Geomechanics and Engineering

Techno-Press (테크노프레스)
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Efficient flexible boundary algorithms for DEM simulations of biaxial and triaxial tests

  • Liu, Donghai (State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University) ;
  • Yang, Jiaqi (State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University)
  • Received : 2019.09.18
  • Accepted : 2020.10.07
  • Published : 2020.11.10
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Abstract

The accurate modeling of boundary conditions is important in simulations of the discrete element method (DEM) and can affect the numerical results significantly. In conventional triaxial compression (CTC) tests, the specimens are wrapped by flexible membranes allowing to deform freely. To accurately model the boundary conditions of CTC, new flexible boundary algorithms for 2D and 3D DEM simulations are proposed. The new algorithms are computationally efficient and easy to implement. Moreover, both horizontal and vertical component of confining pressure are considered in the 2D and 3D algorithms, which can ensure that the directions of confining pressure are always perpendicular to the specimen surfaces. Furthermore, the boundaries are continuous and closed in the new algorithms, which can prevent the escape of particles from the specimens. The effectiveness of the proposed algorithms is validated by biaxial and triaxial simulations of granular materials. The results show that the algorithms allow the boundaries to deform non-uniformly on the premise of maintaining high control accuracy of confining pressure. Meanwhile, the influences of different lateral boundary conditions on the numerical results are discussed. It is indicated that the flexible boundary is more appropriate for the models with large strain or significant localization than rigid boundary.

Keywords

Acknowledgement

This study is supported by the National Key Research and Development Program of China (No. 2017YFC0405105) and National Natural Science Foundation of China (No. 51679164).

