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Archives of Civil Engineering

The Journal of Polish Academy of Sciences

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Fractal Dimension for the Characterization of the Porosity of Asphalt Concretes

G. Leonardi
Published Online: 2010-12-09 | DOI: https://doi.org/10.2478/v.10169-010-0018-5


In the design of asphalt mixtures for paving, the choice of components has a remarkable importance, as requirements of quality and durability must be assured in use, guaranteeing adequate standards of safety and comfort.

In this paper, an approach of analysis on the aggregate materials using fractal geometry is proposed. Following an analytical and an experimental approach, it was possible to find a correlation between characteristics of the asphalt concrete (specific gravity and porosity) and the fractal dimension of the aggregate mixtures.

The studies revealed that this approach allows to draw the optimal fractal dimension and, consequently, it can be used to choose an appropriate aggregate gradation for the specific application; once the appropriate initial physical parameters are finalized.

This fractal approach could be employed for predicting the porosity of mixed asphalt concretes, given as input the fractal characteristics of the aggregate mixtures of the concrete materials

Keywords: fractal geometry; porosity; mixture; aggregate; concrete; pavement


  • 1. C. Atzeni, et al., A geometrical fractal model for the porosity and permeability of hydraulic cement pastes, Construction and Building Materials, 2010.Web of ScienceGoogle Scholar

  • 2. D.N. Winslow, The fractal nature of the surface of cement paste, Cement and Concrete Research, 15, pp. 817-824, 1985.CrossrefGoogle Scholar

  • 3. R.A. Livingston, Fractal nucleation and growth model for the hydration of tricalcium silicate, Cement and Concrete Research, 30, pp. 1853-1860, 2000.CrossrefGoogle Scholar

  • 4. D.A. Lange, et al., Image analysis techniques for characterization of pore structure of cement-based materials, Cement and Concrete Research, 24, pp. 841-853, 1994.CrossrefGoogle Scholar

  • 5. O. Panagouli, A. Kokkalis, Skid resistance and fractal structure of pavement surface, Chaos, Solitons & Fractals, 9, pp. 493-505, 1998.CrossrefGoogle Scholar

  • 6. D. Gim´enez, et al., Fractal models for predicting soil hydraulic properties: a review, Engineering Geology, 48, pp. 161-183, 1997.Google Scholar

  • 7. C. Atzeni,et al., A fractal model of the porous microstructure of earth-based materials, Construction and Building Materials, 22, pp. 1607-1613, 2008.CrossrefGoogle Scholar

  • 8. S. Huang,et al., Correlations and characterization of porous solids by fractal dimension and porosity, Physica A: Statistical Mechanics and its Applications, 274, pp. 419-432, 1999.Google Scholar

  • 9. B. Mandelbrot, The fractal geometry of nature: Wh Freeman, 1982.Google Scholar

  • 10. B. Mandelbrot, A. Blumen, Fractal Geometry: What is it, and What Does it do?[and Discussion], Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 423, pp. 3-16, 1989.Google Scholar

  • 11. H. Peitgen,et al., Bausteine des Chaos: Fraktale: Springer Verl.; Klett-Cotta, 1992.Google Scholar

  • 12. H. Peitgen, P. Richter, The beauty of fractals: Springer-Verlag New York, 1986.Google Scholar

  • 13. H. Peitgen,et al., The science of fractal images: Springer New York etc., 1988.Google Scholar

  • 14. J. Feder, P. Bak, Fractals, Physics Today, 42, p. 90, 1989.CrossrefGoogle Scholar

  • 15. A. Anderson, A. McBratney, Soil aggregates as mass fractals, Australian Journal of Soil Research, 33, pp. 757-772, 1995.CrossrefGoogle Scholar

  • 16. F. Bartoli,et al., Structure and self-similarity in silty and sandy soils: the fractal approach, European Journal of Soil Science, 42, pp. 167-185, 1991.CrossrefGoogle Scholar

  • 17. I.M. Young, J.W. Crawford, Fractal structure of soil aggregates: its measurement and interpretation : J Soil Sci V42, N2, June 1991, P187-192, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 28, pp. A336-A336, 1991.Google Scholar

  • 18. M. Rieu, G. Sposito, Fractal fragmentation, soil porosity, and soil water properties: I. Theory, Soil Sci. Soc. Am. J, 55, p. 1, 1991.Google Scholar

  • 19. E. Perrier, et al., Computer construction of fractal soil structures: simulation of their hydraulic and shrinkage properties, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 33, pp. 259A-260A, 1996.Google Scholar

  • 20. A. Kokkalis, O. Panagouli, Fractal Evaluation of Pavement Skid Resistance Variations. I: Surface Wetting, Chaos, Solitons & Fractals, 9, pp. 1875-1890, 1998.CrossrefGoogle Scholar

  • 21. C.R.R., Code de Bonne Pratique pour la Formulation des Enrob´es Bitumineux Denses. Recommandations CRR - R 61/87, ed. Bruxelles, Belgium: Centre de Recherches Routičres, 1987.Google Scholar

  • 22. R. Cominsky,et al., SHRP-A-407. The Superpave Mix Design Manual for New Construction and Overlays, National Research Council, Washington, DC, 1994.Google Scholar

  • 23. J. Goode, L. Lufsey, A new graphical chart for evaluating aggregate gradations, pp. 176-207, 1962.Google Scholar

  • 24. G. Huber, T. Shuler, Providing Sufficient Void Space for Asphalt Cement: Relationship of Mineral Aggregate Voids and Aggregate Gradation, Effects of Aggregates and Mineral Fillers on Asphalt Mixture Performance, 1992. CrossrefGoogle Scholar

About the article

Received: 2010-09-01

Revised: 2010-12-10

Published Online: 2010-12-09

Published in Print: 2010-12-01

Citation Information: Archives of Civil Engineering, ISSN (Online) 1230-2945, DOI: https://doi.org/10.2478/v.10169-010-0018-5.

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© Polish Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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