Three-dimensional Wadell roundness for particle angularity characterization of granular soils

Abstract

The geologist Hakon Wadell proposed the roundness definition in the 1930s for quantifying the particle angularity of granular soils. Due to the difficulty in obtaining three-dimensional (3D) particle geometries in the 1930s, Wadell used two-dimensional (2D) projections of particles to develop his roundness definition, although it is limited for analyzing 3D particles. This study shows that Wadell’s 2D roundness could be extended to a 3D definition. The 3D roundness is defined as the ratio of the average radius of spheres fitting to corners and ridges of a 3D particle to the radius of the maximum inscribed sphere of the 3D particle. A computational geometry algorithm is proposed to automatically identify corners and ridges, fit appropriate spheres to corners and ridges, identify the maximum inscribed sphere of the 3D particle, and compute 3D roundness. The number of slices per diameter of the maximum inscribed sphere of the particle, NSD, is defined for controlling the sphere fitting process. The minimum required NSD = 300 is established to ensure the reliable use of the proposed 3D computational geometry algorithm. Finally, a total of 20,000 particles from five sand specimens with various angularities are scanned by X-ray computed tomography. The 2D and 3D roundnesses of these 20,000 particles are compared. The 2D roundnesses capture the general trend of the corresponding 3D roundnesses, but vary in a large range, resulting in significant uncertainties when using 2D images to infer 3D particle angularities.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

References

  1. 1.

    Al-Rkaby AHJ, Chegenizadeh A, Nikraz HR (2017) Anisotropic strength of large scale geogrid-reinforced sand: experimental study. Soils Found 57:557–574. https://doi.org/10.1016/j.sandf.2017.03.008

    Article  Google Scholar 

  2. 2.

    Al-Rousan T, Masad E, Tutumluer E, Pan T (2007) Evaluation of image analysis techniques for quantifying aggregate shape characteristics. Constr Build Mater 21:978–990. https://doi.org/10.1016/j.conbuildmat.2006.03.005

    Article  Google Scholar 

  3. 3.

    Altuhafi FN, O’Sullivan C, Cavarretta I (2013) Analysis of an image-based method to quantify the size and shape of sand particles. J Geotech Geoenviron Eng 139:1290–1307. https://doi.org/10.1061/(asce)gt.1943-5606.0000855

    Article  Google Scholar 

  4. 4.

    Altuhafi FN, Coop MR, Georgiannou VN (2016) Effect of particle shape on the mechanical properties of natural sands. J Geotech Geoenviron Eng 142:1–15. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001569

    Article  Google Scholar 

  5. 5.

    Andrade JE, Lim KWK-W, Avila CF et al (2012) Granular element method for computational particle mechanics. Comput Methods Appl Mech Eng 214–244:262–274. https://doi.org/10.1016/j.cma.2012.06.012

    Article  MATH  Google Scholar 

  6. 6.

    Anochie-boateng JK, Komba JJ, Mvelase GM (2013) Three-dimensional laser scanning technique to quantify aggregate and ballast shape properties. Constr Build Mater 43:389–398. https://doi.org/10.1016/j.conbuildmat.2013.02.062

    Article  Google Scholar 

  7. 7.

    Arasan S, Akbulut S, Hasiloglu AS (2011) The relationship between the fractal dimension and shape properties of particles. KSCE J Civ Eng 15:1219–1225. https://doi.org/10.1007/s12205-011-1310-x

    Article  Google Scholar 

  8. 8.

    Azéma E, Radjaï F (2010) Stress–strain behavior and geometrical properties of packings of elongated particles. Phys Rev E. https://doi.org/10.1103/physreve.81.051304

    Article  Google Scholar 

  9. 9.

    Azéma E, Radjaï F, Peyroux R, Saussine G (2007) Force transmission in a packing of pentagonal particles. Phys Rev E. https://doi.org/10.1103/physreve.76.011301

    Article  MATH  Google Scholar 

  10. 10.

    Azéma E, Radjai F, Saussine G (2009) Quasistatic rheology, force transmission and fabric properties of a packing of irregular polyhedral particles. Mech Mater 41:729–741. https://doi.org/10.1016/j.mechmat.2009.01.021

    Article  Google Scholar 

  11. 11.

