Skip to main content
Log in

Dynamic properties of hardened paste, mortar and concrete

  • Published:
Matériaux et Construction Aims and scope Submit manuscript

Abstract

The dynamic moduli and the damping properties of hardened paste, mortar matrix and concrete prisms excited in the fundamental longitudinal, flexural and torsional vibrations are presented. The effects on dynamic properties of curing conditions, water-cement and aggregate-cement ratios, the type of aggregate, mode of vibration and of the presence of rigid inclusions in a relatively soft matrix are investigated. The stress-strain behaviour and the mechanism of damping of cementitious materials are discussed. Relations between dynamic moduli and strength, between damping capacity and compressive strength, and between dynamic moduli and the properties of the constituents are presented.

Résumé

On étudie les modules dynamiques et les caractéristiques d'amortissement de la pâte durcie, du mortier et des prismes de béton sollicités par des vibrations longitudinales, de flexion et de torsion aux fréquences fondamentales. On considère les effets sur les propriétés dynamiques des conditions de conservation, des rapports eau/ciment et agrégat/ciment, du type d'agrégat, du mode de vibration et de la présence d'inclusions rigides dans une matrice relativement molle.

Les modules dynamiques des matériaux liants croissent avec le vieillissement et décroissent avec l'augmentation de la teneur en eau, mais le décrément logarithmique décroît avec le vieillissement et croît avec la teneur en eau. L'addition de sable à la pâte et de gros agrégat au mortier augmente les modules dynamiques mais diminue ensuite la capacité d'amortissement, la vitesse de variation dépendant de la teneur en eau et de la quantité et du type d'agrégat.

Le séchage diminue à la fois le module dynamique et le décrément logarithmique, mais la variation du module élastique est beaucoup plus failble que celle de l'amortissement. La diminution est en partie un processus irréversible et généralement est plus faible pour le mortier que pour le béton. Les résultats montrent qu'il est douteux que les propriétés des liants puissent dépendre uniquement de leurs propriétés de résistance pour tous les composants.

Les modules de résonance longitudinalement et en flexion sont pour les liants à peu près les mêmes dans les éprouvettes humides, tandis que le module de cisaillement est environ de 40 à 45% du module de Young correspondant. L'amortissement est plus fort en vibration longitudinale et moindre pour les vibrations de torsion. On montre que l'amortissement dans les matériaux liants dépend avant tout de la teneur en eau et qu'il résulte d'une combinaison complexe d'effets de viscosité, de frottement et de réactions de l'état solide. L'amortissement se produit surtout dans le mortier, en partie aux interfaces, et dans une moindre mesure dans l'agrégat.

Les relations entre contrainte et déformation, module dynamique et résistance, entre amortissement et résistance à la compression, et entre le module dynamique et les propriétés des constituants sont examinées.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Grime, G.The determination of Young's modulus for building materials by a vibration method. Philosophical Magazine, Series 7, vol. 20, No 132, pp. 304–310, Aug. 1935.

    Google Scholar 

  2. Ide, J. M.Some dynamic methods for determination of Young's modulus. Review of Scientific Instruments, vol. 6, pp. 296–298. Oct. 1935.

    Article  Google Scholar 

  3. Grime, G. andEaton, J. E.The determination of Young's modulus by flexural vibration, Philosophical Magazine, Series 7, vol. 23, No 152, pp. 96–99, Jan. 1937.

    Google Scholar 

  4. Obert, L.Sonic method of determining the modulus of elasticity of building materials under pressure. Proc. American Society for Testing Materials, vol. 39, pp. 987–998, 1939.

    Google Scholar 

  5. Thompson, W. T.Measuring changes in physical properties of concrete by the dynamic method, Proc. American Society for Testing Materials, vol. 40, pp. 1113–1129, 1940.

    Google Scholar 

  6. Obert, L., andDuvall, W. I.Discussion of dynamic methods of testing concrete with suggestions for standardization. Proc. American Society for Testing Materials, vol. 41, pp. 1053–1071, 1941.

    Google Scholar 

  7. Anderson, J., Nerenst, P., andPlum, N. M.The non-destructive testing of concrete with special reference to the wave-velocity method. Building Research Report No 3, The Danish National Institute of Building Research, Copenhagen, pp. 80, 1950.