References

  1. Ai, J., Chen, J.F., Rotter, J.M. and Ooi, J.Y. (2011), "Assessment of rolling resistance models in discrete element simulations", Powder Technol., 206(3), 269-282. http://doi.org/10.1016/j.powtec.2010.09.030.
  2. Bardet, J.P. and Proubet, J. (1991), "A numerical investigation of the structure of persistent shear bands in granular media", Geotechnique, 41(4), 599-613. http://doi.org/10.1680/geot.1991.41.4.599.
  3. Belheine, N., Plassiard, J., Donze, F., Darve, F. and Seridi, A. (2009), "Numerical simulation of drained triaxial test using 3D discrete element modeling", Comput. Geotech., 36(1-2), 320-331. https://doi.org/10.1016/j.compgeo.2008.02.003.
  4. Binesh, S.M., Eslami-Feizabad, E. and Rahmani, R. (2018), "Discrete element modeling of drained triaxial test: Flexible and rigid lateral boundaries", Int. J. Civ. Eng., 16(10), 1463-1474. http://doi.org/10.1007/s40999-018-0293-0.
  5. Cheung, G. and O'Sullivan, C. (2008), "Effective simulation of flexible lateral boundaries in two- and three-dimensional DEM simulations", Particuology, 6(6), 483-500. http://doi.org/10.1016/j.partic.2008.07.018.
  6. Cil, M.B. and Alshibli, K.A. (2013), "3D analysis of kinematic behavior of granular materials in triaxial testing using DEM with flexible membrane boundary", Acta Geotech., 9(2), 287-298. http://doi.org/10.1007/s11440-013-0273-0.
  7. Cui, L., O'Sullivan, C. and O'Neill, S. (2007), "An analysis of the triaxial apparatus using a mixed boundary three-dimensional discrete element model", Geotechnique, 57(10), 831-844. http://doi.org/10.1680/geot.2007.57.10.831.
  8. Cundall, P.A. and Strack, O.D.L. (1979), "A discrete numerical model for granular assemblies", Geotechnique, 29(1), 47-65. http://doi.org/10.1680/geot.1980.30.3.331.
  9. Dai, B., Yang, J. Gu, X.Q. and Zhang, W. (2019), "A numerical analysis of the equivalent skeleton void ratio for silty sand", Geomech. Eng., 17(1), 19-30. http://doi.org/10.12989/gae.2019.17.1.019.
  10. de Bono, J., McDowell, G. and Wanatowski, D. (2012), "Discrete element modelling of a flexible membrane for triaxial testing of granular material at high pressures", Geotech. Lett., 2(4), 199-203. http://doi.org/10.1680/geolett.12.00040.
  11. Evans, T.M. and Frost, J.D. (2010), "Multiscale investigation of shear bands in sand: Physical and numerical experiments", Int. J. Numer. Anal. Meth. Geomech., 34(15), 1634-1650. http://doi.org/10.1002/nag.877.
  12. Evans, T.M. and Valdes, J.R. (2011), "The microstructure of particulate mixtures in one-dimensional compression: Numerical studies", Granul. Matter, 13(5), 657-669. http://doi.org/10.1007/s10035-011-0278-z.
  13. Feng, Y.T. and Owen, D.R.J. (2014), "Discrete element modelling of large scale particle systems-I: Exact scaling laws", Comp. Part. Mech., 1(2), 159-168. http://doi.org/10.1007/s40571-014-0010-y.
  14. Feng, Y.T., Han, K., Owen, D.R.J. and Loughran, J. (2009), "On upscaling of discrete element models: Similarity principles", Eng. Comput., 26(6), 599-609. http://doi.org/10.1108/02644400910975405.
  15. Huang, X., Hanley, K.J., Zhang, Z. and Kwok, C.Y. (2019), "Structural degradation of sands during cyclic liquefaction: Insight from DEM simulations", Comput. Geotech., 114, 103139. http://doi.org/10.1016/j.compgeo.2019.103139
  16. Itasca Consulting Group Inc. (2004), Particle Flow Code in 3D Dimensions (PFC3D) User's Manual, Version 3.1, Itasca, Minneapolis, Minnesota, U.S.A.
  17. Iwashita, K. and Oda, M. (1998), "Rolling resistance at contacts in simulation of shear band development by DEM", J. Eng. Mech., 124(3), 285-292. http://doi.org/10.1061/(ASCE)0733-9399(1998)124:3(285).
  18. Jacobson, D.E., Valdes, J.R. and Evans, T.M. (2007), "A numerical view into direct shear specimen size effects", Geotech. Test. J., 30(6), 512-516. http://doi.org/10.1520/GTJ100923.
  19. Jiang, M.J., Yan, H.B., Zhu, H.H. and Utili, S. (2011), "Modeling shear behavior and strain localization in cemented sands by two-dimensional distinct element method analyses", Comput. Geotech., 38(1), 14-29. http://doi.org/10.1016/j.compgeo.2010.09.001.
  20. Khoubani, A. and Evans, T.M. (2018), "An efficient flexible membrane boundary condition for DEM simulation of axisymmetric element tests", Int. J. Numer. Anal. Meth. Geomech., 42(4), 694-715. http://doi.org/10.1002/nag.2762.
  21. Kuhn, M.R. (1995), "A flexible boundary for three-dimensional DEM particle assemblies", Eng. Comput., 12(2), 175-183. http://doi.org/10.1108/02644409510799541.
  22. Kumara, J.J. and Hayano, K. (2016), "Importance of particle shape on stress-strain behaviour of crushed stone-sand mixtures", Geomech. Eng., 10(4), 455-470. http://doi.org/10.12989/gae.2016.10.4.455.
  23. Lee, S.J., Hashash, Y.M.A. and Nezami, E.G. (2012), "Simulation of triaxial compression tests with polyhedral discrete elements", Comput. Geotech., 43, 92-100. http://doi.org/10.1016/j.compgeo.2012.02.011.
  24. Lu, Y., Li, X. and Wang, Y. (2018), "Application of a flexible membrane to DEM modelling of axisymmetric triaxial compression tests on sands", Eur. J. Environ. Civ. Eng., 22(s1), s19-s36. http://doi.org/10.1080/19648189.2018.1425157.
  25. Ma, G., Chang, X.L., Zhou, W. and Ng, T.T. (2014), "Mechanical response of rockfills in a simulated true triaxial test: A combined FDEM study", Geomech. Eng., 7(3), 317-333. http://doi.org/10.12989/gae.2014.7.3.317.
  26. Meng, J., Huang, J., Sheng, D. and Sloan, S.W. (2017), "Quasi-static rheology of granular media using the static DEM", Int. J. Geomech., 17(11), 04017094. http://doi.org/10.1061/(asce)gm.1943-5622.0001001.
  27. O'Sullivan, C. and Cui, L. (2009), "Micromechanics of granular material response during load reversals: Combined DEM and experimental study", Powder Technol., 193(3), 289-302. http://doi.org/10.1016/j.powtec.2009.03.003
  28. Qu, T., Feng, Y.T., Wang, Y. and Wang, M. (2019), "Discrete element modelling of flexible membrane boundaries for triaxial tests", Comput. Geotech., 115, 103154. http://doi.org/10.1016/j.compgeo.2019.103154.
  29. Rakhimzhanova, A.K., Thornton, C., Minh, N.H., Fok, S.C. and Zhao, Y. (2019), "Numerical simulations of triaxial compression tests of cemented sandstone", Comput. Geotech., 113, 103068. http://doi.org/10.1016/j.compgeo.2019.04.013.
  30. Shi, D., Yang, C., Xue, J. and Wang, W. (2018), "Discrete element modeling of hollow cylinder shear behavior of granular material with fixed principal stress diection", J. Hydraul. Eng., 49(8), 917-925. (In Chinese). http://doi.org/10.13243/j.cnki.slxb.20180233.
  31. Wang, Y. and Tonon, F. (2009), "Modeling triaxial test on intact rock using discrete element method with membrane boundary", J. Eng. Mech., 135(9), 1029-1037. http://doi.org/10.1061/(ASCE)EM.1943-7889.0000017.
  32. Wang, Y.H. and Leung, S.C. (2008), "A particulate-scale investigation of cemented sand behavior", Can. Geotech. J., 45(1), 29-44. http://doi.org/10.1139/t07-070.
  33. Zhao, X. and Evans, T.M. (2009), "Discrete simulations of laboratory loading conditions", Int. J. Geomech., 9(4), 169-178. http://doi.org/10.1007/s10035-011-0284-1.
  34. Zhao, X. and Evans, T.M. (2011), "Numerical analysis of critical state behaviors of granular soils under different loading conditions", Granul. Matter, 13(6), 751-764. http://doi.org/10.1061/(ASCE)1532-3641(2009)9:4(169).
  35. Zhou, L.L., Chu, X.H., Zhang, X. and Xu, Y.J. (2016), "Numerical investigations on breakage behaviour of granular materials under triaxial stresses", Geomech. Eng., 11(5), 639-655. http://doi.org/10.12989/gae.2016.11.5.639.