    Bareither CA, Benson CH, Edil TB (2008) Comparison of shear strength of sand backfills measured in small-scale and large-scale direct shear tests. Can 45:1224–1236

    Google Scholar 

  12. 12.

    Beakawi Al-Hashemi HM, Baghabra Al-Amoudi OS (2018) A review on the angle of repose of granular materials. Powder Technol 330:397–417

    Article  Google Scholar 

  13. 13.

    Bowman ET, Soga K, Drummond W (2001) Particle shape characterisation using Fourier descriptor analysis. Géotechnique 51:545–554. https://doi.org/10.1680/geot.2001.51.6.545

    Article  Google Scholar 

  14. 14.

    Chaney R, Demars K, Santamarina J, Cho G (2001) Determination of critical state parameters in sandy soils—simple procedure. Geotech Test J 24:185. https://doi.org/10.1520/GTJ11338J

    Article  Google Scholar 

  15. 15.

    Cho J, Sohn H (2016) Effects of particle shape and size distribution on the overall fluid-solid reaction rates of particle assemblages. Can J Chem Eng 94:1516–1523. https://doi.org/10.1002/cjce.22533

    Article  Google Scholar 

  16. 16.

    Cleary PW, Sawley ML (2002) DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge. Appl Math Model 26:89–111. https://doi.org/10.1016/S0307-904X(01)00050-6

    Article  MATH  Google Scholar 

  17. 17.

    Cruz-Matías I, Ayala D, Hiller D et al (2019) Sphericity and roundness computation for particles using the extreme vertices model. J Comput Sci 30:28–40. https://doi.org/10.1016/j.jocs.2018.11.005

    Article  Google Scholar 

  18. 18.

    Delaney GW, Cleary PW (2009) Fundamental relations between particle shape and the properties of granular packings. AIP Conf Proc 1145:837–840. https://doi.org/10.1063/1.3180058

    Article  Google Scholar 

  19. 19.

    Fu X, Huckb D, Makeinb L et al (2012) Effect of particle shape and size on flow properties of lactose powders. Particuology 10:203–208. https://doi.org/10.1016/j.partic.2011.11.003

    Article  Google Scholar 

  20. 20.

    Fukunaka T, Sawaguchi K, Golman B, Shinohara K (2005) Effect of particle shape of active pharmaceutical ingredients prepared by fluidized-bed jet-milling on cohesiveness. J Pharm Sci 94:1004–1012. https://doi.org/10.1002/jps.20307

    Article  Google Scholar 

  21. 21.

    Gardner M, Sitar N (2019) Coupled three-dimensional discrete element-lattice Boltzmann methods for fluid-solid interaction with polyhedral particles. Int J Numer Anal Methods Geomech 43:2270–2287. https://doi.org/10.1002/nag.2972

    Article  Google Scholar 

  22. 22.

    Goudarzy M, König D, Schanz T (2018) Interpretation of small and intermediate strain characteristics of Hostun sand for various stress states. Soils Found. https://doi.org/10.1016/j.sandf.2018.09.002

    Article  Google Scholar 

  23. 23.

    Guida G, Viggiani GMB, Casini F (2020) Multi-scale morphological descriptors from the fractal analysis of particle contour. Acta Geotech 15:1067–1080. https://doi.org/10.1007/s11440-019-00772-3

    Article  Google Scholar 

  24. 24.

    Han J, Wang K, Wang X, Monteiro PJM (2016) 2D image analysis method for evaluating coarse aggregate characteristic and distribution in concrete. Constr Build Mater 127:30–42. https://doi.org/10.1016/j.conbuildmat.2016.09.120

    Article  Google Scholar 

  25. 25.

    Han F, Ganju E, Salgado R, Prezzi M (2018) Effects of interface roughness, particle geometry, and gradation on the sand-steel interface friction angle. J Geotech Geoenviron Eng 144:04018096. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001990

    Article  Google Scholar 

  26. 26.

    Han L, Murphy RF, Ramanan D (2018) Learning generative models of tissue organization with supervised GANs. In: 2018 IEEE winter conference on applications of computer vision

  27. 27.

