Skip to main content
SpringerLink
Log in

A Sphere Filling Algorithm for Irregular Aggregate Particle Generation based on Nonlinear Optimization Method

  • Geotechnical Engineering
  • Published:
KSCE Journal of Civil Engineering Aims and scope

Abstract

The angularity of particles has important effects on the mechanical properties of asphalt mixture and other granular materials. To simulate these effects, the glue-sphere method was usually used to create an arbitrary polyhedron particle. Unlike other studies, this paper aims to efficiently fill a polyhedron with as few spheres as possible through optimization technology in order to reduce the cost of calculation during mixture simulation. Four contents are mainly discussed here: a) how to produce non-spherical aggregates and control their sizes with the minimal bounding box; b) how to fill convex non-spherical particles with the fewest balls as possible using the constrained nonlinear optimization method; c) how to compute the typical shape factors of these particles; and d) how the control parameters affect the filling effect. The algorithm for this study was programmed by MATLAB software and was proven to have better filling performance and less computational cost compared to other methods.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abreu, C. R., Tavares, F. W., and Castier, M. (2003). “Influence of particle shape on the packing and on the segregation of spherocylinders via Monte Carlo simulations.” Powder Technology, Vol. 134, No. 1, pp. 167–180, DOI: 10.1016/s0032-5910(03)00151-7.

    Article  Google Scholar 

  • Arasan, S., Yenera, E., Hattatoglu, F., Hinislioglua, S., and Akbuluta, S. (2011). “Correlation between shape of aggregate and mechanical properties of asphalt concrete: Digital image processing approach.” Road Materials and Pavement Design, Vol. 12, No. 2, pp. 239–262, DOI: 10.1080/14680629.2011.9695245.

    Google Scholar 

  • Bandyopadhyaya, R., Das, A., and Basu, S. (2008). “Numerical simulation of mechanical behaviour of asphalt mix.” Construction and Building Materials, Vol. 22, No. 6, pp. 1051–1058, DOI: 10.1016/j.conbuildmat.2007.03.010.

    Article  Google Scholar 

  • Barber, C. B., Dobkin, D. P., and Huhdanpaa, H. (1996). “The quickhull algorithm for convex hulls.” ACM Transactions on Mathematical Software (TOMS), Vol. 22, No. 4, pp. 469–483, DOI: 10.1145/235815.235821.

    Article  MathSciNet  MATH  Google Scholar 

  • Barequet, G. and Har-Peled, S. (2001). “Efficiently approximating the minimum-volume bounding box of a point set in three dimensions.” Journal of Algorithms, Vol. 38, No. 1, pp. 91–109, DOI: 10.1006/jagm.2000.1127.

    Article  MathSciNet  MATH  Google Scholar 

  • Barrett, P. J. (1980). “The shape of rock particles, a critical review.” Sedimentology, Vol. 27, No. 3, pp. 291–303, DOI: 10.1111/j.1365-3091.1980.tb01179.x.

    Article  Google Scholar 

  • Buttlar, W. G. and You, Z. (2001). “Discrete element modeling of asphalt concrete: Microfabric approach.” Transportation Research Record: Journal of the Transportation Research Board, Vol. 1757, No. 1, pp. 111–118, DOI: 10.3141/1757-13.

    Article  Google Scholar 

  • Chang, C. S. and Chao, S. J. (1994). “Discrete element analysis for active and passive pressure distribution on retaining wall.” Computers and Geotechnics, Vol. 16, No. 4, pp. 291–310, DOI: 10.1016/0266-352x(94)90012-4.

    Article  Google Scholar 

  • Chen, J. S., Chang, M. K., and Lin, K. Y. (2005). “Influence of coarse aggregate shape on the strength of asphalt concrete mixtures.” Journal of the Eastern Asia Society for Transportation Studies, Vol. 6, pp. 1062–1075, DOI: 10.11175/easts.6.1062.

