Microstructure Incidence on the Bifurcation Domain Topology in Granular Materials
Publication: Journal of Engineering Mechanics
Volume 144, Issue 6
Abstract
The detection of bifurcation in granular soils is a major concern in geomechanics. Recent advances in geomechanics have highlighted the key role played by the mesoscopic structures composed of grain loops in the stability of granular media. Based on an elementary grain loop pattern, this paper investigates the influence of the microstructure on the bifurcation domain topology at the mesoscopic scale. This study shows that, at the mesoscopic scale, the bifurcation domain cannot be consistently defined in terms of the stress state only. Expressed in a stress-microstructure space, the bifurcation domain becomes invariant with the contact regime, the initial microstructure, and the loading path. It is also shown that the microstructural anisotropy is as determinant as the stress state with respect to the bifurcation domain topology. Finally, the mechanical and volumetric behaviors of the granular assembly are shown to be correlated through a proper microstructural variable.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors express their sincere thanks to the French Research Network MeGe (multiscale and multi-physics couplings in geo-environmental mechanics GDR CNRS 3176/2340, 2008–2015) for having supported this work.
References
Aris, M., Benahmed, N., and Bonelli, S. (2012). “Experimental geomechanics: A laboratory study on the behaviour of granular material using bender elements.” Eur. J. Environ. Civ. Eng., 16(1), 97–110.
Bagi, K. (2007). “On the concept of jammed configurations from a structural mechanics perspective.” Granular Matter, 9(1–2), 109–134.
Bardet, J. (1998). “Introduction to computational granular mechanics.” Behaviour of granular materials, Springer, New York, 99–169.
Bardet, J., and Proubet, J. (1992). “Shear band an analysis idealized granular media.” J. Eng. Mech., 397–415.
Benahmed, N., Canou, J., and Dupla, J.-C. (2004). “Initial structure and static liquefaction properties of sand.” C.R. Mec., 332(11), 887–894.
Calvetti, F. (2008). “Discrete modelling of granular materials and geotechnical problems.” Eur. J. Environ. Civ. Eng., 12(7–8), 951–965.
Castro, G., and Poulos, S. (1977). “Factors affecting liquefaction and cyclic mobility.” J. Geotech. Eng. Div., 103(6), 501–516.
Cates, M., Wittmer, J., Bouchaud, J.-P., and Claudin, P. (1998). “Physical review letters.” Jamming Force Chains Fragile Matter, 81(9), 1841–1844.
Cheng, Y., Bolton, M., and Nakata, Y. (2004). “Crushing and plastic deformation of soils simulated using DEM.” Géotechnique, 54(2), 131–141.
Chu, J., Leong, W., Loke, W., and Wanatowski, D. (2012). “Instability of loose sand under drained conditions.” J. Geotech. Geoenviron. Eng., 207–216.
Chu, J., Leroueil, S., and Leong, W. (2003). “Unstable behaviour of sand and its implication for slope stability.” Can. Geotech. J., 40(5), 873–885.
Cundall, P., and Strack, O. (1979). “A discrete numerical model for granular assemblies.” Géotechnique, 29(1), 47–65.
Daouadji, A., et al. (2011). “Diffuse failure in geomaterials: Experiments, theory and modelling.” Int. J. Num. Anal. Methods Geomech., 35(16), 1731–1773.
Daouadji, A., Al Ghali, H., Darve, F., and Zeghloul, A. (2010). “Instability in granular materials: Experimental evidence of diffuse mode of failure for loose sands.” J. Eng. Mech., 575–588.
Darve, F., and Labanieh, S. (1982). “Incremental constitutive law for sands and clays: Simulations of monotonic and cyclic tests.” Int. J. Num. Anal. Methods Geomech., 6(2), 243–275.
Darve, F., and Nicot, F. (2005). “On incremental non-linearity in granular media: Phenomenological and multi-scale views (Part I).” Int. J. Num. Anal. Methods Geomech., 29(14), 1387–1409.
Darve, F., Servant, G., Laouafa, F., and Khoa, H. (2004). “Failure in geomaterials: Continuous and discrete analyses.” Comput. Methods Appl. Mech. Eng., 193(27–29), 3057–3085.
Darve, F., Sibille, L., Daouadji, A., and Nicot, F. (2007). “Bifurcation in granular media: Macro- and micro-mechanics approaches.” C.R. Mec., 335(9–10), 496–515.
