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An image based clump library for DEM simulations

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Abstract

To create realistic virtual soil specimens for Discrete Element Method simulations, a library containing nearly 100,000 “clumps” was developed. A clump essentially models a soil particle. It consists of numerous overlapping spheres in 3D, or circles in 2D, that are tangent to the particle perimeter. By using a unique corner-preserving algorithm based on the classic 2D definition of particle roundness, the clump generation requires many fewer circles than by previous algorithms. In this paper, the clumps are based on 2D images of real soil particles and they are indexed in the library by their roundness R and sphericity S values. A real soil can be simulated by choosing particles from the library to match the soil’s actual distributions of R and S. The clumps are also enlarged or reduced to match a desired particle size distribution. The utility of the clump library in parametric studies was demonstrated by direct shear tests on five very different virtual materials created from clumps in the library.

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Abbreviations

A :

Particle area

d :

Particle size (diameter)

\(d_{1}\) :

Particle length

\(d_{2}\) :

Particle width

D :

A fitting parameters in the Rosin–Rammler function

\(E_{\mathrm{c}}^{*}\) :

Effective modulus of a clump

\(E_{\mathrm{w}}^{*}\) :

Wall modulus in a DEM model

id:

Identification number for a clump in the library

n :

Porosity of a virtual soil

\(n_{\mathrm{p}}\) :

Presumed porosity of a virtual soil

\(n_{\mathrm{c}}\) :

Number of circles in a clump

N :

Number of clumps required from the clump library

\(N_{\mathrm{c}}\) :

Number of the corners around the particle perimeter

T :

Shear force

\(T_{\mathrm{p}}\) :

Shear force at the peak strength

\(r_{\mathrm{i}}\) :

Radius of the ith corner circle of a particle

\(r_{\mathrm{ins}}\) :

Radius of the maximum inscribed circle in a particle

R :

Particle roundness

\(R_{\mathrm{L}}\) :

Roundness index for a clump in the library

\(R_{\mathrm{m}}\) :

Mean roundness in an assembly of clumps

S :

Particle sphericity

\(S_{\mathrm{L}}\) :

Sphericity index for a clump in the library

\(S_{\mathrm{m}}\) :

Mean sphericity in an assembly of clumps

P :

Normal force

v :

Particle volume

\(V_{\mathrm{t}}\) :

The test vessel dimension

\(\beta _{\mathrm{n}}\) :

Normal critical damping ratio

\(\beta _{\mathrm{s}}\) :

Shear critical damping ratio

\(\Delta u_{\mathrm{x}}\) :

The horizontal displacement rate at the peak strength state

\(\Delta u_{\mathrm{y}}\) :

The vertical displacement rate at the peak strength state

\(\eta \) :

A fitting parameters in a two-dimensional Gaussian probability density function

\(\kappa ^{*}\) :

Normal to shear stiffness

\(\uplambda \) :

A fitting parameters in the Rosin–Rammler function

\(\mu \) :

Clump friction coefficient during the shearing stage

\(\rho \) :

Clump density

\(\Sigma \) :

A fitting parameters in a two-dimensional Gaussian probability density function

\(\phi _{\mathrm{p}}\) :

Peak angle of internal friction

\(\psi _{\mathrm{p}}\) :

Peak dilation angle

References

  1. Eisma, D.: Eolian sorting and roundness of beach and dune sands. Neth. J. Sea Res. 2(4), 541–555 (1965)

    Article  Google Scholar 

  2. Koerner, R.M.: Limiting density behavior of quartz powders. Powder Technol. 3(1), 208–212 (1970)

    Article  Google Scholar 

  3. Holubec, I., D’Appolonia, E.: Effect of particle shape on the engineering properties of granular soils. In: Evaluation of Relative Density and its Role in Geotechnical Projects Involving Cohesionless Soils. pp. 304–315. ASTM International, New York (1973)

  4. Youd, T.L.: Factors controlling maximum and minimum densities of sands. ASTM Spec. Tech. Publ. 523, 98–112 (1973)

    Google Scholar 

  5. Zelasko, J.S., Krizek, R.J., Edil, T.B.: Shear behavior of sands as a function of grain characteristics. In: Istanbul Conference on Soil Mechanics and Foundation Engineering, Turkey, pp. 55–64 (1975)

