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Dependence of shape on particle size for a crushed rock railway ballast

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Abstract

Laboratory testing of railway ballast poses practical difficulties because the particle size is often too large for most standard apparatus. There are therefore advantages in developing a scaled material whose behavior is representative of the full size material. A first stage in validating such an approach is to investigate whether the particle shape is affected by the change in scale. This paper sets out methods for evaluating form and roundness (aspects of shape) and proposes a new measure for evaluating roundness, termed ellipseness. These methods are then applied to a crushed rock railway ballast over a range of particle sizes. Statistical analysis demonstrates a measurable variation in the distributions of form and roundness with particle size over a range of sieve intervals, although the differences are slight and do not necessarily rule out the use of a scaled material for investigating the factors influencing macro mechanical behavior.

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Abbreviations

L :

Longest dimension

I :

Intermediate dimension

S :

Shortest dimension

\({\varvec{G}}_{{\varvec{s}}}\) :

Specific gravity

\(\varvec{\rho }_{{\varvec{w}}}\) :

Density of water

W :

Mass of particle

\({\varvec{P}}_{{\varvec{o}}}\) :

Perimeter of object

\({\varvec{P}}_{{\varvec{e}}}\) :

Equivalent perimeter

\({\varvec{A}}_{{\varvec{o}}}\) :

Area of object

\({\varvec{A}}_{{\varvec{e}}}\) :

Equivalent area

E :

Ellipseness

a :

Major radius of ellipse

b :

Minor radius of ellipse

PDF :

Probability density function

CDF :

Cumulative distribution function

References

  1. Indraratna, B., Ionescu, D., Christie, H.: Shear behavior of railway ballast based on large-scale triaxial tests. J. Geotech. Geoenviron. Eng. 124, 439–450 (1998)

    Article  Google Scholar 

  2. Anderson, W., Fair, P.: Behavior of railroad ballast under monotonic and cyclic loading. J. Geotech. Geoenviron. Eng. 134, 316 (2008)

    Article  Google Scholar 

  3. Aursudkij, B., McDowell, G.R., Collop, A.C.: Cyclic loading of railway ballast under triaxial conditions and in a railway test facility. Granul. Matter 11, 391–401 (2009)

    Article  Google Scholar 

  4. Cho, G.-C., Dodds, J., Santamarina, J.C.: Particle shape effects on packing density, stiffness and strength: natural and crushed sands. J. Geotech. Geoenviron. Eng. ASCE 132, 591–602 (2006)

    Article  MATH  Google Scholar 

  5. Marachi, N.D., Chan, C.K., Seed, H.B.: Evaluation of properties of rockfill materials. J. Soil Mech. Found. Div. Proc. Am. Soc. Civ. Eng. 98, 95–114 (1972)

    Google Scholar 

  6. Sevi, A.F.: Physical Modeling of Railroad Ballast Using the Parallel Gradation Scaling Technique Within the Cyclical Triaxial Framework. Doctor of Philosophy Ph.D. thesis, Missouri University of Science and Technology (2008)

  7. Harkness, J.: Potential particles for the modelling of interlocking media in three dimensions. Int. J. Numer. Methods Eng. 80, 1573–1594 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Zeller, J., Wullimann, R.: The shear strength of the shell materials for the Go-Schenenalp Dam, Switzerland. In: Proceedings of the 4th Institutional Journal on SMFE London, pp. 399–404 (1957)

  9. Lowe, J.: Shear strength of coarse embankment dam materials. In: Proceedings, 8th Congress on Large dams, pp. 745–761 (1964)

  10. Varadarajan, A., Sharma, K.G., Venkatachalam, K., Gupta, A.K.: Testing and modeling two rockfill materials. J. Geotech. Geoenviron. Eng. ASCE 129, 203–218 (2003)

    Article  Google Scholar 

  11. McDowell, G.R.: Statistics of soil particle strength. Geotechnique 51, 90 (2001)

    Google Scholar 

  12. Frossard, E., Hu, E., Dano, C., Hicher, P.-Y.: Rockfill shear strength evaluation: a rational method based on size effects. Geotechnique 62, 415–427 (2012)

    Article  Google Scholar 

  13. Hertz, H.R.: Miscellaneous Papers. London MacMillan and Co Ltd, MacMillan and Co, New York (1896)

    MATH  Google Scholar 

  14. Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1985)

    Book  MATH  Google Scholar 

  15. Cavarretta, I., Coop, M., O’sullivan, C.: The influence of particle characteristics on the behaviour of coarse grained soils. Geotechnique 60, 413–423 (2010)

    Article  Google Scholar 

  16. Abbireddy, C.: Particle Form and Its Impact on Packing and Shear Behaviour of Particulate Materials. Doctor of Philosophy, University of Southampton (2008)