    Google Scholar 

  8. Kesler, C. E. andHiguchi, Y.Problems in the sonic testing of plain concrete. RILEM International Symposium on the Non-destructive Testing of Materials and Structures, Vol. 1, Paper No A4, pp. 45–53, Paris 1953.

    Google Scholar 

  9. Kesler, C. E. andChang, T. S.A review of sonic methods for the determination of mechanical properties of solid materials. ASTM Bulletin No 225, pp. 40–46, Oct. 1957.

    Google Scholar 

  10. Spinner, S. andTefft, W. E.A method for determining mechanical resonance frequencies and for calculating elastic moduli from these frequencies. Proc. American Society for Testing Materials, vol. 61, pp. 1212–1238, 1961.

    Google Scholar 

  11. Jones, R.Non-destructive testing of concrete, Cambridge University Press, pp. 104, 1962.

  12. Whitehurst, E. A.Evaluation of concrete properties from sonic tests. ACI Monograph No 2, American Concrete Institute, pp. 94, 1966.

  13. Malhotra, V. M.Non-destructive methods for testing concrete. Mines Branch Monograph 875, Department of Energy, Mines and Resources, Ottawa, pp. 66, 1968.

    Google Scholar 

  14. Non-destructive testing of concrete. RILEM Technical Comittee, Chairman's Report, RILEM Materials and Structures, vol. 2, No 10, pp. 251–267, July–Aug. 1969.

  15. Courbon, J.Vibrations des poutres, Annales de l'Institut Technique du Bâtiment et des Travaux Publics, No 262, octobre 1969, pp. 1539–1570.

    Google Scholar 

  16. Ide, J. M.Comparison of statically and dynamically determined Young's modulus of rocks, Proc. National Academy of Sciences of the U.S.A., vol. 22, No 2, pp. 81–92, 1936.

    Article  Google Scholar 

  17. Ide, J. M.The elastic properties of orcks: a correlation of theory and experiment. Proc. National Academy of Sciences of the U.S.A., vol. 22, pp. 482–496, 1936.

    Article  Google Scholar 

  18. Hornibrook, F. B.Application for sonic method to freezing and thawing studies of concrete. ASTM Bulletin, no 101, pp. 5–8, dec. 1939.

    Google Scholar 

  19. Willis, T. F. andDe Reus, M. E.Discussion on measuring changes in physical properties of concrete by the dynamic method. Proc. American Society for Testing Materials, vol. 40, pp. 1123–1129, 1940.

    Google Scholar 

  20. Long, B. G. andKurtz, H. J.Effect of curing methods upon the durability of concrete as measured by changes in the dynamic modulus of elasticity. Proc. American Society for Testing Materials, vol. 43, pp. 1051–1068, 1943.

    Google Scholar 

  21. Batchelder, G. M. andLewis, D. W.Comparison of dynamic methods of testing concretes subjected to freezing and thawing. Proc. American Society for Testing Materials, vol. 53, pp. 1053–1068, 1953.

    Google Scholar 

  22. Rayleigh, J. W.Theory of Sound, Dover Press, New York, 2nd Edition, 1945.

    Google Scholar 

  23. Bancroft, D.The velocity of longitudinal waves in cylindrical bars. Physical Review vol. 59, No 7, Second Series, pp. 588–593, April 1, 1941.

    Article  Google Scholar 

  24. Kolsky, H.The propagation of longitudinal elastic waves along cylindrical bars. Philosophical Magazine, vol. 45, pp. 712–725, 1954.

    Google Scholar 

  25. Mason, W. P.The motion of a bar vibrating in flexure, including the effects of rotary and laterial inertia. Jl of the Acoustical Society of America, vol. 6, No 4, pp. 246–249, April 1935.

    Article  MATH  Google Scholar 

  26. Thomson, W. T.The effect of rotatory and lateral inertia on flexural vibration of prismatic bars. Jl. of the Acoustical Society of America, vol. 11, no 2, pp. 198–204, Oct. 1939.