  6. Edil, T., Krizek, R., Zelasko, J.: Effect of grain characteristics on packing of sands. In: Proceedings of the Istanbul Conference on Soil Mechanics and Foundation Engineering, Istanbul, Turkey, pp. 46–54. Istanbul Technical University (1975)

  7. Oda, M., Koishikawa, I., Higuchi, T.: Experimental study of anisotropic shear strength of sand by plane strain test. Soils Found. 18(1), 25–38 (1978)

    Article  Google Scholar 

  8. Sladen, J.A., D’Hollander, R.D., Krahn, J.: The liquefaction of sands, a collapse surface approach. Can. Geotech. J. 22(4), 564–578 (1985)

    Article  Google Scholar 

  9. Vepraskas, M.J., Cassel, D.K.: Sphericity and roundness of sand in coastal plain soils and relationships with soil physical properties. Soil Sci. Soc. Am. J. 51(5), 1108 (1987)

    Article  Google Scholar 

  10. Moroto, N., Ishii, T.: Shear strength of uni-sized gravels under triaxial compression. Soils Found. 30(2), 23–32 (1990)

    Article  Google Scholar 

  11. Sukumaran, B., Ashmawy, A.K.: Quantitative characterisation of the geometry of discret particles. Géotechnique 51(7), 619–627 (2001)

    Article  Google Scholar 

  12. Sukumaran, B., Ashmawy, A.K.: Influence of inherent particle characteristics on hopper flowrate. Powder Technol. 138(1), 46–50 (2003)

    Article  Google Scholar 

  13. Cubrinovski, M., Ishihara, K.: Maximum and minimum void ratio characteristics of sands. Soils Found. 42(6), 65–78 (2002)

    Article  Google Scholar 

  14. Yasin, S.J.M., Safiullah, A.M.M.: Effect of particle characteristics on the strength and volume change behavior of sand. J. Civil Eng. 31(2), 127–148 (2003)

    Google Scholar 

  15. Santamarina, J.C., Cho, G.C.: Soil behaviour: the role of particle shape. In: Advances in Geotechnical Engineering: The Skempton Conference, London, pp. 604–617 (2004)

  16. Cerato, A., Lutenegger, A.: Specimen size and scale effects of direct shear box tests of sands. Geotech. Test. J. 29(6), 1–10 (2006)

    Google Scholar 

  17. 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. 132(5), 591–602 (2006)

    Article  Google Scholar 

  18. Guo, P., Su, X.: Shear strength, interparticle locking, and dilatancy of granular materials. Can. Geotech. J. 44(5), 579–591 (2007)

    Article  Google Scholar 

  19. Masad, E., Al-Rousan, T., Button, J., Little, D., Tutumluer, E.: Test methods for characterizing aggregate shape texture, and angularity. In: National Cooperative Highway Research Program Report 555. Transportation Research Board, Washington, DC (2007)

  20. Rousé, P.C., Fannin, R.J., Shuttle, D.A.: Influence of roundness on the void ratio and strength of uniform sand. Géotechnique 58(3), 227–231 (2008)

    Article  Google Scholar 

  21. Bareither, C.A., Edil, T.B., Benson, C.H., Mickelson, D.M.: Geological and physical factors affecting the friction angle of compacted sands. J. Geotech. Geoenviron. Eng. 134(10), 1476–1489 (2008)

    Article  Google Scholar 

  22. Cavarretta, I., O’Sullivan, C., Coop, M.: The influence of particle characteristics on the behaviour of coarse grained soils. Géotechnique 60(6), 413–423 (2010)

    Article  Google Scholar 

  23. Shin, H., Santamarina, J.C.: Role of particle angularity on the mechanical behavior of granular mixtures. J. Geotech. Geoenviron. Eng. 139(2), 353–355 (2013)