    Google Scholar 

  • Cho, G., Dodds, J., and Santamarina, J. C. (2006). “Particle shape effects on packing density, stiffness, and strength: Natural and crushed sands.” Journal of Geotechnical and Geoenvironmental Engineering, Vol. 132, No. 5, pp. 591–602, DOI: 10.1061/(asce)1090-0241(2006) 132:5(591).

    Article  Google Scholar 

  • Collop, A. C., McDowell, G. R., and Lee, Y. (2004). “Use of the distinct element method to model the deformation behavior of an idealized asphalt mixture.” International Journal of Pavement Engineering, Vol. 5, No. 1, pp. 1–7, DOI: 10.1080/10298430410001709164.

    Article  Google Scholar 

  • Cundall, P. A. (1971). “A computer model for simulating progressive, large-scale movements in block rock systems.” Proc. Symp. Int. Soc. Rock Mech, France.

    Google Scholar 

  • Legland, D. (2009). File: geom3d, http://www.mathworks.cn/matlabcentral/fileexchange/24484-geom3d.

    Google Scholar 

  • Ferellec, J. F. and McDowell, G. R. (2010). “A method to model realistic particle shape and inertia in DEM.” Granular Matter, Vol. 12, No. 5, pp. 459–467, DOI: 10.1007/s10035-010-0205-8.

    Article  MATH  Google Scholar 

  • Hentschel, M. L. and Page, N. W. (2003). “Selection of descriptors for particle shape characterization.” Particle & Particle Systems Characterization, Vol. 20, No. 1, pp. 25–38, DOI: 10.1002/ppsc.200390002.

    Article  Google Scholar 

  • Hosseininia, E. S. and Mirghasemi, A. A. (2006). “Numerical simulation of breakage of two-dimensional polygon-shaped particles using discrete element method.” Powder Technology, Vol. 166, No. 2, pp. 100–112, DOI: 10.1016/j.powtec.2006.05.006.

    Article  Google Scholar 

  • Korsawe, J. (2008). File: Minimal Bounding Box, http://www.mathworks.com/matlabcentral/fileexchange/18264-minimal-bounding-box.

    Google Scholar 

  • Kalcheff, I. V. and Tunnicliff, D. G. (1986). “Effects of crushed stone aggregate size and shape on properties of asphalt concrete.” In Proc. of AAPT, Vol. 51, pp. 453–483.

    Google Scholar 

  • Kim, H. and Buttlar, W. G. (2005). “Micromechanical fracture modeling of asphalt mixture using the discrete element method.” GSP 130: Advances in Pavement Engineering, Proc., Sessions of the Geo-Frontiers 2005 Congress, ASCE, Reston, USA, pp. 209–223.

    Google Scholar 

  • Langston, P. A., Al-Awamleh, M. A., Fraige, F. Y., and Asmar, B. N. (2004). “Distinct element modelling of non-spherical frictionless particle flow.” Chemical Engineering Science, Vol. 59, No. 2, pp. 425–435, DOI: 10.1016/j.ces.2003.10.008.

    Article  Google Scholar 

  • Lee, C., Suh, H. S., Yoon, B., and Yun, T. S. (2017). “Particle shape effect on thermal conductivity and shear wave velocity in sands.” Acta Geotechnica, Vol. 12, No. 3, pp. 615–625, DOI: 10.1007/s11440-017-0524-6.

    Article  Google Scholar 

  • Lin, X. and Ng, T. T. (1997) “A three-dimensional discrete element model using arrays of ellipsoids.” Geotechnique, Vol. 47, No. 2, pp. 319–329, DOI: 10.1680/geot.1997.47.2.319.

    Article  Google Scholar 

  • Liu, Y. and You, Z. (2009). “Visualization and simulation of asphalt concrete with randomly generated three-dimensional models.” Journal of Computing in Civil Engineering, Vol. 23, No. 6, pp. 340–347, DOI: 10.1061/(asce)0887-3801(2009)23:6(340).

    Article  Google Scholar 

  • Liu, Y., You, Z., and Zhao, Y. (2012). “Three-dimensional discrete element modeling of asphalt concrete: Size effects of elements.” Construction and Building Materials, Vol. 37, pp. 775–782, DOI: 10.1016/j.conbuildmat.2012.08.007.

