1950.Google Scholar
  7. [7]
    Duvall, W. I., and B. Petkof: Spherical Propagation of Explosion-generated Strain Pulses in Rock, U.S. Bureau of Mines Report of Investigations 5483, 1959.Google Scholar
  8. [8]
    Pearse, G. E.: Rock Blasting, Mine and Quarry Engineering 21, 25 (1955).Google Scholar
  9. [9]
    Hino, K.: Fragmentation of Rock through Blasting, Quarterly of the Colorado School of Mines 51, 191 (1956).Google Scholar
  10. [10]
    Hino, K.: Velocity of Rock Fragments and Shape of Shock Wave, J. of Industrial Explosives (Japan) 17, 236 (1956).Google Scholar
  11. [11]
    Rinehart, J. S., and J. Pearson: Behavior of Metals under Impulsive Loads, American Society for Metals, Cleveland, Ohio, 1954.Google Scholar
  12. [12]
    Rinehart, J. S.: On Fractures Caused by Explosions and Impacts, Quarterly of the Colorado School of Mines 55, No. 4 (1960).Google Scholar
  13. [13]
    Broberg, K. B.: Shock Waves in Elastic and Elastic-Plastic Media, Kungl. Tekniska Högskolan (Stockholm), Avhandling No. 11, 1956.Google Scholar
  14. [14]
    Duvall, W. I., and T. C. Atchison: Rock Breakage by Explosives, U.S. Bureau of Mines Report of Investigations 5356, 1957.Google Scholar
  15. [15]
    Bacon, L. O.: A Method of Determining Dynamic Tensile Strength of Rock at Minimum Loading, U.S. Bureau of Mines Report of Investigations 6067, 1962.Google Scholar
  16. [16]
    Grine, D. R.: Finite Amplitude Stress Waves in Rocks, Stanford Research Institute, Poulter Laboratories Technical Report 012–59, 1959.Google Scholar
  17. [17]
    Knopoff, L., and G.J. F. McDonald: Models for Acoustic Loss in Solids, J. Geophysical Research 65, 2191 (1960).ADSCrossRefGoogle Scholar
  18. [18]
    Zener, C.: Elasticity and Anelasticity of Metals, University of Chicago Press 1948.Google Scholar
  19. [19]
    Collins, F., and C. C. Lee: Seismic Wave Attenuation Characteristics from Pulse Experiments, Geophysics 21, 16 (1956).ADSCrossRefGoogle Scholar
  20. [20]
    Peselnick, L., and I. Zietz: Internal Friction of Fine-grained Limestones at Ultrasonic Frequencies, Geophysics 24, 285 (1959).ADSCrossRefGoogle Scholar
  21. [21]
    Auberger, M., and J. S. Rinehart: Ultrasonic Velocity and Attenuation of Longitudinal Waves in Rocks, J. Geophysical Research 66, 191 (1961).ADSCrossRefGoogle Scholar
  22. [22]
    Bruckshaw, J. McG., and P. C. Mahanta: The Variation of the Elastic Constants of Rocks with Frequency, Petroleum 17, 14 (1954).Google Scholar
  23. [23]
    Knopoff, L.: The Seismic Pulse in Materials Possessing Solid Friction, I: Plane Waves, Bulletin of the Seismological Society of America 46, 175 (1956).Google Scholar
  24. [24]
    Knopoff, L., and G. J. F. MacDonald: Attenuation of Small Amplitude Stress Waves in Solids, Reviews of Modern Physics 30, 1178 (1958).MathSciNetADSCrossRefGoogle Scholar
  25. [25]
    Ricker, N.: Form and Nature of Seismic Waves and the Structure of Seismograms, Geophysics 5, 348 (1940).ADSCrossRefGoogle Scholar
  26. [26]
    Ricker, N.: The Form and Law of Propagation of Seismic Wavelets, Proceedings of the Third World Petroleum Congress, Sec. I, 1951, p. 514.Google Scholar
  27. [27]
    McDonal, F. J., F. A. Angona, R.L. Mills, R. L. Sengbush, R. G. Van Nostrand and J. E. White: Attenuation of Shear and Compressional Waves in Pierre Shale, Geophysics 23, 421 (1958).ADSCrossRefGoogle Scholar