    Article  Google Scholar 

  24. Zheng, J., Hryciw, R.D.: Index void ratios of sands from their intrinsic properties. J. Geotech. Geoenviron. Eng. 06016019. doi:10.1061/(ASCE)GT11.1943-5606.0001575 (2016)

  25. Cundall, P.A.: A computer model for simulating progressive large scale movements in blocky rock systems. In: Proceedings of Proceedings of the Symposium of the International Society of Rock Mechanics. International Society for Rock Mechanics (ISRM) vol. 1, paper no. II-8, pp. 129–136 (1976)

  26. Lin, X., Ng, T.T.: A three-dimensional discrete element model using arrays of ellipsoids. Géotechnique 47(2), 319–329 (1997)

    Article  Google Scholar 

  27. Mustoe, G.G.W., Miyata, M.: Material flow analyses of noncircular-shaped granular media using discrete element methods. J. Eng. Mech. 127(10), 1017–1026 (2001)

    Article  Google Scholar 

  28. Ouadfel, H., Rothenburg, L.: ‘Stress-force-fabric’ relationship for assemblies of ellipsoids. Mech. Mater. 33(4), 201–221 (2001)

    Article  Google Scholar 

  29. Ng, T.-T.: Particle shape effect on macro- and micro-behaviors of monodisperse ellipsoids. Int. J. Numer. Anal. Meth. Geomech. 33(4), 511–527 (2009)

    Article  MATH  Google Scholar 

  30. Fu, P., Dafalias, Y.F.: Fabric evolution within shear bands of granular materials and its relation to critical state theory. Int. J. Numer. Anal. Meth. Geomech. 35(18), 1918–1948 (2010)

    Article  Google Scholar 

  31. Pournin, L., Weber, M., Tsukahara, M., Ferrez, J.A., Ramaioli, M., Liebling, T.M.: Three-dimensional distinct element simulation of spherocylinder crystallization. Granular Matter 7(2–3), 119–126 (2005)

    Article  MATH  Google Scholar 

  32. Azéma, E., Radjaï, F., Peyroux, R., Saussine, G.: Force transmission in a packing of pentagonal particles. Phys. Rev. E 76(1), 011301 (2007). doi:10.1103/PhysRevE.76.011301

    Article  ADS  Google Scholar 

  33. Azéma, E., Radjaï, F.: Stress–strain behavior and geometrical properties of packings of elongated particles. Phys. Rev. E 81(5), 051304 (2010). doi:10.1103/PhysRevE.81.051304

    Article  ADS  Google Scholar 

  34. Azéma, E., Radjai, F., Saussine, G.: Quasistatic rheology, force transmission and fabric properties of a packing of irregular polyhedral particles. Mech. Mater. 41(6), 729–741 (2009)

    Article  Google Scholar 

  35. Galindo-Torres, S.A., Pedroso, D.M.: Molecular dynamics simulations of complex-shaped particles using Voronoi-based spheropolyhedra. Phys. Rev. E 81(6), 061303 (2010). doi:10.1103/PhysRevE.81.061303

    Article  ADS  Google Scholar 

  36. Mollon, G., Zhao, J.: 3D generation of realistic granular samples based on random fields theory and Fourier shape descriptors. Comput. Methods Appl. Mech. Eng. 279, 46–65 (2014)

    Article  ADS  Google Scholar 

  37. Ferellec, J.-F., McDowell, G.R.: A method to model realistic particle shape and inertia in DEM. Granular Matter 12(5), 459–467 (2010)

    Article  MATH  Google Scholar 

  38. Langston, P., Ai, J., Yu, H.: Simple shear in 3D DEM polyhedral particles and in a simplified 2D continuum model. Granular Matter 2013(15), 595–606 (2013)

    Article  Google Scholar 

  39. Boton, M., Azéma, E., Estrada, N., Radjaï, F., Lizcano, A.: Quasistatic rheology and microstructural description of sheared granular materials composed of platy particles. Phys. Rev. E 87(3), 032206 (2013). doi:10.1103/PhysRevE.87.032206

