Technical Papers
Jul 6, 2020

Numerical Investigation of the Elastic Properties of Binary Mixtures as a Function of the Size Ratio and Fines Content

Publication: International Journal of Geomechanics
Volume 20, Issue 9

Abstract

This paper examines the influences of the size ratio and fines content on Young's modulus and the shear modulus of binary mixtures using the discrete element method. The moduli were gained by numerical simulations of drained triaxial compression tests. The contribution of each contact type is quantified, and the results indicate that the moduli are controlled by the combined action of various contact types. The analysis of microscopic characteristics shows that the moduli rely on the modified void ratio and 2/3 power of the modified volume-weighted coordination number. Additionally, a good relationship among the normalized modulus, the volume-weighted coordination number, and the peak friction angle is found.

Get full access to this article

View all available purchase options and get full access to this article.

Acknowledgments

The authors are grateful for the financial support given by these projects, including the Fundamental Research Funds for the Central Universities of Central South University (No. 2018zzts195), Beijing Municipal Science and Technology Project: Research and Application of Design and Construction Technology of Railway Engineering Traveling the Rift Valley (No. Z181100003918005), and the National Natural Science Foundation of China (No. 51809292).

References

Abbireddy, C. O. R., and C. R. I. Clayton. 2010. “Varying initial void ratios for DEM simulations.” Géotechnique 60 (6): 497–502. https://doi.org/10.1680/geot.2010.60.6.497.
Andrus, R. D., and K. H. Stokoe, II. 2000. “Liquefaction resistance of soils from shear-wave velocity.” J. Geotech. Geoenviron. Eng. 126 (11): 1015–1025. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:11(1015).
Azema, E., and F. Radjai. 2012. “Force chains and contact network topology in sheared packings of elongated particles.” Phys. Rev. E 85 (3): 031303. https://doi.org/10.1103/PhysRevE.85.031303.
Bellotti, R., M. Jamiolkowski, D. C. F. L. Presti, and D. A. O’Neill. 1996. “Anisotropy of small strain stiffness in Ticino sand.” Géotechnique 46 (1): 115–131. https://doi.org/10.1680/geot.1996.46.1.115.
Bian, X., W. Li, Y. Qian, and E. Tutumluer. 2019. “Micromechanical particle interactions in railway ballast through DEM simulations of direct shear tests.” Int. J. Geomech. 19 (5): 04019031. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001403.
Chang, C. S., M. Anil, and S. S. Sundaram. 1991. “Properties of granular packings under low amplitude cyclic loading.” Soil Dyn. Earthquake Eng. 10 (4): 201–211. https://doi.org/10.1016/0267-7261(91)90034-W.
Chien, L. K., and Y. N. Oh. 2002. “Influence of fines content and initial shear stress on dynamic properties of hydraulic reclaimed soil.” Can. Geotech. J. 39 (1): 242–253. https://doi.org/10.1139/t01-082.
Cho, G.-C., J. Dodds, and J. C. Santamarina. 2006. “Particle shape effects on packing density, stiffness, and strength: Natural and crushed sands.” J. Geotech. Geoenviron. Eng. 132 (5): 591–602. https://doi.org/10.1061/(ASCE)1090-0241(2006)132:5(591).
Choo, H., and S. E. Burns. 2015. “Shear wave velocity of granular mixtures of silica particles as a function of finer fraction, size ratios and void ratios.” Granular Matter 17 (5): 567–578. https://doi.org/10.1007/s10035-015-0580-2.
Cundall, P. A., J. T. Jenkins, and I. Ishibashi. 1989. Evolution of elastic moduli in a deforming granular assembly. Rotterdam, Netherlands: Powders and Grains.