    He H, Zheng J (2020) Simulations of realistic granular soils in oedometer tests using physics engine. Int J Numer Anal Methods Geomech 44:983–1002. https://doi.org/10.1002/nag.3031

    Article  Google Scholar 

  28. 28.

    Hilton JE, Cleary PW (2011) The influence of particle shape on flow modes in pneumatic conveying. Chem Eng Sci 66:231–240. https://doi.org/10.1016/j.ces.2010.09.034

    Article  Google Scholar 

  29. 29.

    Hogg R, Turek ML, Kaya E (2004) The role of particle shape in size analysis and the evaluation of comminution processes. Part Sci Technol 22:355–366. https://doi.org/10.1080/02726350490516019

    Article  Google Scholar 

  30. 30.

    Hryciw RD, Zheng J, Shetler K (2016) Comparison of particle roundness and sphericity by traditional chart and computer methods. J Geotech Geoenviron Eng 142:04016038. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001485

    Article  Google Scholar 

  31. 31.

    Jerves AX, Kawamoto RY, Andrade JE (2016) Effects of grain morphology on critical state: a computational analysis. Acta Geotech 11:493–503. https://doi.org/10.1007/s11440-015-0422-8

    Article  Google Scholar 

  32. 32.

    Kandasami R, Murthy T (2014) Effect of particle shape on the mechanical response of a granular ensemble. In: Geomechanics from Micro to Macro, pp 1093–1098

  33. 33.

    Kawamoto R, Andò E, Viggiani G, Andrade JE (2018) All you need is shape: predicting shear banding in sand with LS-DEM. J Mech Phys Solids 111:375–392. https://doi.org/10.1016/j.jmps.2017.10.003

    Article  Google Scholar 

  34. 34.

    Krumbein WC (1941) Measurement and geological significance of shape and roundness of sedimentary particles. SEPM J Sediment Res. https://doi.org/10.1306/d42690f3-2b26-11d7-8648000102c1865d

    Article  Google Scholar 

  35. 35.

    Krumbein WC, Sloss LL (1951) Stratigraphy and sedimentation. W.H. Freeman and Company, San Francisco

    Google Scholar 

  36. 36.

    Lai Z, Chen Q (2019) Reconstructing granular particles from X-ray computed tomography using the TWS machine learning tool and the level set method. Acta Geotech 14:1–18. https://doi.org/10.1007/s11440-018-0759-x

    Article  Google Scholar 

  37. 37.

    Lanaro F, Tolppanen P (2002) 3D characterization of coarse aggregates. Eng Geol 65:17–30. https://doi.org/10.1016/S0013-7952(01)00133-8

    Article  Google Scholar 

  38. 38.

    Lashkari A, Falsafizadeh SR, Shourijeh PT, Alipour MJ (2020) Instability of loose sand in constant volume direct simple shear tests in relation to particle shape. Acta Geotech. https://doi.org/10.1007/s11440-019-00909-4

    Article  Google Scholar 

  39. 39.

    Lee C, Suh HS, Yoon B, Yun TS (2017) Particle shape effect on thermal conductivity and shear wave velocity in sands. Acta Geotech 12:615–625. https://doi.org/10.1007/s11440-017-0524-6

    Article  Google Scholar 

  40. 40.

    Li C, Ashlock JC, White DJ et al (2017) Gyratory abrasion with 2D image analysis test method for evaluation of mechanical degradation and changes in morphology and shear strength of compacted granular materials. Constr Build Mater. https://doi.org/10.1016/j.conbuildmat.2017.07.013

    Article  Google Scholar 

  41. 41.

    Lin X, Ng TT (1997) A three-dimensional discrete element model using arrays of ellipsoids. Géotechnique 47:319–329. https://doi.org/10.1680/geot.1997.47.2.319

    Article  Google Scholar 

  42. 42.

    Liu X, Yang J (2018) Shear wave velocity in sand: effect of grain shape. Géotechnique 68:742–748. https://doi.org/10.1680/jgeot.17.t.011

    Article  Google Scholar 

  43. 43.