    Article  ADS  Google Scholar 

  40. Spellings, M., Marson, R.L., Anderson, J.A., Glotzer, S.C.: GPU accelerated Discrete Element Method (DEM) molecular dynamics for conservative, faceted particle simulations. J. Comput. Phys. 334, 460–467

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

    Article  MATH  Google Scholar 

  42. Taghavi, R.: Automatic Clump Generation Based on Mid-Surface. In: Al, D.S.e. (ed.) Proceedings, 2nd International FLAC/DEM Symposium, Melbourne, pp. 791–797. Minneapolis: Itasca International Inc. (2011)

  43. Zheng, J., Hryciw, R.D.: A corner preserving algorithm for realistic DEM soil particle generation. Granular Matter 18(4), 1–18 (2016). doi:10.1007/s10035-016-0679-0

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  45. Wadell, H.: Sphericity and roundness of rock particles. J. Geol. 41(3), 310–331 (1933)

    Article  ADS  Google Scholar 

  46. Wadell, H.: Volume, shape, and roundness of quartz particles. J. Geol. 43(3), 250–280 (1935)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  48. Tickell, F.G.: The Examination of Fragmental Rocks. Stanford University Press, Stanford, CA (1931)

    Google Scholar 

  49. Altuhafi, F., O’Sullivan, C., Cavarretta, I.: Analysis of an image based method to quantify the size and shape of sand particles. J. Geotech. Geoenviron. Eng. 139(8), 1290–1307 (2013)

    Article  Google Scholar 

  50. Krumbein, W.C., Sloss, L.L.: Stratigraphy and Sedimentation. W.H. Freeman and Company, San Francisco (1951)

    Google Scholar 

  51. Zheng, J., Hryciw, R.D.: Traditional soil particle sphericity, roundness and surface roughness by computational geometry. Géotechnique 65(6), 494–506 (2015)

    Article  Google Scholar 

  52. Zheng, J., Hryciw, R.D.: Roundness and sphericity of soil particles in assemblies by computational geometry. J. Comput. Civ. Eng. (2016). doi:10.1061/(ASCE)CP.1943-5487.0000578

  53. Zheng, J., Hryciw, R.D.: Index void ratios of sands from their intrinsic properties. J. Geotech. Geoenviron. Eng. (2016). doi:10.1061/(ASCE)GT.1943-5606.0001575

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

    Google Scholar 

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

    Google Scholar 

  56. Hryciw, R.D., Zheng, J., Shetler, K.: Particle roundness and sphericity from images of assemblies by chart estimates and computer methods. J. Geotech. Geoenviron. Eng. (2016). doi:10.1061/(ASCE)GT.1943-5606.0001485

  57. Rao, C., Tutumluer, E., Stefanski, J.A.: Coarse aggregate shape and size properties using a new image analyzer. J. Test. Eval. 29(5), 461–471 (2001)

    Article  Google Scholar 

  58. Rao, C., Tutumluer, E.: Determination of volume of aggregates: new image-analysis approach. Trans. Res. Record J Transp. Res. Board 1721, 73–80 (2000)

    Article  Google Scholar 

  59. Pan, T., Tutumluer, E., Carpenter, S.H.: Effect of coarse aggregate morphology on permanent deformation behavior of hot mix asphalt. J. Trans. Eng. 132(7), 580–589 (2006)

    Article  Google Scholar 

  60. Tutumluer, E., Pan, T.: Aggregate morphology affecting strength and permanent deformation behavior of unbound aggregate materials. J. Mater. Civ. Eng. 20(9), 617–627 (2008)

  61. Al-Rousan, T., Masad, E., Tutumluer, E., Pan, T.: Evaluation of image analysis techniques for quantifying aggregate shape characteristics. Constr. Build. Mater. 21(5), 978–990 (2007)

    Article  Google Scholar 

  62. Mahmoud, E., Masad, E.: Experimental methods for the evaluation of aggregate resistance to polishing, abrasion, and breakage. J. Mater. Civ. Eng. 19(11), 977–985 (2007)

    Article  Google Scholar 

  63. Fletcher, T., Chandan, C., Masad, E., Sivakumar, K.: Aggregate imaging system for characterizing the shape of fine and coarse aggregates. Transp. Res. Record J Transp. Res. Board 1832, 67–77 (2003)

