The relationship between the fractal dimension and shape properties of particles
 Seracettin Arasan,
 Suat Akbulut,
 A. Samet Hasiloglu
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Due to their irregularity, the shape of particles is not accurately described by Euclidian geometry. However, fractal geometry uses the concept of fractal dimension, D_{R}, as a way to describe the shape of particles. In this study, the fractal dimensions and shape properties of particles were determined using image analysis. Exponential relationships between the fractal dimension and roundness, sphericity, angularity, convexity were described. A set of empirical correlations were also presented which clearly demonstrated the link between fractal dimension and shape properties of particles. Additionally, a new classification chart proposed for use in describing and comparing particle shape and fractal dimension.
 Akbulut, S. (2002) Fractal Dimensioning of sand grains using image analysis system. Pamukkale University Journal of Engineering Science 8: pp. 329334
 AlRousan, T., Masad, E., Tutumluer, E., Pan, T. (2007) Evaluation of image analysis techniques for quantifying aggregate shape characteristics. Construction and Building Materials 21: pp. 978990 CrossRef
 Alshibli, K. A., Alsaleh, M. I. (2004) Characterizing surface roughness and shape of sands using digital microscopy. Journal of Computing in Civil Engineering 18: pp. 3645 CrossRef
 Arasan, S. and Akbulut, S. (2008). “Determination of grainsize distribution of soils wýth image analysis.” 12. National Soil Mechanic and Foundation Engineering Congress, pp. 323–332 (in Turkish with an English summary).
 Arasan, S., Yener, E., Hattatoglu, F., Hinislioglu, S., Akbulut, S. (2010) The correlation between shape of aggregate and mechanical properties of asphalt concrete: Digital image processing approach. Road Materials and Pavement Design 12: pp. 239262 CrossRef
 Arasan, S., Akbulut, S., Hasiloglu, A.S. (2010) Shape properties of natural and crushed aggregate using image analysis. International Journal of Civil and Structural Engineering 1: pp. 221233
 Arasan, S., Akbulut, S., and Hasiloglu, A. S. (2010c). “Effect of particle roundness on the maximum and minimum void ratios of granular soils.” 13. National Soil Mechanic and Foundation Engineering Congress, (in Turkish with an English summary).
 Arasan, S., Yener, E., Hattatoglu, F., Akbulut, S., Hinislioglu, S. (2010) The relationship between the fractal dimension and mechanical properties of asphalt Concrete. International Journal of Civil and Structural Engineering 1: pp. 165170
 Arasan, S., Akbulut, S., and Hasiloglu, A. S. (2010e). “Fractal dimension and void ratios of granular materials.” (under review).
 Barrett, P. J. (1980) The shape of rock particles, a critical review. Sedimentology 27: pp. 291303 CrossRef
 Chan, C. Y., Page, W. P. (1997) Particle fractal and load effects on internal friction in powders. Powder Technology 90: pp. 259266 CrossRef
 Cho, G. C., Dodds, J., Santamarina, J. C. (2006) Particle shape effects on packing density, stiffness and strengthnatural and creshed sands. Journal of Geotechnical and Geoenvironmental Engineering 132: pp. 591602 CrossRef
 Cox, E. A. (1927) A method for assigning numerical and percentage values to the degree of roundness of sand grains. Journal of Paleontology 1: pp. 179183
 Cubrinovski, M., Ishihara, K. (1999) Empirical correlation between SPT Nvalues and relative density for sandy soils. Soils and Foundations 40: pp. 103119
 Cubrinovski, M., Ishihara, K. (2002) Maximum and minimum void ratio characteristics of sands. Soils and Foundations 42: pp. 6578
 Erdogan, S. T. (2005). Determination of aggregate shape properties using Xray tomographic methods and the effect of shape on concrete rheology. PhD Dissertation, University of Texas at Austin.