Dai, B.-B., and J. Yang. 2017. “Shear strength of assemblies of frictionless particles.” Int. J. Geomech. 17 (11): 04017102. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001005.
Deluzarche, R., and B. Cambou. 2006. “Discrete numerical modelling of rockfill dams.” Int. J. Numer. Anal. Methods Geomech. 30 (11): 1075–1096. https://doi.org/10.1002/nag.514.
Deng, X., and R. N. Dave. 2017. “Properties of force networks in jammed granular media.” Granular Matter 19 (2): 27. https://doi.org/10.1007/s10035-017-0715-8.
Ezaoui, A., and H. Di Benedetto. 2009. “Experimental measurements of the global anisotropic elastic behaviour of dry Hostun sand during triaxial tests, and effect of sample preparation.” Géotechnique 59 (7): 621–635. https://doi.org/10.1680/geot.7.00042.
Fioravante, V., D. Giretti, and M. Jamiolkowski. 2013. “Small strain stiffness of carbonate Kenya Sand.” Eng. Geol. 161: 65–80. https://doi.org/10.1016/j.enggeo.2013.04.006.
Gong, J., X. Wang, L. Li, and Z. Nie. 2019. “DEM study of the effect of fines content on the small-strain stiffness of gap-graded soils.” Comput. Geotech. 112: 35–40. https://doi.org/10.1016/j.compgeo.2019.04.008.
Gu, X. Q., J. Hu, and M. Huang. 2017a. “Anisotropy of elasticity and fabric of granular soils.” Granular Matter 19 (2): 33. https://doi.org/10.1007/s10035-017-0717-6.
Gu, X. Q., J. Hu, M. Huang, and J. Yang. 2018. “Discrete element analysis of the K0 of granular soil and its relation to small strain shear stiffness.” Int. J. Geomech. 18 (3): 06018003. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001102.
Gu, X. Q., L. Lu, and J. Qian. 2017b. “Discrete element modeling of the effect of particle size distribution on the small strain stiffness of granular soils.” Particuology 32: 21–29. https://doi.org/10.1016/j.partic.2016.08.002.
Gu, X. Q., and J. Yang. 2013. “A discrete element analysis of elastic properties of granular materials.” Granular Matter 15 (2): 139–147. https://doi.org/10.1007/s10035-013-0390-3.
Gu, X. Q., J. Yang, and M. Huang. 2013a. “DEM simulations of the small strain stiffness of granular soils: Effect of stress ratio.” Granular Matter 15 (3): 287–298. https://doi.org/10.1007/s10035-013-0407-y.
Gu, X. Q., J. Yang, and M. Huang. 2013b. “Laboratory measurements of small strain properties of dry sands by bender element.” Soils Found. 53 (5): 735–745. https://doi.org/10.1016/j.sandf.2013.08.011.
Gu, X. Q., J. Yang, M. S. Huang, and G. Y. Gao. 2015. “Bender element tests in dry and saturated sand: Signal interpretation and result comparison.” Soils Found. 55 (5): 951–962. https://doi.org/10.1016/j.sandf.2015.09.002.
Hardin, B. O., and F. E. Richart. 1963. “Elastic wave velocities in granular soils.” J. Soil Mech. Found. Div. 89 (1): 33–65.
Hoque, E., and F. Tatsuoka. 1998. “Anisotropy in elastic deformation of granular materials.” Soils Found. 38 (1): 163–179. https://doi.org/10.3208/sandf.38.163.
Hoque, E., and F. Tatsuoka. 2004. “Effects of stress ratio on small-strain stiffness during triaxial shearing.” Géotechnique 54 (7): 429–439. https://doi.org/10.1680/geot.2004.54.7.429.
Ishibashi, I., and O. F. Capar. 2003. “Anisotropy and its relation to liquefaction resistance of granular material.” Soils Found. 43 (5): 149–159. https://doi.org/10.3208/sandf.43.5_149.
Iwasaki, T., and F. Tatsuoka. 1977. “Effects of grain size and grading on dynamic shear moduli of sands.” Soils Found. 17 (3): 19–35. https://doi.org/10.3208/sandf1972.17.3_19.