    Article  Google Scholar 

  64. Chandan, C., Sivakumar, K., Masad, E., Fletcher, T.: Application of imaging techniques to geometry analysis of aggregate particles. J. Comput. Civil Eng. 18(1), 75–82 (2004)

    Article  Google Scholar 

  65. Ohm, H.-S., Hryciw, R.D.: Translucent segregation table test for sand and gravel particle size distribution. Geotech. Test. J. 36(4), 20120221 (2013)

    Article  Google Scholar 

  66. Zheng, J., Hryciw, R.D., Ohm, H.S.: Three-dimensional translucent segregation table (3D-TST) test for soil particle size and shape distribution. In: International Symposium on Geomechanics from Micro to Macro, London, pp. 1037–1042. Taylor & Francis Group, Abingdon (2014)

  67. Raschke, S.A., Hryciw, R.D.: Vision cone penetrometer for direct subsurface soil observation. J. Geotech. Geoenviron. Eng. 123(11), 1074–1076 (1997)

    Article  Google Scholar 

  68. Ghalib, A.M., Hryciw, R.D., Susila, E.: Soil stratigraphy delineation by VisCPT. In: Innovations and Applications in Geotechnical Site Characterization, Reston, VA, pp. 65–79. ASCE, New York (2000)

  69. Hryciw, R.D., Ohm, H.S.: Soil migration and piping susceptibility by the VisCPT. In: Geo-Congress, San Diego, CA, pp. 192–195 (2013)

  70. Zheng, J., Hryciw, R.D.: Optical flow analysis of internal erosion and soil piping in images captured by the VisCPT. In: Geo-Shanghai 2014, Shanghai, China, pp. 55–64. ASCE, New York (2014)

  71. Ohm, H.-S., Hryciw, R.D.: Size distribution of coarse-grained soil by sedimaging. J. Geotech. Geoenviron. Eng. (2014). doi:10.1061/(ASCE)GT.1943-5606.0001075, 04013053

  72. Rosin, P., Rammler, E.: The laws governing the fineness of powdered coal. J. Inst. Fuel 7, 29–36 (1933)

    Google Scholar 

  73. Itasca Consulting Group. Particle Flow Code in Two Dimensions.: User’s Manual, Version 5.0.: Minneapolis, MN (2015)

  74. Plimpton, S.: Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117(1), 1–19 (1995)

    Article  ADS  MATH  Google Scholar 

  75. Kloss, C., Goniva, C., Hager, A., Amberger, S., Pirker, S.: Models, algorithms and validation for opensource DEM and CFD-DEM. Prog. Comput. Fluid Dyn. Int. J. 12(2/3), 140–152 (2012)

    Article  MathSciNet  Google Scholar 

  76. Lings, M.L., Dietz, M.S.: An improved direct shear apparatus for sand. Géotechnique 54(4), 245–256 (2004)

    Article  Google Scholar 

  77. Jewell, R.A.: Direct shear tests on sand. Géotechnique 39(2), 309–322 (1989)

    Article  Google Scholar 

  78. Kokusho, T., Hara, T., Hiraoka, R.: Undrained shear strength of granular soils with different particle gradations. J. Geotech. Geoenviron. Eng. 13(6), 621–629 (2004)

    Article  Google Scholar 

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Acknowledgements

This paper is based upon work supported by the U.S. National Science Foundation under Grant No. CMMI 1300010. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation. Itasca is thanked for their educational sponsorship of software PFC. ConeTec Investigations Ltd. and the ConeTec Education Foundation are acknowledged for their support to the Geotechnical Engineering Laboratories at the University of Michigan.

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  1. Department of Civil and Environmental Engineering, University of Michigan, 2340 GG Brown, Ann Arbor, MI, 48109-2125, USA

    Junxing Zheng & Roman D. Hryciw

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Zheng, J., Hryciw, R.D. An image based clump library for DEM simulations. Granular Matter 19, 26 (2017). https://doi.org/10.1007/s10035-017-0713-x

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