    Masad E, Olcott D, White T, Tashman L (2001) Correlation of fine aggregate imaging shape indices with asphalt mixture performance. Transp Res Rec J Transp Res Board 1757:148–156. https://doi.org/10.3141/1757-17

    Article  Google Scholar 

  44. 44.

    Masad E, Al-Rousan T, Button J et al (2007) Test methods for characterizing aggregate shape texture, and angularity. Transportation Research Board, Washington, DC

    Google Scholar 

  45. 45.

    Medina DA, Jerves AX (2019) A geometry-based algorithm for cloning real grains 2.0. Granul Matter 21:1–12. https://doi.org/10.1007/s10035-018-0851-9

    Article  Google Scholar 

  46. 46.

    Mehring JL, McBride EF (2007) Origin of modern quartzarenite beach sands in a temperate climate, Florida and Alabama, USA. Sediment Geol 201:432–445. https://doi.org/10.1016/j.sedgeo.2007.07.010

    Article  Google Scholar 

  47. 47.

    Miller NA, Henderson JJ (2011) Correlating particle shape parameters to bulk properties and load stress at two water contents. Agron J 103:1514–1523. https://doi.org/10.2134/agronj2010.0235

    Article  Google Scholar 

  48. 48.

    Mukunoki T, Miyata Y, Mikami K, Shiota E (2016) X-ray CT analysis of pore structure in sand. Solid Earth 7:929–942. https://doi.org/10.5194/se-7-929-2016

    Article  Google Scholar 

  49. 49.

    Nouguier-Lehon C, Cambou B, Vincens E (2003) Influence of particle shape and angularity on the behaviour of granular materials: a numerical analysis. Int J Numer Anal Methods Geomech 27:1207–1226. https://doi.org/10.1002/nag.314

    Article  MATH  Google Scholar 

  50. 50.

    Pan T, Tutumluer E, Carpenter SH (2006) Effect of coarse aggregate morphology on permanent deformation behavior of hot mix asphalt. J Transp Eng 132:580–589. https://doi.org/10.1061/(asce)0733-947x(2006)132:7(580)

    Article  Google Scholar 

  51. 51.

    Peralta AF (2016) Identification of optimum aggregate gradation for transportation applications of multiaxial geogrids. Georgia Institute of Technology, Atlanta

    Google Scholar 

  52. 52.

    Pournin L, Weber M, Tsukahara M et al (2005) Three-dimensional distinct element simulation of spherocylinder crystallization. Granul Matter 7:119–126. https://doi.org/10.1007/s10035-004-0188-4

    Article  MATH  Google Scholar 

  53. 53.

    Powers MC (1953) A new roundness scale for sedimentary particles. SEPM J Sediment Res. https://doi.org/10.1306/d4269567-2b26-11d7-8648000102c1865d

    Article  Google Scholar 

  54. 54.

    Resentini A, AndÒ S, Garzanti E (2018) Quantifying roundness of detrital minerals by image analysis: sediment transport, shape effects, and provenance implications. J Sediment Res 88:276–289. https://doi.org/10.2110/jsr.2018.12

    Article  Google Scholar 

  55. 55.

    Shin H, Santamarina JC (2013) Role of particle angularity on the mechanical behavior of granular mixtures. J Geotech Geoenviron Eng 139:353–355. https://doi.org/10.1061/(asce)gt.1943-5606.0000768

    Article  Google Scholar 

  56. 56.

    Smith A, Dixon N, Fowmes GJ (2017) Early detection of first-time slope failures using acoustic emission measurements: large-scale physical modelling. Géotechnique 67:138–152. https://doi.org/10.1680/jgeot.15.P.200

    Article  Google Scholar 

  57. 57.

    Suh HS, Kim KY, Lee J, Yun TS (2017) Quantification of bulk form and angularity of particle with correlation of shear strength and packing density in sands. Eng Geol 220:256–265. https://doi.org/10.1016/j.enggeo.2017.02.015

    Article  Google Scholar 

  58. 58.

    Sukumaran B, Ashmawy AK (2001) Quantitative characterisation of the geometry of discret particles. Géotechnique 51:619–627. https://doi.org/10.1680/geot.2001.51.7.619

    Article  Google Scholar 

  59. 59.

