Granular Matter

, 21:54 | Cite as

A benchmark strategy for the experimental measurement of contact fabric

  • Max WiebickeEmail author
  • Edward Andò
  • Václav Šmilauer
  • Ivo Herle
  • Gioacchino Viggiani
Original Paper


The mechanics of granular materials can be better understood by experimental measurement of fabric and its evolution under load. X-ray tomography is a tool that is increasingly used to acquire three-dimensional images and thus, enables such measurements. Our previous study on the metrology of interparticle contacts revealed that the most common approaches either fail to accurately measure contact fabric or introduce a strong bias. Methods to improve these measurements (i.e., the detection and orientation of contacts) were proposed and validated. This work develops a strategy to benchmark image analysis tools that can be used for the determination of contact fabric from tomographic images. The discrete element method is used to create and load a reference specimen for which the fabric and its evolution is precisely known. Chosen states of this synthetic specimen are turned into realistic images taking into account inherent image properties, such as the partial volume effect, blur and noise. The application of the image analysis tools on these images validates the findings of the metrological study and highlights the importance of addressing the identified shortcomings, i.e., the systematical over-detection of contacts and the strong bias of orientations when using common watersheds.


Image analysis Fabric Interparticle contacts DEM X-ray CT 



We express our thanks to Félix Bertoni for implementing Kalisphera in C++. Laboratoire 3SR is part of the LabEx Tec 21 (Investissements d’Avenir—Grant Agreement No. ANR-11-LABX-0030). We thank the Center for Information Services and High Performance Computing (ZIH) at TU Dresden for generous allocations of computing resources.