  28. [28]
    Ricker, N.: Further Developments in the Wavelet Theory of Seismogram Structure, Bulletin of the Seismological Society of America 33, 197 (1943).Google Scholar
  29. [29]
    Ricker, N.: Wavelet Functions and their Polynomials, Geophysics 9, 314 (1944).ADSCrossRefGoogle Scholar
  30. [30]
    Ricker, N.: The Computation of Output Disturbances from Amplifiers for True Wavelet Inputs, Geophysics 10, 207 (1945).ADSCrossRefGoogle Scholar
  31. [31]
    Jeffreys, H.: Damping in Bodily Seismic Waves, Monthly Notices of the Royal Astronomical Society, Geophysical Supplement 2, 318 (1931).MATHCrossRefGoogle Scholar
  32. [32]
    Ricker, N., and W.A. Sorge: The Primary Seismic Disturbance in Shale, Bulletin of the Seismological Society of America 41, 181 (1951).Google Scholar
  33. [33]
    van Melle, F. A.: Note on The Primary Seismic Disturbance in Shale, Bulletin of the Seismological Society of America 44, 123 (1954).Google Scholar
  34. [34]
    Sezawa, K.: On the Decay of Waves in Viscoelastic Solid Bodies, Bulletin of the Earthquake Research Institute, Tokyo University, Vol. 3, 1927, p. 43.Google Scholar
  35. [35]
    Knopoff, L.: The Attenuation of Compression Waves in Lossy Media, Bulletin of the Seismological Society of America 46, 47 (1956).Google Scholar
  36. [36]
    Futterman, W. I.: Dispersive Body Waves, J. Geophysical Research 67, 5279 (1962).MathSciNetADSMATHCrossRefGoogle Scholar
  37. [37]
    Lamb, G. L.: The Attenuation of Waves in a Dispersive Medium, J. Geophysical Research 67, 5273 (1962).MathSciNetADSCrossRefGoogle Scholar
  38. [38]
    Birch, F., and D. Bancroft: Elasticity and Internal Friction in a Long Column of Granite, Bulletin of the Seismological Society of America 28, 243 (1938).Google Scholar
  39. [39]
    Reich, H.: Geologische Unterlagen der angewandten Geophysik, Handbuch der Experimentalphysik, Vol. 25, pt. 3, Leipzig: Akademische Verlagsgesellschaft 1930, p. 1.Google Scholar
  40. [40]
    Dobrin, M. B.: Introduction to Geophysical Prospecting, 2nd ed., New York: McGraw-Hill 1960.Google Scholar
  41. [41]
    Birch, F., J. F. Schairer and H. C. Spicer (Editors): Handbook of Physical Constants, Geological Society of America Special Paper 36, 1942.Google Scholar
  42. [42]
    Protodyakonov, M. M.: Methods of Studying the Strength of Rocks, used in the U.S.S.R., International Symposium on Mining Research, Vol. 2, New York: Pergamon Press 1962, p. 649.Google Scholar
  43. [43]
    Griffith, J. H.: Physical Properties of Typical American Rocks, Iowa State College of Agriculture, Engineering Experiment Station Bulletin 131, 1937.Google Scholar
  44. [44]
    Obert, L., S.L. Windes and W. I. Duvall: Standardized Tests for Detennining the Physical Properties of Mine Rock, U.S. Bureau of Mines Report of Investigations 3891, 1946.Google Scholar
  45. [45]
    Windes, S. L.: Physical Properties of Mine Rock, Parts I and II, U.S. Bureau of Mines Report of Investigations 4459 and 4727, 1949 and 1950.Google Scholar
  46. [46]
    Blair, B. E.: Physical Properties of Mine Rock, Parts III and IV, U.S. Bureau of Mines Report of Investigations 5130 and 5244, 1955 and 1956.Google Scholar
  47. [47]
    Nicholls, H. R.: In Situ Determination of the Dynamic Elastic Constants of Rock, International Symposium on Mining Research, ed. by G. B. Clark, New York: Pergamon Press 1962, p. 727.Google Scholar