    Sun Q, Zheng J (2019) Two-dimensional and three-dimensional inherent fabric in cross-anisotropic granular soils. Comput Geotech 116:103197. https://doi.org/10.1016/j.compgeo.2019.103197

    Article  Google Scholar 

  60. 60.

    Sun Q, Zheng J, Li C (2019) Improved watershed analysis for segmenting contacting particles of coarse granular soils in volumetric images. Powder Technol 356:295–303. https://doi.org/10.1016/j.powtec.2019.08.028

    Article  Google Scholar 

  61. 61.

    Sun Q, Zheng Y, Li B et al (2019) Three-dimensional particle size and shape characterisation using structural light. Géotech Lett 9:72–78

    Article  Google Scholar 

  62. 62.

    Tutumluer E, Pan T (2008) Aggregate morphology affecting strength and permanent deformation behavior of unbound aggregate materials. J Mater Civ Eng 20:617–627. https://doi.org/10.1061/(asce)0899-1561(2008)20:9(617)

    Article  Google Scholar 

  63. 63.

    Tutumluer E, Pan T, Carpenter SH (2005) Investigation of aggregate shape effects on hot mix performance using an image analysis approach. Transportation Engineering Series No. 137, Federal Highway Administration, Washington, D.C

  64. 64.

    Vangla P, Roy N, Latha GM (2016) Quantification of particle morphology through image based techniques and its importance in forensic studies. In: Proceedings of the 5th International Conference on Forensic Geotechnical Engineering

  65. 65.

    Vangla P, Roy N, Gali ML (2017) Image based shape characterization of granular materials and its effect on kinematics of particle motion. Granul Matter. https://doi.org/10.1007/s10035-017-0776-8

    Article  Google Scholar 

  66. 66.

    Vanimisetti SK, Ramakrishnan N (2012) Effect of the electrode particle shape in Li-ion battery on the mechanical degradation during charge–discharge cycling. J Mech Eng Sci 226:2192–2213

    Article  Google Scholar 

  67. 67.

    Wadell H (1932) Volume, shape, and roundness of rock particles. J Geol 40:443–451. https://doi.org/10.1086/623964

    Article  Google Scholar 

  68. 68.

    Wadell H (1933) Sphericity and roundness of rock particles. J Geol 41:310–331. https://doi.org/10.1086/624040

    Article  Google Scholar 

  69. 69.

    Wadell H (1935) Volume, shape, and roundness of quartz particles. J Geol 43:250–280. https://doi.org/10.1086/624298

    Article  Google Scholar 

  70. 70.

    Wang W, Coop M (2016) An investigation of breakage behaviour of single sand particles using a high-speed microscope camera. Géotechnique 66:984–998. https://doi.org/10.1680/jgeot.15.P.247

    Article  Google Scholar 

  71. 71.

    Wang L, Wang X, Mohammad L, Abadie C (2005) Unified method to quantify aggregate shape angularity and texture using fourier analysis. J Mater Civ Eng 17:498–504. https://doi.org/10.1061/(asce)0899-1561(2005)17:5(498)

    Article  Google Scholar 

  72. 72.

    Wang X, Liang Z, Nie Z, Gong J (2018) Stochastic numerical model of stone-based materials with realistic stone-inclusion features. Constr Build Mater. https://doi.org/10.1016/j.conbuildmat.2018.10.062

    Article  Google Scholar 

  73. 73.

    Wettimuny R, Penumadu D (2004) Application of Fourier analysis to digital imaging for particle shape analysis. J Comput Civ Eng 18:2–9. https://doi.org/10.1061/(asce)0887-3801(2004)18:1(2)

    Article  Google Scholar 

  74. 74.

    Xiao Y, Long L, Matthew Evans T et al (2018) Effect of particle shape on stress-dilatancy responses of medium-dense sands. J Geotech Geoenviron Eng 145:04018105. https://doi.org/10.1061/(asce)gt.1943-5606.0001994

    Article  Google Scholar 

  75. 75.

    Xiao Y, Yuan Z, Lin J et al (2019) Effect of particle shape of glass beads on the strength and deformation of cemented sands. Acta Geotech 14:2123–2131. https://doi.org/10.1007/s11440-019-00830-w

    Article  Google Scholar 

  76. 76.