Jaky, J. 1944. “The coefficient of earth pressure at rest.” J. Soc. Hung. Arch. Eng. 78 (22): 355–358.
Jiang, G. L., F. Tatsuoka, A. Flora, and J. Koseki. 1997. “Inherent and stress-state-induced anisotropy in very small strain stiffness of a sandy gravel.” Géotechnique 47 (3): 509–521. https://doi.org/10.1680/geot.1997.47.3.509.
Kuwano, R., and R. J. Jardine. 2002. “On the applicability of cross-anisotropic elasticity to granular materials at very small strains.” Géotechnique 52 (10): 727–749. https://doi.org/10.1680/geot.2002.52.10.727.
Lashkari, A., M. Khodadadi, S. M. Binesh, and M. M. Rahman. 2019. “Instability of particulate assemblies under constant shear drained stress path: DEM approach.” Int. J. Geomech. 19 (6): 04019049. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001407.
Lopez, R. D., J. Ekblad, and J. Silfwerbrand. 2016. “Resilient properties of binary granular mixtures: A numerical investigation.” Comput. Geotech. 76: 222–233. https://doi.org/10.1016/j.compgeo.2016.03.002.
Lu, X., Y. Ma, J. Qian, and M. Huang. 2019. “Discrete-element simulation of scaling effect of strain localization in dense granular materials.” Int. J. Geomech. 19 (6): 04019059. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001443.
Magnanimo, V., L. L. Ragione, J. T. Jenkins, P. Wang, and H. A. Makse. 2008. “Characterizing the shear and bulk moduli of an idealized granular material.” Europhys. Lett. 81 (3): 34006. https://doi.org/10.1209/0295-5075/81/34006.
Meng, J., J. Huang, D. Sheng, and S. W. Sloan. 2017. “Quasi-static rheology of granular media using the static DEM.” Int. J. Geomech. 17 (11): 04017094. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001001.
Ng, T. T. 2009. “Particle shape effect on macro- and micro-behaviors of monodisperse ellipsoids.” Int. J. Numer. Anal. Methods Geomech. 33 (4): 511–527. https://doi.org/10.1002/nag.732.
Ng, T. T., W. Zhou, G. Ma, and X. L. Chang. 2018. “Macroscopic and microscopic behaviors of binary mixtures of different particle shapes and particle sizes.” Int. J. Solids Struct. 135: 74–84. https://doi.org/10.1016/j.ijsolstr.2017.11.011.
Salgado, R., P. Bandini, and A. Karim. 2000. “Shear strength and stiffness of silty sand.” J. Geotech. Geoenviron. Eng. 126 (5): 451–462. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:5(451).
Shaebani, M. R., M. Madadi, S. Luding, and D. E. Wolf. 2012. “Influence of polydispersity on micromechanics of granular materials.” Phys. Rev. E 85 (1): 011301. https://doi.org/10.1103/PhysRevE.85.011301.
Shire, T., and C. O’Sullivan. 2013. “Micromechanical assessment of an internal stability criterion.” Acta Geotech. 8 (1): 81–90. https://doi.org/10.1007/s11440-012-0176-5.
Shire, T., C. O’Sullivan, and K. J. Hanley. 2016. “The influence of fines content and size-ratio on the micro-scale properties of dense bimodal materials.” Granular Matter 18 (3): 52. https://doi.org/10.1007/s10035-016-0654-9.
Skempton, A. W., and J. M. Brogan. 1994. “Experiments on piping in sandy gravels.” Géotechnique 44 (3): 449–460. https://doi.org/10.1680/geot.1994.44.3.449.
Thevanayagam, S., T. Shenthan, S. Mohan, and J. Liang. 2002. “Undrained fragility of clean sands, silty sands, and sandy silts.” J. Geotech. Geoenviron. Eng. 128 (10): 849–859. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:10(849).
Thornton, C. 2000. “Numerical simulations of deviatoric shear deformation of granular media.” Géotechnique 50 (1): 43–53. https://doi.org/10.1680/geot.2000.50.1.43.
Vallejo, L. E., and R. Mawby. 2000. “Porosity influence on the shear strength of granular material–clay mixtures.” Eng. Geol. 58 (2): 125–136. https://doi.org/10.1016/S0013-7952(00)00051-X.