    Article  Google Scholar 

  • Mollanouri Shamsi, M. M. and Mirghasemi, A. A. (2012). “Numerical simulation of 3D semi-real-shaped granular particle assembly.” Powder Technology, Vol. 221, pp. 431–446, DOI: 10.1016/j.powtec.2012.01.042.

    Article  Google Scholar 

  • Ng, T. T. and Wang, C. (2001). “Comparison of a 3-D DEM simulation with MRI data.” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 25, No. 5, pp. 497–507, DOI: 10.1002/nag.139.

    Article  MATH  Google Scholar 

  • Oduroh, P. K., Mahboub, K. C., and Anderson, R. M. (2000). “Flat and elongated aggregates in superpave regime.” Journal of Materials in Civil Engineering, Vol. 12, No. 2, pp. 124–130, DOI: 10.1061/(asce)0899-1561(2000)12:2(124).

    Article  Google Scholar 

  • Pourghahramani, P. and Forssberg, E. (2005). “Review of applied particle shape descriptors and produced particle shapes in grinding environments. Part I: Particle shape descriptors.” Mineral Processing & Extractive Metall. Rev., Vol. 26, No. 2, pp. 145–166, DOI: 10.1080/08827500590912095.

    Article  Google Scholar 

  • Shin, H. and Santamarina, J. C. (2012). “Role of particle angularity on the mechanical behavior of granular mixtures.” Journal of Geotechnical and Geoenvironmental Engineering, Vol. 139, No. 2, pp. 353–355, DOI: 10.1061/(asce)gt.1943-5606.0000768.

    Article  Google Scholar 

  • Suh, H. S., Kim, K. Y., Lee, J., and Yun, T. S. (2017). “Quantification of bulk form and angularity of particle with correlation of shear strength and packing density in sands.” Engineering Geology, Vol. 220, pp. 256–265, DOI: 10.1016/j.enggeo.2017.02.015.

    Article  Google Scholar 

  • Taghavi, R. (2011). “Automatic clump generation based on mid-surface.” 2nd International FLAC/DEM Symposium, Melbourne, pp. 791–797.

    Google Scholar 

  • Ting, J. M., Khwaja, M., Meachum, L. R., and Rowell, J. D. (1993). “An ellipse-based discrete element model for granular materials.” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 17, No. 9, pp. 603–623, DOI: 10.1002/nag.1610170902.

    Article  MATH  Google Scholar 

  • Wikipedia (2017). On http://en.wikipedia.org/wiki/Discrete_element_method#Software.

  • Williams, J. R. and O’Connor, R. (1995). “A linear complexity intersection algorithm for discrete element simulation of arbitrary geometries.” Engineering Computations, Vol. 12, No. 2, pp. 185–201, DOI: 10.1108/02644409510799550.

    Article  Google Scholar 

  • You, Z., Adhikari, S., and Dai, Q. (2008). “Three-dimensional discrete element models for asphalt mixtures.” Journal of Engineering Mechanics, Vol. 134, No. 12, pp. 1053–1063, DOI: 10.1061/(asce) 0733-9399(2008)134:12(1053).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Transportation and Logistics, Dalian University of Technology, Dalian, 116023, China

    Changhong Zhou, Yuhua Li, Miaomiao Zhang & Shahroz Aijaz

  2. Shandong Hi-speed Group Co., Ltd (SDHS), Jinan, 250098, China

    Hongzhi Yue

  3. School of Ocean and Civil Engineering, Dalian Ocean University, Dalian, 116023, China

    Jiayin Liu

Authors
  1. Changhong Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hongzhi Yue
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yuhua Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Miaomiao Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jiayin Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Shahroz Aijaz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Changhong Zhou.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhou, C., Yue, H., Li, Y. et al. A Sphere Filling Algorithm for Irregular Aggregate Particle Generation based on Nonlinear Optimization Method. KSCE J Civ Eng 23, 120–129 (2019). https://doi.org/10.1007/s12205-018-0182-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12205-018-0182-8

Keywords

Search

Navigation