Technical Notes
Dec 13, 2021

Simulation of Split Hopkinson Pressure Bar Tests on Sands Using the Discrete-Element Method

Publication: International Journal of Geomechanics
Volume 22, Issue 2

Abstract

Split Hopkinson pressure bar (SHPB) tests have been used extensively to study the stress–strain behavior of sand under high strain-rate conditions. However, the low impedance of sand leads to specimens not attaining stress equilibrium; therefore, the reported results from SHPB tests, assuming stress equilibrium, might be invalid at low stresses. In this study, a model based on the discrete-element method (DEM) was developed to model SHPB tests on dry sand reported in the literature. The DEM model was calibrated and validated by comparing the simulated and reported stress–strain responses. The validated model was subsequently used to conduct a parametric study to investigate the effect of particle rotational resistance on the stress–strain response and stress equilibrium of the specimens. It was found that the DEM specimens did not attain strict stress equilibrium; however, the stress–strain responses obtained using the transmission bar stress (assuming stress equilibrium) and the average stress between the transmission and incident bars (assuming stress nonequilibrium) were within the error bar reported in the experiment. The parametric study showed that a higher particle rotational resistance resulted in a stiffer stress–strain response, and particle rotation meaningfully contributed to the sand response during SHPB tests.

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Acknowledgments

The authors would like to thank Dr Weinong Chen for providing SHPB test data from his research group at Purdue University.