  17. Barrett, P.J.: The shape of rock particles, a critical review. Sedimentology 27, 291–303 (1980)

    Article  ADS  Google Scholar 

  18. Wadell, H.: Volume, shape and roundness of rock particles. J. Geol. 40, 443–451 (1932)

    Article  ADS  Google Scholar 

  19. Francus, P. (ed.): Image Analysis, Sediments and Paleoenvironments, vol. 7. Springer, The Netherlands (2004)

    Google Scholar 

  20. 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.: Three-dimensional shape analysis of coarse aggregates: new techniques for and preliminary results on several different coarse aggregates and reference rocks. Cem. Concr. Res. 36, 1619–1627 (2006)

    Article  Google Scholar 

  21. Masad, E., Saadeh, S., Al-Rousan, T., Garboczi, E., Little, D.: Computations of particle surface characteristics using optical and X-ray CT images. Comput. Mater. Sci. 34, 406–424 (2005)

    Google Scholar 

  22. Taylor, M.A., Garboczi, E.J., Erdogan, S.T., Fowler, D.W.: Some properties of irregular 3-D particles. Powder Technol. 162, 1–15 (2006)

    Article  Google Scholar 

  23. Quiroga, P.N., Fowler, D.W.: The Effects of Aggregates Characteristics on the Performance of Portland Cement Concrete, Research Report ICAR: 104–1F. International Center for Aggregate Research, ICAR (2004)

  24. Zingg, T.: Contribution to the gravel analysis (Beitrag zur Schotteranalyse). Schweiz. Petrog. Mitt. 15(38–140) (1935)

    Google Scholar 

  25. Blott, S.J., Pye, K.: Particle shape: a review and new methods of characterization and classification. Sedimentology 55, 31–63 (2008)

    Google Scholar 

  26. Sneed, E.D., Folk, R.L.: Pebbles in the lower Colorado River, Texas, a study in particle morphogenesis. J. Geol. 66, 114–150 (1958)

    Article  ADS  Google Scholar 

  27. Pirard, E.: Image measurements. In: Francus, P. (ed.) Image Analysis, Sediments and Paleoenvironments. Kluwer Academic Publishers, Dordrecht (2005)

    Google Scholar 

  28. Abbireddy, C.O.R., Clayton, C.R.I., Schiebel, R.: A method of estimating the form of coarse particulates. Geotechnique 59(6), 493–501 (2009)

    Article  Google Scholar 

  29. Garboczi, E.J.: Three-dimensional mathematical analysis of particle shape using X-ray tomography and spherical harmonics: application to aggregates used in concrete. Cem. Concr. Res. 32(10), 1621–1638 (2002)

    Article  Google Scholar 

  30. Krumbein, W.C.: Measurement and geological significance of shape and roundness of sedimentary particles. J. Sedim. Petrol. 11, 64–72 (1941)

    Article  Google Scholar 

  31. Krumbein, W.C., Sloss, L.L.: Stratigraphy and Sedimentation. W. H. Freeman and Company, San Francisco (1963)

    Google Scholar 

  32. Pirard, E.: Shape processing and analysis using the calypter. J. Microsc. 175(3), 214–221 (1994)

    Google Scholar 

  33. Mediacy (2011) Image Pro Plus webpage: http://www.mediacy.com/index.aspx?page=IPP Accessed March 2011

  34. Ramanujan, S.: Modular equations and approximations to \(\pi \). Q. J. Pure Appl. Math. 45, 350–372 (1913–1914)

    Google Scholar 

  35. Almkvist, G., Berndt, B.: Gauss, Landen, Ramanujan, the arithmeticgeometric mean, ellipses, and the Ladies Diary. Am. Math. Mon. 95, 585–608 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  36. Corder, G. W., Foreman, D. I.: Nonparametric Statistics for Non-statisticians, 1st edn. Wiley, Hoboken (2009)

  37. Weibull, W.: A statistical distribution function of wide applicability. J. Appl. Mech. 18, 293–297 (1951)

    MATH  Google Scholar 

  38. Mathworks: Matlab [Online]. Available: http://www.mathworks.co.uk/products/matlab/ (2012). Accessed May 2012

  39. Houlsby, G.T.: Potential particles: a method for modelling non-circular particles in DEM. Comput. Geotech. 36(6), 953–959 (2009)

    Article  Google Scholar 

  40. Radjaï, F., Dubois, F. (eds.): Discrete Numerical Modeling of Granular Materials: Hardcover, Wiley-Iste, ISBN 978-1-84821-260-2 (2011)

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Acknowledgments

This research was facilitated by a grant from the Engineering and Physical Sciences Research Council for the project titled “Development and role of structure in railway ballast” (Reference: EP/F062591/1). We also acknowledge the work of Ben Powrie in carrying out particle imaging and Andrew Cresswell for his contributions to the original research proposal.

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Authors and Affiliations

  1. University of Southampton, Southampton, Hampshire, UK

    L. M. Le Pen, W. Powrie, A. Zervos, S. Ahmed & S. Aingaran

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  1. L. M. Le Pen
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  2. W. Powrie
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Correspondence to L. M. Le Pen.

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Le Pen, L.M., Powrie, W., Zervos, A. et al. Dependence of shape on particle size for a crushed rock railway ballast. Granular Matter 15, 849–861 (2013). https://doi.org/10.1007/s10035-013-0437-5

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