    Yan B, Regueiro RA (2019) Three-dimensional discrete element method parallel computation of Cauchy stress distribution over granular materials. Int J Numer Anal Methods Geomech 43:974–1004. https://doi.org/10.1002/nag.2917

    Article  Google Scholar 

  77. 77.

    Yang J, Luo XD (2015) Exploring the relationship between critical state and particle shape for granular materials. J Mech Phys Solids 84:196–213. https://doi.org/10.1016/j.jmps.2015.08.001

    Article  Google Scholar 

  78. 78.

    Zhao B, Wang J (2016) 3D quantitative shape analysis on form, roundness, and compactness with μCT. Powder Technol. https://doi.org/10.1016/j.powtec.2015.12.029

    Article  Google Scholar 

  79. 79.

    Zhao S, Zhao J (2019) A poly-superellipsoid-based approach on particle morphology for DEM modeling of granular media. Int J Numer Anal Methods Geomech 43:2147–2169. https://doi.org/10.1002/nag.2951

    Article  Google Scholar 

  80. 80.

    Zheng J, Hryciw RD (2014) Soil particle size characterization by stereophotography. En: Geotechnical Special Publication, pp 64–73

  81. 81.

    Zheng J, Hryciw RD (2015) Traditional soil particle sphericity, roundness and surface roughness by computational geometry. Géotechnique. https://doi.org/10.1680/geot.14.P.192

    Article  Google Scholar 

  82. 82.

    Zheng J, Hryciw RD (2016) Index void ratios of sands from their intrinsic properties. J Geotech Geoenviron Eng 142:1–10. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001575,06016019

    Article  Google Scholar 

  83. 83.

    Zheng J, Hryciw RD (2016) A corner preserving algorithm for realistic DEM soil particle generation. Granul Matter 18:84. https://doi.org/10.1007/s10035-016-0679-0

    Article  Google Scholar 

  84. 84.

    Zheng J, Hryciw RD (2016) Roundness and sphericity of soil particles in assemblies by computational geometry. J Comput Civ Eng 30:1–13. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000578,04016021

    Article  Google Scholar 

  85. 85.

    Zheng J, Hryciw RD (2017) Particulate material fabric characterization by rotational haar wavelet transform. Comput Geotech 88:46–60. https://doi.org/10.1016/j.compgeo.2017.02.021

    Article  Google Scholar 

  86. 86.

    Zheng J, Hryciw RD (2017) Soil particle size and shape distributions by stereophotography and image analysis. Geotech Test J 40:317–328. https://doi.org/10.1520/GTJ20160165

    Article  Google Scholar 

  87. 87.

    Zheng J, Hryciw RD (2018) Cross-anisotropic fabric of sands by wavelet-based simulation of human cognition. Soils Found 58:1028–1041. https://doi.org/10.1016/j.sandf.2018.06.001

    Article  Google Scholar 

  88. 88.

    Zheng J, Hryciw RD, Ohm H-S (2014) Three-dimensional translucent segregation table (3D-TST) test for soil particle size and shape distribution. In: Geomechanics from micro to macro, pp 1037–1042

  89. 89.

    Zheng J, Hryciw RD, Ventola A (2017) Compressibility of sands of various geologic origins at pre-crushing stress levels. Geol Geotech Eng. https://doi.org/10.1007/s10706-017-0225-9

    Article  Google Scholar 

  90. 90.

    Zhou WH, Jing XY, Yin ZY, Geng X (2019) Effects of particle sphericity and initial fabric on the shearing behavior of soil–rough structural interface. Acta Geotech 14:1699–1716. https://doi.org/10.1007/s11440-019-00781-2

    Article  Google Scholar 

Download references

Acknowledgements

This material is based upon work supported by the U.S. National Science Foundation under Grant No. CMMI 1917332. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Junxing Zheng.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zheng, J., He, H. & Alimohammadi, H. Three-dimensional Wadell roundness for particle angularity characterization of granular soils. Acta Geotech. (2020). https://doi.org/10.1007/s11440-020-01004-9

Download citation

Keywords

  • Computational geometry
  • Particle angularity
  • Particle shape characterization
  • Wadell roundness