  48. [48]
    Hughes, D.S., and H.J. Jones: Variation of Elastic Moduli of Igneous Rocks with Pressure and Temperature, Bulletin of the Geological Society of America 61, 843 (1950).CrossRefGoogle Scholar
  49. [49]
    Hughes, D. S., and C. Maurette: Variation of Elastic Wave Velocities in Basic Igneous Rocks with Pressure and Temperature, Geophysics 22, 23 (1957). (See also Institut Français du Pétrole et Annales des Combustibles Liquides, Revue 12, 730 (1957).)ADSCrossRefGoogle Scholar
  50. [50]
    Birch, F.: The Velocity of Compressional Waves in Rocks to 10 Kilobars, J. Geophysical Research 65, 1083 (1960);ADSCrossRefGoogle Scholar
  51. [50]a
    Birch, F.: The Velocity of Compressional Waves in Rocks to 10 Kilobars, J. Geophysical Research 66, 2199 (1961).ADSCrossRefGoogle Scholar
  52. [51]
    Bridgman, P. W.: The Physics of High Pressure, London: Bell & Sons 1949.Google Scholar
  53. [52]
    Adams, L. H., and E. D. Williamson: On the Compressibility of Minerals and Rocks at High Pressures, J. of the Franklin Institute 195, 474 (1923).CrossRefGoogle Scholar
  54. [53]
    Rice, M. H., R. G. McQueen and J. M. Walsh: Compression of Solids by Strong Shock Waves, Solid State Physics, Vol. 6, New York: Academic Press 1958, p. 1.Google Scholar
  55. [54]
    Hughes, D. S., and R. G. McQueen: Density of Basic Rocks at Very High Pressures, Transactions of the American Geophysical Union 39, 959 (1958).Google Scholar
  56. [55]
    Lombard, D. B.: The Hugoniot Equation of State of Rocks, Proceedings of the 4th Symposium on Rock Mechanics, 1961. Bulletin of the Mineral Industries Experiment Station, Mining Engineering Series, College of Mineral Industries, Pennsylvania State University. [See also University of California Lawrence Radiation Laboratory (Livermore) Report No. 6311.]Google Scholar
  57. [56]
    Austin, C.F., and J.K. Pringle: Rocks that occur as Brittle Solid Test Materials at the U.S. Naval Ordnance Test Station, China Lake, California, NAVWEPS Report 7928, NOTS TP 2955, July 1962.Google Scholar
  58. [57]
    Cunningham, D. M., and W. Goldsmith: Short-time Impulses produced by Longitudinal Impact, Proceedings of the Society for Experimental Stress Analysis 16, No. 2, 153 (1959).Google Scholar
  59. [58]
    Goldsmith, W., and P. T. Lyman Jr.: The Penetration of Hard-Steel Spheres into Plane Metal Surfaces, J. Appl. Mech. 27, 717 (1960).ADSCrossRefGoogle Scholar
  60. [59]
    Goldsmith, W., and G. W. Norris Jr.: Stresses in Curved Beams due to Transverse Impact, Proceedings of the Third U.S. National Congress of Applied Mechanics, 1958, p. 153.Google Scholar
  61. [60]
    Grosvenor, N. E.: Specimen Proportion Key to Better Compressive Strength Tests, Mining Engineering 15, 31 (1963).Google Scholar
  62. [61]
    Goranson, R. W., D. Bancroft, B. L. Burton, T. Blechar, E. E. Houston, E. F. Gittings and S. A. Landeen: Dynamic Determination of the Compressibility of Metals, J. Appl. Phys. 26, 1472 (1955).ADSCrossRefGoogle Scholar

Copyright information

© Springer Verlag, Berlin / Göttingen / Heidelberg 1964

Authors and Affiliations

  • Werner Goldsmith
    • 1
    • 2
  • Carl F. Austin
    • 1
    • 2
  1. 1.University of CaliforniaBerkeleyUSA
  2. 2.U.S. Naval Ordnance Test StationChina LakeUSA

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