References

Ai, J., J. F. Chen, J. M. Rotter, and J. Y. Ooi. 2011. “Assessment of rolling resistance models in discrete element simulations.” Powder Technol. 206 (3): 269–282. https://doi.org/10.1016/j.powtec.2010.09.030.
Bolton, M. D., Y. Nakata, and Y. P. Cheng. 2008. “Micro- and macro-mechanical behaviour of DEM crushable materials.” Géotechnique 58 (6): 471–480. https://doi.org/10.1680/geot.2008.58.6.471.
Calvetti, F. 2008. “Discrete modelling of granular materials and geotechnical problems.” Eur. J. Environ. Civ. Eng. 12 (7–8): 951–965. https://doi.org/10.1080/19648189.2008.9693055.
Calvetti, F., C. G. di Prisco, and E. Vairaktaris. 2017. “DEM assessment of impact forces of dry granular masses on rigid barriers.” Acta Geotech. 12 (1): 129–144. https://doi.org/10.1007/s11440-016-0434-z.
Calvetti, F., C. Tamagnini, and G. Viggiani. 2002. “On the incremental behavior of granular soils.” In NUMOG VIII, edited by G. N. Pande and S. Pietrusczczak, 3–9. Rotterdam, Netherlands: Balkema, Lisse.
Challita, G., and R. Othman. 2010. “Finite-element analysis of SHPB tests on double-lap adhesive joints.” Int. J. Adhes. Adhes. 30 (4): 236–244. https://doi.org/10.1016/j.ijadhadh.2010.02.004.
Chen, W., B. Song, D. J. Frew, and M. J. Forrestal. 2003. “Dynamic small strain measurements of a metal specimen with a split Hopkinson pressure bar.” Exp. Mech. 43 (1): 20–23. https://doi.org/10.1007/BF02410479.
De Bono, J. P., and G. R. McDowell. 2014. “DEM of triaxial tests on crushable sand.” Granular Matter 16 (4): 551–562. https://doi.org/10.1007/s10035-014-0500-x.
Felice, C. W. 1985. “The response of soil to impulse loads using the S.H.P.B technique.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of Utah.
Felice, C. W., E. S. Gaffney, J. A. Brown, and J. M. Olsen. 1987. “Dynamic high stress experiments on soil.” Geotech. Test. J. 10 (4): 192–202. https://doi.org/10.1520/GTJ10545J.
Frost, J. D., J. T. DeJong, and M. Recalde. 2002. “Shear failure behavior of granular-continuum interfaces.” Eng. Fract. Mech. 69 (17): 2029–2048. https://doi.org/10.1016/S0013-7944(02)00075-9.
Gabrieli, F., S. Cola, and F. Calvetti. 2009. “Use of an up-scaled DEM model for analysing the behaviour of a shallow foundation on a model slope.” Geomech. Geoeng. 4 (2): 109–122. https://doi.org/10.1080/17486020902855688.
Gray, G. T. 2000. “Classic split-Hopkinson pressure bar testing.” In ASM handbook, Vol. 8, mechanical testing and evaluation, edited by H. Kuhn and D. Medlin, 462–476. Materials Park, OH: ASM Int.
Huang, J., S. Xu, and S. Hu. 2013. “Effects of grain size and gradation on the dynamic responses of quartz sands.” Int. J. Impact Eng. 59: 1–10. https://doi.org/10.1016/j.ijimpeng.2013.03.007.
Huang, J., S. Xu, and S. Hu. 2014. “Influence of particle breakage on the dynamic compression responses of brittle granular materials.” Mech. Mater. 68 (1): 15–28. https://doi.org/10.1016/j.mechmat.2013.08.002.
Itasca Consulting Group. 2016. Particle flow code in three dimensions: Software manual. Minneapolis: Itasca Consulting Group.
Kabir, M. E., B. Song, E. Martin, and W. Chen. 2010. “Compressive behavior of fine sand. Albuquerque, NM: Terminal Ballistics Technology Dept., Sandia Laboratories.
Kermani, E., T. Qiu, and T. Li. 2015. “Simulation of collapse of granular columns using the discrete element method.” Int J Geomech. 15 (6): 04015004. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000467.
Lu, H., H. Luo, and R. Komoduri. 2009. “Dynamic compressive response of sand under confinements.” In Proc., Annual Conf., Society for Experimental Mechanics, 1–7. Albuquerque, New Mexico: Society for Experimental Mechanics.
Luo, H., W. L. Cooper, and H. Lu. 2014. “Effects of particle size and moisture on the compressive behavior of dense Eglin sand under confinement at high strain rates.” Int. J. Impact Eng. 65: 40–55. https://doi.org/10.1016/j.ijimpeng.2013.11.001.
Luo, H., H. Lu, W. L. Cooper, and R. Komanduri. 2011. “Effect of mass density on the compressive behavior of dry sand under confinement at high strain rates.” Exp. Mech. 51 (9): 1499–1510. https://doi.org/10.1007/s11340-011-9475-2.
Martin, B. E. 2007. “Moisture effects on the high strain rate behavior of sand.” Master of Science thesis, Dept. of Mechanical Engineering, Univ. of Florida.
Mindlin, R. D. 1949. “Compliance of elastic bodies in contact.” J. Appl. Mech. 16 (3): 259–268. https://doi.org/10.1115/1.4009973.
Omidvar, M., M. Iskander, and S. Bless. 2012. “Stress–strain behavior of sand at high strain rates.” Int. J. Impact Eng. 49: 192–213. https://doi.org/10.1016/j.ijimpeng.2012.03.004.