    Article  MATH  MathSciNet  Google Scholar 

  27. Pickett, G.Equations for computing elastic constants from flexural and torsional resonant frequencies of vibration of prisms and cylinders. Proc. American Society for Testing Materials, vol. 45, pp. 847–865, 1945.

    Google Scholar 

  28. Spinner, S., Reichard, T. W. andTefft, W. E.A comparison of experimental and theoretical relations between Young's modulus and the flexural and longitudinal resonance frequencies of uniform bars. Jl of Research, National Bureau of Standards, vol. 64A, No 2, pp. 147–155, March–April 1960.

    Google Scholar 

  29. Tefft, W. E.Numerical solution of the frequency equations for the flexural vibration of cylindrical rods. Jl of Research, National Bureau of Standards, Vol. 64B, No 4, pp. 237–242, Oct–Dec. 1960.

    MathSciNet  Google Scholar 

  30. Davies, R. M.The frequency of longitudinal and torsional vibration of unloaded and loaded bars. Philosophical Magazine, Series 7, vol. 25, No 167, pp. 364–386, Feb. 1938.

    MATH  Google Scholar 

  31. Spinner, S. andValore, R. C.Comparison of theoretical and empirical relations between the shear modulus and torsional resonance frequencies for bars of rectangular cross-section. Jl of Research, National Bureau of Standards, vol. 60, No 5, pp. 459–464, May 1958.

    MATH  Google Scholar 

  32. Tefft, W. E. andSpinner, S.Torsional resonance vibrations of uniform bars of square cross-section. Jl of Research, National Bureau of Standards, vol. 65A, No 3, pp. 167–171 May–June 1961.

    Google Scholar 

  33. British Standard B.S. 1881–1952:Methods of Testing Concrete, British Standards Institution, London.

    Google Scholar 

  34. Standard Method of test for fundamental transverse, longitudinal and torsional frequencies of concrete specimens. ASTM Standard C 215–60, 1968 Book of ASTM Standards, Part 10, pp. 155–159.

  35. Brunarski, L.Recommendations for the use of resonance methods for testing concrete, 1— Resonance frequency measurements, RILEM Materials and Structures, vol. 2, No 10, pp. 269–273, July–Aug. 1969.

    Google Scholar 

  36. Lethersich, W. andPelzer, H.The measurement of the cœfficient of internal friction of solid rods by a resonance method. British Jl of Applied Physics, vol. 1, pp. 18–22, Jan. 1950.

    Article  Google Scholar 

  37. Jones, R.The theory and measurement of the elastic constants and the internal friction of road materials by a longitudinal vibration method. Road Research Laboratory Note No RN 1570 RJ, pp. 5, June 1951.

  38. British Standard B.S. 812: 1967:Methods for sampling and testing of mineral aggregates sands and fillers, British standards institution, London.

    Google Scholar 

  39. Powers, T. C.The non evaporable water content of hardened Portland-cement paste— its significance for concrete research and its method of determination. ASTM Bulletin No 158, pp. 68–76, may 1949.

    Google Scholar 

  40. Klieger, P.Long-time study of cement performance in concrete: Chapter 10— Progress Report on strength and elastic properties of concrete. Jl American Concrete Institute, Proc. vol. 54, No 6, pp. 481–504, dec. 1957.

    Google Scholar 

  41. Bennett, E. W. andKhilji, Z. M.The effect of some properties of the coarse aggregate in hardened concrete. Jl of the British Granite and Whinstone Federation, vol. 3, no 2, pp. 17–28 Autumn 1963, and vol. 4, No 1, pp. 17–24, Spring 1964.

    Google Scholar 

  42. Anson, M.An investigation into a hypothetical deformation and failure mechanism for concrete. Magazine of Concrete Research, vol. 16, no 47, pp. 73–82, June, 1964.

    Google Scholar 

  43. Swamy, R. N.Aggregate-matrix interaction in concrete systems. Paper 31, International Conference on Structure, Solid Mechanics and Engineering Design in Civil Engineering Materials, University of Southampton, April 1969.

  44. Larue, H. A.Modulus of elasticity of aggregates and its effect on concrete. Proc. American Society for Testing Materials, vol. 46, pp. 1298–1309, 1946.