 Erdogan, S. T., Quiroga, P. N.,., Fowler, D. W., Saleh, H. A., Livingston, R. A., Garboczi, E. J., Ketcham, P. M., Hagedorn, J. G., Satterfield, S. G. (2006) Threedimensional shape analysis of coarse aggregates: New techniques for and preliminary results on several different coarse aggregates and reference rocks. Cement and Concrete Research 36: pp. 16191627 CrossRef
 Gori, U., Mari, M. (2001) The correlation between the fractal dimension and internal friction angle of different granular materials. Soils and Foundations 41: pp. 1723
 Hasiloglu, A. S., Arasan, S., and Akbulut, S. (2010). “Determination of fractal dimensions of coarse grained soils with image analysis.” 9 ^{th} International Congress on Advances in Civil Engineering, Trabzon, Turkey.
 Holubec, I. and D’Appolonia, E. (1973). Effect of particle shape on the engineering properties of granular soils, ASTM Special Technical Publication, pp. 304–318.
 Hoyez, B. (1994) The roughness of sand grains: an application of Fourier analysis and of fractal dimension. Ann. Soc. Géol. du Nord 3: pp. 7383
 Huber, G. A., Heiman, G. H. (1987) Effect of asphalt concrete parameters on rutting performance: A field investigation. Proceedings of the Association of Asphalt Paving Technologist 56: pp. 3361
 Hudson, B. (1999). “Modification to the fine aggregate angularity test.” Proceedings, Seventh Annual International Center for Aggregates Research Symposium, Austin, TX.
 Hyslip, J. P., Vallejo, L. E. (1997) Fractal analysis of roughness and size distribution of granular materials. Engineering Geology 48: pp. 231244 CrossRef
 Jamkar, S. S., Rao, C. B. K. (2004) Index of aggregate particle shape and texture of coarse aggregate as a parameter for concrete mix proportioning. Cement and Concrete Research 34: pp. 20212027 CrossRef
 Kalcheff, I. V., Tunnicliff, D. G. (1982) Effects of crushed stone aggregate size and shape on properties of asphalt concrete. Proceedings of Association of Asphalt Paving Technologists 51: pp. 453483
 Kaye, B. H. (1978) Specification of the ruggedness and/or texture of a fine particle profile by its fractal dimension. Powder Technology 21: pp. 116 CrossRef
 Kennedy, S. K., Lin, W.H. (1992) A comparison of Fourier and fractal techniques in the analysis of closed forms. Journal of Sedimentary Petrology 62: pp. 842848
 Kolay, E., Kayaball, K. (2006) Investigation of the effect of aggregate shape and surface roughness on the slake durability index using the fractal dimension approach. Engineering Geology 86: pp. 271284 CrossRef
 Krumbein, W. C. (1941) Measurement and geological significance of shape and roundness of sedimentary particles. Journal of Sedimentary Petrology 11: pp. 6472
 Krutz, N. C., Sebaaly, P. E. (1993) Effect of aggregate gradation on permanent deformation of asphaltic concrete. Proceedings of the Association of Asphalt Paving Technologists 62: pp. 450473
 Kuo, C. Y., Freeman, R. B. (2000) Imaging indices for quantification of shape, angularity, and surface texture of aggregates. Transportation Research Record 1721: pp. 5765 CrossRef
 Kuo, C. Y., Frost, J. D., Lai, J. S., Wang, L.B. (1996) Threedimensional image analysis of aggregate particles from orthogonal projections. Transportation Research Record 1526: pp. 98103 CrossRef
 Kwan, A. K. H., Mora, C. F., Chan, H. C. (1999) Particle shape analysis of coarse aggregate using digital image processing. Cement and Concrete Research 29: pp. 14031410 CrossRef
 Lade, P. V., Liggio, C. D., Yamamuro, J. A. (1998) Effects of nonplastic fines on minimum and maximum void ratios of sand. Geotechnical Testing Journal 21: pp. 336347 CrossRef
 Li, M. C., Kett, I. (1967) Influence of coarse aggregate shape on the strength of asphalt concrete mixtures. Highway Research Record 178: pp. 93106
 Mandelbort, B. B. (1977). Fractals form, change and dimension, Freeman, San Francisco, p. 273.
 Mandelbrot, B. B. (1983) The fractal geometry of nature. W.H. Freeman, San Francisco, CA
 Masad, E., Olcott, D., White, T., Tashman, L. (2001) Correlation of fine aggregate imaging shape indices with asphalt mixture performance. Transportation Research Record 1757: pp. 148156 CrossRef
 Masad, E. (2004) Aggregate Imaging System (AIMS) basics and applications. Texas Department of Transportation and Federal Highway Administration, Washington, D.C.
