The sand specimens analysed here were then tested in triaxial compression under a cell confine-421
ment of 100 kPa (Andò, 2013). The stress level applied in these tests is well below that required 422
for breakage and indeed no breakage was visible in tomography. Using a reduced subset of grains 423
(2000) a check was made on the evolution of shape parameters during the triaxial test. The sum-424
mary statistics for some parameters at the final state are reported in Table 12. The averages and 425
standard deviations remain practically unchanged when compared with the initial values (Table 426
5), particularly for the harder Hostun sand. Minor changes are noted in skew, a statistic that is 427
highly sensitive to changes at the extremes of the distribution. A tiny decrease in particle size is 428
detected in Caicos. These very small changes are consistent with previous work (e.g. Altuhafi and 429
True Sphericity 0.82 0.95
Flatness index 0.73 0.84
Elongation index 0.76 0.80
Intercept sphericity 0.74 0.81
Operational Sphericity 0.58
Convexity 0.77 0.93
Alshibli Sphericity 1.96 0.86
Table 12: Statistics of the 3D shape descriptors for the two sands at the critical state on 2000 grains 432
Conclusion
433
Measuring how different a sand grain is from a sphere is interesting for a variety of purposes. The 434
sphericity measure proposed by Wadell (1932), true sphericity, was obtained for all grains in two 435
different sand specimens, totalling more than 100 thousand measurements. Together, the values 436
acquired cover the most likely range of this parameter in non-microporous soils. Within the size 437
range explored, true sphericity is independent of particle size. True sphericity appears to be well 438
correlated with 3D convexity and, more usefully, with a 2D measure, perimeter sphericity. This 439
last correlation is sensitive to the particle orientation when the 2D image is acquired, being much 440
stronger when maximum particle projection is used than when random orientation is employed.
441
The traditional Krumbein-Sloss measure of sphericity is poorly correlated with true sphericity.
442 443
Acknowledgments. The work here described has been supported by the Spanish Ministry of 444
Economy through grants BIA2014-59467-R and BIA2017-84752-R. The authors are grateful to 445
Prof. Cino Viggiani for his encouragement.
446
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