    Google Scholar 

  45. Kesler, C. E. andHiguchi, Y.Determination of compressive strength of concrete by using its sonic properties Proc. American Society for Testing Materials, vol. 53, pp. 1044–1052, 1953.

    Google Scholar 

  46. Chefdeville, M. J.Nouvelles méthodes pour l'évaluation de la qualité du béton par la mesure de la vitesse de propagation du son. Deuxième partie: Application de la méthode à l'estimation de la qualité du béton, RILEM Bulletin, No 15, pp. 61–78, Aug. 1953.

    Google Scholar 

  47. Kaplan, M. F.Flexural and compressive strength of concrete as affected by the properties of coarse aggregates. Jl American Concrete Institute, Proc. vol. 55, pp. 1193–1208, May 1959.

    Google Scholar 

  48. Stanton, T. E.Tests comparing the modulus of elasticity of Portland cement concrete as determined by the dynamic (sonic) and compression (secant at 1000 psi) methods, ASTM Bulletin, No 131, pp. 17–20, Dec. 1944.

    Google Scholar 

  49. Wright, P. J. F.A comparison of two standard methods of determining the elastic modulus of concrete. Road Research Laboratory Note CC. 372, pp. 8, June 1954.

    Google Scholar 

  50. Philleo, R. E.Comparison of results of three methods for determining Young's modulus of elasticity of concrete. Jl American Concrete Institute, Proc. vol. 51, pp. 461–469, Jan. 1955.

    Google Scholar 

  51. Witte, L. P., andPrice, W. H.Discussion on Tests comparing the modulus of elasticity of Portland cement concrete as determined by the dynamic (sonic) and compression (secant at 1000 psi) methods. ASTM Bulletin, No 131, pp. 20–22, Dec. 1944.

    Google Scholar 

  52. Swamy, R. N.Inelastic deformation of concrete. Paper presented at the Highway Research Board Symposium on Deformations of Concrete, January 1970.

  53. King, J. W. H.Discussion on: Poisson's Ratio of concrete: a comparison of dynamic and static measurements. Magazine of Concrete Research, vol. 8, No 22, pp. 39–40, March 1956.

    Google Scholar 

  54. Takabayashi, T.Comparison of dynamic Young's modulus and static Young's modulus for concrete. RILEM International Symposium on Non-destructive Testing of Materials and Structures, Paris, 1953, vol. 1, Paper no A-3, pp. 34–44.

  55. Simmons, J. C.Poisson's ratio of concrete: a comparison of dynamic and static measurements. Magazine of Concrete Research, vol. 7, no 20, pp. 61–68, July 1955.

    Google Scholar 

  56. Sharma, M. R. andGupta, B. L.Sonic modulus as related to strength and static modulus of high strength concrete, Indian Concrete Journal, Vol. 34, No 4 pp. 139–141 April 1960.

    Google Scholar 

  57. Jones, R.The effect of frequency on the dynamic modulus and damping coefficient of concrete, Magazine of Concrete Research vol. 9, No 26, pp. 69–72, Aug. 1957.

    Google Scholar 

  58. Kaplan, M. F.Ultrasonic pulse velocity, dynamic modulus of elasticity, Poisson's ratio and the strength of concrete made with thirteen different coarse aggregates. RILEM Bulletin No 1, pp. 58–73, March 1959.

    Google Scholar 

  59. Axon, E. O., Willis, T. F. andReagel, F. V.Effect of air-entrapping Portland cement on the resistance to freezing and thawing of concrete containing inferior coarse aggregate. Proc. American Society for Testing Materials, vol. 43, pp. 981–1000, 1943.

    Google Scholar 

  60. Preece, E. F.The use of the dynamic modulus of elasticity in predicting the 28-day flexural strength of concrete. Proc. American Society for Testing Materials, vol. 46, pp. 1311–1319, 1946.

    Google Scholar 

  61. L'hermite, R.La résistance du béton et sa mesure. Compléments. Annales de l'Institut Technique du Bâtiment et des Travaux Publics, New Series, no 114, pp. 3–11, Jan. 1950.

    Google Scholar 

  62. Takano, S.Determination of concrete strength by a non-destructive method. RILEM International Symposium on Non-destructive Testing of Materials and Structures, Paris 1953, vol. 1, Paper A-7, pp. 61–67.