Wang, Y. H., and C. M. B. Mok. 2008. “Mechanisms of small-strain shear-modulus anisotropy in soils.” J. Geotech. Geoenviron. Eng. 134 (10): 1516–1530. https://doi.org/10.1061/(ASCE)1090-0241(2008)134:10(1516).
Wichtmann, T., M. A. Navarrete Hernández, and T. Triantafyllidis. 2015. “On the influence of a non-cohesive fines content on small strain stiffness, modulus degradation and damping of quartz sand.” Soil Dyn. Earthquake Eng. 69: 103–114. https://doi.org/10.1016/j.soildyn.2014.10.017.
Wichtmann, T., and T. Triantafyllidis. 2009. “Influence of the grain-size distribution curve of quartz sand on the small strain shear modulus Gmax.” J. Geotech. Geoenviron. Eng. 135 (10): 1404–1418. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000096.
Wichtmann, T., and T. Triantafyllidis. 2010. “On the influence of the grain size distribution curve on P-wave velocity constrained elastic modulus Mmax and Poisson’s ratio of quartz sands.” Soil Dyn. Earthquake Eng. 30 (8): 757–766. https://doi.org/10.1016/j.soildyn.2010.03.006.
Xu, W. J., Q. Xu, and R. L. Hu. 2011. “Study on the shear strength of soil–rock mixture by large scale direct shear test.” Int. J. Rock Mech. Min. Sci. 48 (8): 1235–1247. https://doi.org/10.1016/j.ijrmms.2011.09.018.
Yan, W. M., and J. J. Dong. 2011. “Effect of particle grading on the response of an idealized granular assemblage.” Int. J. Geomech. 11 (4): 276–285. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000085.
Yang, J., and X. Q. Gu. 2013. “Shear stiffness of granular material at small strains: Does it depend on grain size?” Géotechnique 63 (2): 165–179. https://doi.org/10.1680/geot.11.P.083.
Yang, J., and X. Liu. 2016. “Shear wave velocity and stiffness of sand: The role of non-plastic fines.” Géotechnique 66 (6): 500–514. https://doi.org/10.1680/jgeot.15.P.205.
Yang, J., and X. R. Yan. 2009. “Site response to multi-directional earthquake loading: A practical procedure.” Soil Dyn. Earthquake Eng. 29 (4): 710–721. https://doi.org/10.1016/j.soildyn.2008.07.008.
Zhou, W., K. Xu, G. Ma, L. Yang, and X. Chang. 2016. “Effects of particle size ratio on the macro- and microscopic behaviors of binary mixtures at the maximum packing efficiency state.” Granular Matter 18 (4): 81. https://doi.org/10.1007/s10035-016-0678-1.
Zhou, Y.-G., and Y.-M. Chen. 2007. “Laboratory investigation on assessing liquefaction resistance of sandy soils by shear wave velocity.” J. Geotech. Geoenviron. Eng. 133 (8): 959–972. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:8(959).
Zhu, H., W.-H. Zhou, and Z.-Y. Yin. 2018. “Deformation mechanism of strain localization in 2D numerical interface tests.” Acta Geotech. 13 (3): 557–573. https://doi.org/10.1007/s11440-017-0561-1.

Information & Authors

Information

Published In

Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 20Issue 9September 2020

History

Received: Jun 19, 2019
Accepted: Apr 27, 2020
Published online: Jul 6, 2020
Published in print: Sep 1, 2020
Discussion open until: Dec 6, 2020

Permissions

Request permissions for this article.

Authors

Affiliations

Ph.D. Candidate, School of Civil Engineering, Central South Univ., Changsha 410075, China. Email: [email protected]
Postdoctor, School of Civil Engineering, Central South Univ., Changsha 410075, China. Email: [email protected]
Professor, School of Civil Engineering, Central South Univ., Changsha 410075, China (corresponding author). ORCID: https://orcid.org/0000-0002-9660-1737. Email: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share