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A geometry-based algorithm for cloning real grains

Abstract

We introduce a computational algorithm to “clone” the grain morphologies of a sample of real grains that have been digitalized. This cloning algorithm allows us to generate an arbitrary number of cloned grains that satisfy the same distributions of morphological features displayed by their parents and can be included into a numerical Discrete Element Method simulation. This study is carried out in three steps. First, distributions of morphological parameters such as aspect ratio, roundness, principal geometric directions, and spherical radius, called the morphological DNA, are extracted from the parents. Second, the geometric stochastic cloning (GSC) algorithm, relying purely on statistical distributions of the aforementioned parameters, is explained, detailed, and used to generate a pool of clones from its parents’ morphological DNA. Third, morphological DNA is extracted from the pool of clones and compared to the one obtained from a similar pool of parents, and the distribution of volume-surface ratio is used to perform quality control. Then, from these results, the error (mutation) in the GSC process is analyzed and used to discuss the algorithm’s drawbacks, knobs (parameters) tuning, as well as potential improvements.

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References

  1. 1.

    Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Géotechnique 29, 47–65 (1979)

    Article  Google Scholar 

  2. 2.

    Cundall, P.A.: Formulation of a three-dimensional distinct element model—Part I: A scheme to detect and represent contacts in a system composed of many polyhedral blocks. Int. J. Rock Mech. Min. Sci. 25(3), 107–116 (1988)

    Article  Google Scholar 

  3. 3.

    Rothenburg, L., Selvadurai, A.P.S.: A micromechanical definition of the cauchy stress tensor for particular media. In: Selvadurai, A.P.S. (ed.) Mechanics of Structured Media, pp. 469–486. Elsevier, Amsterdam (1981)

    Google Scholar 

  4. 4.

    Peters, J.F., Muthuswasmy, M., Wibowo, J., Tordesillas, A.: Characterization of force chains in granular material. Phys. Rev. E 72, 041397 (2005)

    ADS  Article  Google Scholar 

  5. 5.

    Nitka, M., Bilbie, B., Combe, G., Dascalu, C., Desrues, J.: A micro-macro (DEM-FEM) model of the behavior of granular solids. In: 1st International Symposium on Computational Geomechanics (ComGeo I), pp. 38–48. Juan-les-Pins (2009)

  6. 6.

    Andrade, J.E., Avila, C.F.: Granular element method (GEM): linking inter-particle forces with macroscopic loading. Granul. Matter 14, 1–13 (2012)

    ADS  Article  Google Scholar 

  7. 7.

    Jerves, A.X., Andrade, J.E.: A micro-mechanical study of peak strength and critical state. Int. J. Numer. Anal. Methods Geomech. 40, 1184–1202 (2015)

  8. 8.

    Wang, L., Park, J.Y., Fu, Y.: Representation of real particles for DEM simulation using X-ray tomography. Constr. Build. Mater. 21, 338–346 (2005)

    Article  Google Scholar 

  9. 9.

    Peña, A.A., Lind, P.G., Herrmann, H.J.: Modeling slow deformation of polygonal particles using dem. Particuology 6, 506–514 (2008)

    Article  Google Scholar 

  10. 10.

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

    Article  Google Scholar 

  11. 11.

    Andrade, J.E., Lim, K.-W., Avila, C.F., Vlahinich, I.: Granular element method for computational particle mechanics. Comput. Methods Appl. Mech. Eng. 241–244, 262–274 (2012)

    Article  MATH  Google Scholar 

  12. 12.

    Jerves, A.X., Kawamoto, R.Y., Andrade, J.E.: Effects of grain morphology on critical state: a computational analysis. Acta Geotech. 11, 493–503 (2015)

  13. 13.

    Ashmawy, A.K., Sukumaran, B., Hoang, A.V.: Evaluating the influence of particle shape on liquefaction behavior using discrete element method. In: Proceedings of the Thirteenth International Offshore and Polar Engineering Conference (ISOPE 2003), Honolulu (2003)

  14. 14.

    Garcia, X., Latham, J.-P., Xiang, J., Harrison, J.P.: A clustered overlapping sphere algorithm to represent real particles in discrete element modelling. Geotechnique 59, 779–784 (2009)

    Article  Google Scholar 

  15. 15.

    Kawamoto, R., Andò, E., Viggiani, G., Andrade, J.E.: Level set discrete element method for three-dimensional computations with triaxial case study. J. Mech. Phys. Solids 91, 1–13 (2016)

    ADS  MathSciNet  Article  Google Scholar 

  16. 16.

