Granular Matter

, Volume 15, Issue 6, pp 849–861 | Cite as

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

  • L. M. Le Pen
  • W. Powrie
  • A. Zervos
  • S. Ahmed
  • S. Aingaran
Original Paper


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.


Ballast Shape Form Statistics Weibull  Scale Roundness Angularity Ellipseness 

List of symbols


Longest dimension


Intermediate dimension


Shortest dimension


Specific gravity

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

Density of water


Mass of particle


Perimeter of object


Equivalent perimeter


Area of object


Equivalent area




Major radius of ellipse


Minor radius of ellipse


Probability density function


Cumulative distribution function



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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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • L. M. Le Pen
    • 1
  • W. Powrie
    • 1
  • A. Zervos
    • 1
  • S. Ahmed
    • 1
  • S. Aingaran
    • 1
  1. 1.University of SouthamptonSouthamptonUK

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