O'Sullivan, C., and L. Cui. 2009. “Micromechanics of granular material response during load reversals: Combined DEM and experimental study.” Powder Technol. 193 (3): 289–302. https://doi.org/10.1016/j.powtec.2009.03.003.
Prabhu, S., and T. Qiu. 2019. “Effect of particle size on high-strain rate response of sand.” In Proc., 8th Int. Conf. on Case Histories in Geotechnical Engineering, Geotechnical Special Publication 310, edited by C. L. Meehan, S. Kumar, M. A. Pando, and J. T. Coe, 155–164. Reston, VA: ASCE.
Prabhu, S., and T. Qiu. 2020. “Simulation of split Hopkinson pressure bar tests on sands with low water content.” J. Eng. Mech. 146 (8): 04020082. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001819.
Prabhu, S., and T. Qiu. 2021. “Modeling of sand particle crushing in split Hopkinson pressure bar tests using the discrete element method.” Int. J. Impact Eng. 156: 103974. https://doi.org/10.1016/j.ijimpeng.2021.103974.
Ravichandran, G., and G. Subhash. 1994. “Critical appraisal of limiting strain rates for compression testing of ceramics in a split Hopkinson pressure bar.” J. Am. Ceram. Soc. 77 (1): 263–267. https://doi.org/10.1111/j.1151-2916.1994.tb06987.x.
Semblat, J. F., M. P. Luong, and G. Gary. 1999. “3D-Hopkinson bar: New experiments for dynamic testing on soils.” Soils Found. 39 (1): 1–10. https://doi.org/10.3208/sandf.39.1.
Song, B., and W. Chen. 2004. “Dynamic stress equilibration in split Hopkinson pressure bar tests on soft materials.” Exp. Mech. 44 (3): 300–312. https://doi.org/10.1007/BF02427897.
Song, B., W. Chen, and V. Luk. 2009. “Impact compressive response of dry sand.” Mech. Mater. 41 (6): 777–785. https://doi.org/10.1016/j.mechmat.2009.01.003.
Song, B., M. J. Forrestal, and W. Chen. 2006. “Dynamic and quasi-static propagation of compaction waves in a low-density epoxy foam.” Exp. Mech. 46 (2): 127–136. https://doi.org/10.1007/s11340-006-5871-4.
Teufelsbauer, H., Y. Wang, M. C. Chiou, and W. Wu. 2009. “Flow–obstacle interaction in rapid granular avalanches: DEM simulation and comparison with experiment.” Granular Matter 11 (4): 209–220. https://doi.org/10.1007/s10035-009-0142-6.
Teufelsbauer, H., Y. Wang, S. P. Pudasaini, R. I. Borja, and W. Wu. 2011. “DEM simulation of impact force exerted by granular flow on rigid structures.” Acta Geotech. 6 (3): 119–133. https://doi.org/10.1007/s11440-011-0140-9.
Wang, S., L. Shen, F. Maggi, A. El-Zein, G. D. Nguyen, Y. Zheng, H. Zhang, and Z. Chen. 2018. “Influence of dry density and confinement environment on the high strain rate response of partially saturated sand.” Int. J. Impact Eng. 116: 65–78. https://doi.org/10.1016/j.ijimpeng.2018.02.006.
Whitman, R. V., and K. A. Healy. 1962. “Shear strength of sands during rapid loadings.” J. Soil Mech. Found. Div. 88 (2): 99–132. https://doi.org/10.1061/JSFEAQ.0000411.
Yang, L. M., and V. P. W. Shim. 2005. “An analysis of stress uniformity in split Hopkinson bar test specimens.” Int. J. Impact Eng. 31 (2): 129–150. https://doi.org/10.1016/j.ijimpeng.2003.09.002.
Yimsiri, S., and K. Soga. 2010. “DEM analysis of soil fabric effects on behaviour of sand.” Geotechnique 60 (6): 483–495.
Zencker, U., and R. Clos. 1999. “Limiting conditions for compression testing of flat specimens in the split Hopkinson pressure bar.” Exp. Mech. 39 (4): 343–348. https://doi.org/10.1007/BF02329815.
Zhu, J., S. Hu, and L. Wang. 2009. “An analysis of stress uniformity for concrete-like specimens during SHPB tests.” Int. J. Impact Eng. 36 (1): 61–72. https://doi.org/10.1016/j.ijimpeng.2008.04.007.
Zhu, W. C., Y. Bai, X. B. Li, and L. L. Niu. 2012. “Numerical simulation on rock failure under combined static and dynamic loading during SHPB tests.” Int. J. Impact Eng. 49: 142–157. https://doi.org/10.1016/j.ijimpeng.2012.04.002.

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Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 22Issue 2February 2022

History

Received: Jul 10, 2020
Accepted: Oct 11, 2021
Published online: Dec 13, 2021
Published in print: Feb 1, 2022
Discussion open until: May 13, 2022

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Authors

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Sudheer Prabhu, S.M.ASCE [email protected]
Senior Staff Professional, Geosyntec Consultants, 10211 Wincopin Cir Floor 4, Columbia, MD 21044; formerly Ph.D. Candidate, Dept. of Civil and Environmental Engineering, Pennsylvania State Univ., University Park, PA 16802. Email: [email protected]
Tong Qiu, M.ASCE [email protected]
Professor, Dept. of Civil and Environmental Engineering, Pennsylvania State Univ., University Park, PA 16802 (corresponding author). Email: [email protected]

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