The research leading to these results has received funding from the German Research Foundation (DFG) No. 254872581 and from the European Research Council under the European Union’s Seventh Framework Program FP7-ERC-IDEAS Advanced Grant Agreement No. 290963 (SOMEF).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Wiendieck, K.: Zur Struktur körniger Medien. Die Bautechnik 6, 196–199 (1967)Google Scholar
  2. 2.
    Calvetti, F., Combe, G., Lanier, J.: Experimental micromechanical analysis of a 2D granular material: relation between structure evolution and loading path. Mech. Cohesive Frict. Mater. 2(2), 121–163 (1997)CrossRefGoogle Scholar
  3. 3.
    Desrues, J., Viggiani, G.: Strain localization in sand: an overview of the experimental results obtained in Grenoble using stereophotogrammetry. Int. J. Numer. Anal. Methods Geomech. 28(4), 279–321 (2004)CrossRefGoogle Scholar
  4. 4.
    Oda, M.: Initial fabrics and their relations to mechanical properties of granular material. Soils Found. 12(1), 17–36 (1972)CrossRefGoogle Scholar
  5. 5.
    Oda, M., Nemat-Nasser, S., Konishi, J.: Stress-induced anisotropy in granular masses. Soils Found. 25(3), 85–97 (1985)CrossRefGoogle Scholar
  6. 6.
    Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Géotechnique 29(1), 47–65 (1979)CrossRefGoogle Scholar
  7. 7.
    Dobry, R., Ng, T.-T.: Discrete modelling of stress–strain behaviour of granular media at small and large strains. Eng. Comput. 9, 129–143 (1992)CrossRefGoogle Scholar
  8. 8.
    O’Sullivan, C., Cui, L.: Micromechanics of granular material response during load reversals: combined DEM and experimental study. Powder Technol. 193(3), 289–302 (2009)CrossRefGoogle Scholar
  9. 9.
    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)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    Desrues, J., Chambon, R., Mokni, M., Mazerolle, F.: Void ratio evolution inside shear bands in triaxial sand specimens studied by computed tomography. Géotechnique 46(3), 529–546 (1996)CrossRefGoogle Scholar
  11. 11.
    Hall, S.A., Bornert, M., Desrues, J.: Discrete and continuum analysis of localised deformation in sand using X-ray \(\mu \)CT and volumetric digital image correlation. Géotechnique 60(5), 315–322 (2010)CrossRefGoogle Scholar
  12. 12.
    Butterfield, R., Harkness, R.M., Andrews, K.Z.: A stero-photogrammetric method for measuring displacement fields. Géotechnique 20(3), 308–314 (1970)CrossRefGoogle Scholar
  13. 13.
    Andò, E., Viggiani, G., Hall, S.A., Desrues, J.: Experimental micro-mechanics of granular media studied by X-ray tomography: recent results and challenges. Géotech. Lett. 3, 142–146 (2013)CrossRefGoogle Scholar
  14. 14.
    Andò, E., Hall, S.A., Viggiani, G., Desrues, J., Bésuelle, P.: Grain-scale experimental investigation of localised deformation in sand: a discrete particle tracking approach. Acta Geotech. 7, 1–13 (2012)CrossRefGoogle Scholar
  15. 15.
    Alshibli, K.A., Alramahi, B.A.: Microscopic evaluation of strain distribution in granular materials during shear. J. Geotech. Geoenviron. Eng. 132(1), 80–91 (2006)CrossRefGoogle Scholar
  16. 16.
    Fonseca, J., O’Sullivan, C., Coop, M.R., Lee, P.D.: Quantifying the evolution of soil fabric during shearing using directional parameters. Géotechnique 63(6), 487–499 (2013)CrossRefGoogle Scholar
  17. 17.
    Fonseca, J., Nadimi, S., Reyes-Aldasoro, C.C., O’Sullivan, C., Coop, M.R.: Image-based investigation into the primary fabric of stress-transmitting particles in sand. Soils Found. 56(5), 818–834 (2016)CrossRefGoogle Scholar
  18. 18.
    Druckrey, A.M., Alshibli, K.A., Al-Raoush, R.I.: 3D characterization of sand particle-to-particle contact and morphology. Comput. Geotech. 74, 26–35 (2016)CrossRefGoogle Scholar
  19. 19.
    Cnudde, V., Boone, M.N.: High-resolution X-ray computed tomography in geosciences: a review of the current technology and applications. Earth Sci. Rev. 123, 1–17 (2013)ADSCrossRefGoogle Scholar
  20. 20.
    Weis, S., Schröter, M.: Analyzing X-ray tomographies of granular packings. Rev. Sci. Instrum. 88, 051809 (2017)ADSCrossRefGoogle Scholar
  21. 21.
    Wiebicke, M., Andò, E., Herle, I., Viggiani, G.: On the metrology of interparticle contacts in sand from X-ray tomography images. Meas. Sci. Technol. 28(12), 124007 (2017)ADSCrossRefGoogle Scholar
  22. 22.
    Tengattini, A., Andò, E.: Kalisphera: an analytical tool to reproduce the partial volume effect of spheres imaged in 3D. Meas. Sci. Technol. 26(9), 095606 (2015)ADSCrossRefGoogle Scholar
  23. 23.
    Fox, M., Aste, T., Weaire, D.: The pursuit of perfect packing. Math. Gaz. 85(503), 370 (2001)CrossRefGoogle Scholar
  24. 24.
    Song, C., Wang, P., Makse, H.A.: A phase diagram for jammed matter. Nat. Lett. 453, 629–632 (2008)ADSCrossRefGoogle Scholar
  25. 25.
    Bi, D., Zhang, J., Chakraborty, B., Behringer, R.P.: Jamming by shear. Nature 480(7377), 355–358 (2011)ADSCrossRefGoogle Scholar
  26. 26.
    Baule, A., Makse, H.A.: Fundamental challenges in packing problems: from spherical to non-spherical particles. Soft Matter 10(25), 4423–4429 (2014)ADSCrossRefGoogle Scholar
  27. 27.