  63. Higuchi, Y.—Studies presented by Y. Higuchi, RILEM International Symposium on Nondestructive Testing of Materials and Structures, Paris, 1953, vol. 1, paper A-8, pp. 69–70.

  64. Kilian, G.Evolution of the mechanical and elastic properties of concretes as a function of age, the proportion of binder and the nature of the aggregates, RILEM International Symposium on Non-destructive Testing of Materials and Structures, Paris 1953, vol. 1, paper A-11, pp. 75–79.

  65. Kameda, Y., Awaya, K. andYokayama, I.The non-destructive testing of concrete, RILEM International Symposium on Non-destructive Testing of Materials and Structures, Paris 1953, vol. 2, Paper A-20, pp. 209–215.

  66. Shrivastava, J. P. andSen, B.Factors affecting resonant frequency and compressive strength of concrete. Indian Concrete Journal, vol. 37, no 1, pp. 27–31, Jan. 1963, no 3, pp. 105–110, March 1963.

    Google Scholar 

  67. Jones, R. andWelch, G. B.The damping properties of plain concrete: effect of composition and relations with elasticity and strength, Road Research Laboratory Report LR 111, pp. 16, 1967.

    Google Scholar 

  68. Girgrah, M. andKesler, C. E.A study of the rheological and damping properties of concrete, Theoretical and Applied Mechanics Report no 173, University of Illinois, pp. 35, Aug. 1960.

  69. Cole, D. G.The damping capacity of hardened cement paste, mortar and concrete specimens, Proc. of Symposium on Vibration in Civil Engineering, April 1965, Butterworths, London, 1966, pp. 235–247.

    Google Scholar 

  70. Cole, D. G. andSpooner, D. C.The damping capacity of concrete, Proc. International Conference on the Structure of Concrete, London, Sept. 1965, Cement and Concrete Association, pp. 217–225, 1968.

  71. Elvery, R. H.—Private communication.

  72. Wiebenga, J. G.Evaluation of the cube strength of concrete with the pulse velocity and the damping constant, Report NR. BI-64-60/12-1-33, p. 5. Institute TNO for Building Materials and Building Structures, Delft Sept. 1964.

    Google Scholar 

  73. Kreijger, P. C.Further analysis of the evaluation of the compressive strength of concrete, derived from pulse velocity and damping constant, Report NR. BI-64-61/12-1-33, p. 4, Institute T.N.O. for Building Materials and Building Structures, Delft, Sept. 1964.

    Google Scholar 

  74. Baker, L. S. andKesler, C. E.A study of the damping properties of mortar, Theoretical and Applied Mechanics Report no 598, University of Illinois, pp. 54, Aug. 1961.

  75. Goldsmith, W., Polivka, M. andYang, T.Dynamic behaviour of concrete, Experimental Mechanics, vol. 6, pp. 65–79, Feb. 1966.

    Article  Google Scholar 

  76. Pozzo, E.Le forze smorzanti nella dinamica dei ponti in cemento armato. Indagine e risultati sperimentalli, Il Cemento, vol. 58, no 7, pp. 5–13, July 1961, No 8, pp. 3–13. Aug. 1961.

    Google Scholar 

  77. Cole, D. G. andSpooner, D. C.The damping capacity of hardened cement paste and mortar in specimens vibrating at very low frequencies, Proc. American Society for Testing Materials, vol. 65, pp. 661–667, 1965.

    Google Scholar 

  78. Swamy, R. N.The damping mechanisms in cementitious systems, Paper to be presented at the Conference on Dynamic Waves in Civil Engineering, July 1970. Institution of Civil Engineers, London.

  79. Vaishnav, R. N. andKesler, C. E.Correlation of creep of concrete with its dynamic properties, Theoretical and Applied Mechanics Report No 603, University of Illinois, Sept. 1961, pp. 207.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Swamy, N., Rigby, G. Dynamic properties of hardened paste, mortar and concrete. Mat. Constr. 4, 13–40 (1971). https://doi.org/10.1007/BF02473927

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02473927

Keywords

Navigation