    Santamarina, J.C., Cho, G.C.: Soil behaviour: the role of particle shape. In: Jardine, R.J., Potts, D.M., Higgins, K.G. (eds.) Advances in Geotechnical Engineering: The Skempton Conference, vol. 1, pp. 604–617. Thomas Telford Ltd, London (2004)

    Google Scholar 

  17. 17.

    Cho, G.C., Dodds, J., Santamarina, J.C.: Particle shape effects on packing density, stiffness, and strength: natural and crushed sands. J. Geotech. Geoenvironmental Eng. 132(5), 591–602 (2006)

  18. 18.

    Wadell, H.: Volume, shape, and roundness of rock particles. J. Geol. 40(5), 443–451 (1932)

    ADS  Article  Google Scholar 

  19. 19.

    Krumbein, W.C.: Measurement and geological significance of shape and roundness of sedimentary particles. J. Sediment. Res. 11(2), 64–72 (1941)

    Google Scholar 

  20. 20.

    Powers, M.C.: A new roundness scale for sedimentary particles. J. Sediment. Res. 23(2), 117–119 (1953)

    Google Scholar 

  21. 21.

    Krumbein, W.C., Sloss, L.L.: Stratigraphy and Sedimentation, 2nd edn. Freeman and Company, San Francisco (1963)

    Google Scholar 

  22. 22.

    Barrett, P.J.: The shape of rock particles, a critical review. Sedimentology 27(3), 291–303 (1980)

    ADS  Article  Google Scholar 

  23. 23.

    Zhou, B., Wand, J.: Random generation of natural sand assembly using micro x-ray tomography and spherical harmonics. Géotech. Lett. 5, 6–11 (2015)

    Article  Google Scholar 

  24. 24.

    Zhou, B., Wang, J., Zhao, B.: Micromorphology characterization and reconstruction of sand particles using micro x-ray tomography and spherical harmonics. Eng. Geol. 184, 126–137 (2015)

    Article  Google Scholar 

  25. 25.

    Vlahinic, I., Ando, E., Viggiani, G., Andrade, J.E.: Towards a more accurate characterization of granular media: extracting quantitative descriptors from tomographic images. Granul. Matter (2013). doi:10.1007/s10035-013-0460-6

    Google Scholar 

  26. 26.

    Rubinstein, R.Y., Kroese, D.P.: Simulation and the Monte Carlo Method, 2nd edn. Wiley, New York (2007)

    Book  MATH  Google Scholar 

  27. 27.

    Mitchell, I.M.: A Toolbox of Level Set Methods (Version 1.1). University of British Columbia (2007)

  28. 28.

    Rabbani, A., Jamshidi, S., Salehi, S.: Determination of specific surface of rock grains by 2d imaging. J. Geolog. Res. 71, 25–32 (2014)

    Google Scholar 

  29. 29.

    Arnepalli, D.N., Shanthakumar, S., Rao, B.H., Singh, D.N.: Comparison of methods for determining specifi-surface area of fine-grained soils. Geotech. Geolog. Eng. 26(2), 121–132 (2008)

    Article  Google Scholar 

  30. 30.

    Man, K.F., Tang, K.S., Kwong, S.: Genetic Algorithms: Concepts and Designs with Disk, 2nd edn. Springer, Secaucus (1999)

    Book  MATH  Google Scholar 

  31. 31.

    Andrade, J.E., Vlahinić, I., Lim, K.-W., Jerves, A.X.: Multiscale ‘tomography-to-simulation’ framework for granular matter: the road ahead. Géotech. Lett. 2, 135–139 (2012)

    Article  Google Scholar 

  32. 32.

    Zhao, J., Li, S., Zou, R., Yu, A.: Dense random packings of spherocylinders. Soft Matter 8(4), 1003–1009 (2012)

    ADS  Article  Google Scholar 

  33. 33.

    Gibson, R.N., Atkinson, R.J.A., Gordon, J.D.M. (eds.): Oceanography and Marine Biology: An Annual Review, vol. 50. CRC Press, Boca Raton, FL (2012)

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Correspondence to José E. Andrade.

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Jerves, A.X., Kawamoto, R.Y. & Andrade, J.E. A geometry-based algorithm for cloning real grains. Granular Matter 19, 30 (2017). https://doi.org/10.1007/s10035-017-0716-7

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Keywords

  • Geometric stochastic cloning algorithm
  • Grain’s morphological parameters
  • Monte Carlo sampling
  • Level sets
  • Discrete element method