    Delaney, G.W., Di Matteo, T., Aste, T.: Combining tomographic imaging and DEM simulations to investigate the structure of experimental sphere packings. Soft Matter 6, 2992–3006 (2010)ADSCrossRefGoogle Scholar
  28. 28.
    Shire, T., O’Sullivan, C., Taylor, H., Sim, W.: Measurement of constriction size distributions using three grain-scale methods. In: Harris, J., Whitehouse, R., Moxon, S. (eds.) Proceedings of the 8th International Conference on Scour and Erosion, pp. 1067–1073. Taylor & Francis Group, London (2016)CrossRefGoogle Scholar
  29. 29.
    Andò, E., Cailletaud, R., Roubin, E., Stamati, O., the spam contributors: Spam: the software for the practical analysis of materials. (2017)
  30. 30.
    Wiebicke, M.: Benchmark analysis of synthetical images: source code and example DEM data.
  31. 31.
    Iassonov, P., Gebrenegus, T., Tuller, M.: Segmentation of X-ray computed tomography images of porous materials: a crucial step for characterization and quantitative analysis of pore structures. Water Resour. Res. 45(9), 1–12 (2009)CrossRefGoogle Scholar
  32. 32.
    Otsu, N.: A threshold selection method from gray-level histograms. IEEE Trans. Syst. Man Cybern. 9, 62–66 (1979)CrossRefGoogle Scholar
  33. 33.
    Meyer, F., Beucher, S.: Morphological segmentation. J. Vis. Commun. Image Represent. 1(1), 21–46 (1990)CrossRefGoogle Scholar
  34. 34.
    Grady, L.: Random walks for image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 28, 1768–1783 (2006)CrossRefGoogle Scholar
  35. 35.
    van der Walt, S., Schönberger, J.L., Nunez-Iglesias, J., Boulogne, F., Warner, J.D., Yager, N., Gouillart, E., Yu, T., the scikit-image contributors: Scikit-image: image processing in Python. PeerJ 2, e453 (2014)Google Scholar
  36. 36.
    Andò, E.: Experimental investigation of microstructural changes in deforming granular media using X-ray tomography. Ph.D. thesis, Université de Grenoble (2013)Google Scholar
  37. 37.
    Aste, T., Saadatfar, M., Senden, T.J.: Local and global relations between the number of contacts and density in monodisperse sphere packs. J. Stat. Mech. Theory Exp. 7, P07010 (2006)Google Scholar
  38. 38.
    Aste, T., Saadatfar, M., Senden, T.J.: Geometrical structure of disordered sphere packings. Phys. Rev. E 71, 061302 (2005)ADSCrossRefGoogle Scholar
  39. 39.
    Schaller, F.M., Neudecker, M., Saadatfar, M., Delaney, G., Mecke, K., Schröder-Turk, G.E., Schröter, M.: Tomographic analysis of jammed ellipsoid packings. AIP Conf. Proc. 1542, 377–380 (2013)ADSCrossRefGoogle Scholar
  40. 40.
    Schaller, F.M., Neudecker, M., Saadatfar, M., Delaney, G.W., Schröder-Turk, G.E., Schröter, M.: Local origin of global contact numbers in frictional ellipsoid packings. Phys. Rev. Lett. 114(15), 1–5 (2015)CrossRefGoogle Scholar
  41. 41.
    Šmilauer, V.: Woo documentation. (2016)
  42. 42.
    Jaquet, C., Andó, E., Viggiani, G., Talbot, H.: Estimation of separating planes between touching 3D objects using power watershed. In: International Symposium on Mathematical Morphology, vol. 11 (2013)Google Scholar
  43. 43.
    Viggiani, G., Andò, E., Jaquet, C., Talbot, H.: Identifying and following particle-to-particle contacts in real granular media: an experimental challenge. In: AIP Conference Proceedings, Powders and Grains 2013, vol. 60, pp. 60–65 (2013)Google Scholar
  44. 44.
    Kanatani, K.-I.: Distribution of directional data and fabric tensors. Int. J. Eng. Sci. 22(2), 149–164 (1984)MathSciNetCrossRefGoogle Scholar
  45. 45.
    Gu, X., Hu, J., Huang, M.: Anisotropy of elasticity and fabric of granular soils. Granul. Matter 19(2), 1–15 (2017)ADSCrossRefGoogle Scholar
  46. 46.
    Hall, S.A., Wright, J., Pirling, T., Andò, E., Hughes, D.J., Viggiani, G.: Can intergranular force transmission be identified in sand? First results of spatially-resolved neutron and X-ray diffraction. Granul. Matter 13(3), 251–254 (2011)CrossRefGoogle Scholar
  47. 47.
    Hurley, R., Marteau, E., Ravichandran, G., Andrade, J.E.: Extracting inter-particle forces in opaque granular materials: beyond photoelasticity. J. Mech. Phys. Solids 63, 154–166 (2014)ADSCrossRefGoogle Scholar
  48. 48.
    Hurley, R.C., Hall, S.A., Andrade, J.E., Wright, J.: Force measurements in stiff, 3D, opaque granular materials. In: EPJ Web of Conferences, Powders and Grains 2017, vol. 140 (2017)CrossRefGoogle Scholar
  49. 49.
    Imseeh, W.H., Alshibli, K.A.: 3D finite element modelling of force transmission and particle fracture of sand. Comput. Geotech. 94, 184–195 (2018)CrossRefGoogle Scholar
  50. 50.
    Imseeh, W.H., Druckrey, A.M., Alshibli, K.A.: 3D experimental quantification of fabric and fabric evolution of sheared granular materials using synchrotron micro-computed tomography. Granul. Matter 20, 24 (2018)CrossRefGoogle Scholar
  51. 51.
    Kuhn, M.R., Sun, W.C., Wang, Q.: Stress-induced anisotropy in granular materials: fabric, stiffness, and permeability. Acta Geotech. 10(4), 399–419 (2015)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Geotechnical EngineeringTechnische Universität DresdenDresdenGermany
  2. 2.CNRS, Grenoble INP, 3SRUniv. Grenoble AlpesGrenobleFrance
  3. 3.woodem.euPragueCzech Republic

Personalised recommendations