 Masad, E., Button, J. (2000) Unified imaging approach for measuring aggregate angularity and texture. Journal of ComputerAided Civil and Infrastructure Engineering 15: pp. 273280 CrossRef
 Masad, E., Saadeh, S., Rousan, T. A., Garboczi, E., Little, D. (2005) Computations of particle surface characteristics using optical and Xray CT images. Computational Materials Science 34: pp. 406424 CrossRef
 Miura, K., Maeda, K., Furukawa, M., Toki, S. (1997) Physical characteristics of sands with different primary properties. Soils and Foundations 37: pp. 5364
 Oduroh, P. K., Mahboub, K. C., Anderson, R. M. (2000) Flat and elongated aggregates in superpave regime. Journal of Materials in Civil Engineering 12: pp. 124130 CrossRef
 Ozol, M. A. (1978). Test and properties of concrete aggregates: Chapter 35Shape, surface texture, surface area, and coatings. STP169BEB, 584–628
 Pettijohn, F. J. (1949) Sedimentary rocks. Harper and Brothers, New York
 Powers, M. C. (1953) A new roundness scale for sedimentary particles. Journal of Sedimentary Petrology 23: pp. 117119
 Rao, C., Tutumluer, E. (2000) Determination of volume of aggregates: New imageanalysis approach. Transportation Research Record 1721: pp. 7380 CrossRef
 Rittenhouse, G. (1943) A visual method of estimating twodimensional sphericity. Journal of Sedimentary Petrology 13: pp. 7981
 Russell, R. D., Taylor, R. E. (1937) Roundness and shape of Mississippi River sands. Journal of Geology 45: pp. 225267 CrossRef
 Santamarina, J. C. and Cho, G. C. (2004). “Soil behaviour: The role of the particle shape.” Proceedings Skempton Conference, March, London.
 Shklarsky, E., Livneh, M. (1964) The use of gravels for bituminous mixtures. Proceedings of The Association of Asphalt Paving Technologists 33: pp. 2365
 Stephens, J. E., Sinha, K. C. (1978) Influence of aggregate shape on bituminous mix character. Journal of the Association of Asphalt Paving Technologists 47: pp. 434456
 Topal, T., Sengoz, B. (2005) Determination of fine aggregate angularity in relation with the resistance to rutting of hotmix asphalt. Construction and Building Materials 19: pp. 155163 CrossRef
 Vallejo, L. E. (1995) Fractal analysis of granular materials. Geotechnique 45: pp. 159163 CrossRef
 Vallejo, L. E., Zhou, Y. (1995) The relationship between the fractal dimension and Krumbein’s roundness number. Soils and Foundations 35: pp. 163167
 Xu, Y. F., Sun, D. A. (2005) Correlation of surface fractal dimension with frictional angle at critical state of sands. Geotechnique 55: pp. 691695 CrossRef
 Yilmaz, Y. (2009) A study on the limit void ratio characteristics of medium to fine mixed graded sands. Engineering Geology 104: pp. 290294 CrossRef
 Youd, T. L. (1973). Factors controlling maximum and minimum densities of sands, ASTM Special Technical Publication, pp. 98–112.
 Title
 The relationship between the fractal dimension and shape properties of particles
 Journal

KSCE Journal of Civil Engineering
Volume 15, Issue 7 , pp 12191225
 Cover Date
 20110901
 DOI
 10.1007/s122050111310x
 Print ISSN
 12267988
 Online ISSN
 19763808
 Publisher
 Korean Society of Civil Engineers
 Additional Links
 Topics
 Keywords

 fractal dimension
 particle shape
 roundness
 image analysis
 Industry Sectors
 Authors

 Seracettin Arasan ^{(1)}
 Suat Akbulut ^{(1)}
 A. Samet Hasiloglu ^{(2)}
 Author Affiliations

 1. Dept. of Civil Engineering, Ataturk University, Erzurum, 25240, Turkey
 2. Dept. of Computer Engineering, Ataturk University, Erzurum, 25240, Turkey