Doanh, T., Bot, A. L., Abdelmoula, N., Hans, S., and Boutin, C. (2014). “Liquefaction of immersed granular media under isotropic compression.” Europhys. Lett., 108(2), 24004.
Gajo, A. (2004). “The influence of system compliance on collapse of triaxial sand samples.” Can. Geotech. J., 41(2), 257–273.
Gong, G., Thornton, C., and Chan, A. (2012). “DEM simulations of undrained triaxial behavior of granular material.” J. Eng. Mech., 560–566.
Hadda, N. (2013). “Aspects micromécaniques de la rupture dans les milieux granulaires.” Ph.D. thesis, Université de Grenoble, Grenoble, France (in French).
Hadda, N., Nicot, F., Wan, R., and Darve, F. (2015). “Microstructural self-organization in granular materials during failure.” C.R. Mec., 343(2), 143–154.
Hamadi, K., Modaressi-Farahmand-Razavi, A., and Darve, F. (2008). “Bifurcation and instability modelling by a multimechanism elasto-plastic model.” Int. J. Num. Anal. Methods Geomech., 32(5), 461–492.
Hill, R. (1958). “A general theory of uniqueness and stability in elastic plastic solids.” J. Mech. Phys. Solids, 6(3), 236–249.
Itasca Consulting Group (2014). PFC particle flow code, Minneapolis.
Kruyt, N., and Rothenburg, L. (2014). “On the mechanical characteristics of the critical state of two-dimensional granular materials.” Acta Mech., 225(8), 2301–2318.
Kuhn, M. (1999). “Structure deformation in granular materials.” Mech. Mater., 31(6), 407–429.
Lade, P. (1992). “Static instability and liquefaction of loose fine sandy slopes.” J. Geotech. Eng., 51–71.
Lerbet, J., Challamel, N., Nicot, F., and Darve, F. (2016). “Kinematical structural stability.” Discrete Discontinuous Dyn. Syst. Ser. S, 9(2), 529–536.
Nguyen, N., Magoariec, H., Cambou, B., and Danescu, A. (2009). “Analysis of structure and strain at the meso-scale in 2D granular media.” Int. J. Solids Struct., 46(17), 3257–3271.
Nicot, F., and Darve, F. (2005). “A multi-scale approach to granular materials.” Mech. Mater., 37(9), 980–1006.
Nicot, F., and Darve, F. (2006). “Micro-mechanical investigation of material instability in granular assemblies.” Int. J. Solids Struct., 43(11–12), 3569–3595.
Nicot, F., and Darve, F. (2011). “The H-microdirectional model: Accounting for a mesoscopic scale.” Mech. Mater., 43(12), 918–929.
Nicot, F., Hadda, N., Bourrier, F., Sibille, L., Wan, R., and Darve, F. (2012a). “Inertia effects as a possible missing link between micro and macro second-order work in granular media.” Int. J. Solids Struct., 49(10), 1252–1258.
Nicot, F., Sibille, L., and Darve, F. (2009). “Bifurcation in granular materials: An attempt at a unified framework.” Int. J. Solids Struct., 46(22–23), 3938–3947.
Nicot, F., Sibille, L., and Darve, F. (2012b). “Failure in rate-independant granular materials as a bifurcation toward a dynamic regime.” Int. J. Plast., 29, 136–154.
Nicot, F., Veylon, G., Zhu, H., Lerbet, J., and Darve, F. (2016). “Mesoscopic-scale instability in particulate materials.” J. Eng. Mech., 04016047.
Oda, M. (1972). “Initial fabrics and their relations to mechanical properties of granular materials.” Soils Found., 12(1), 17–36.
Radjai, F., Wolf, D., Jean, M., and Moreau, J.-J. (1998). “Bimodal character of stress transmission in granular packings.” Phys. Rev. Lett., 80(1), 61–64.
Sasitharan, S., Robertson, P. K., Sega, D. C., and Morgenstern, N. R. (1993). “Collapse behavior of sand.” Can. Geotech. J., 30(4), 569–577.
Satake, M. (1982). “Fabric tensor in granular materials.” Proc., Int. Union of Theoretical and Applied Mechanics (IUTAM) Symp. on Deformation and Failure of Granular Materials, P. Vermeer and H. Luger, eds., A.A. Balkema, Amsterdam, Netherlands, 63–68.
Satake, M. (1992). “A discrete-mechanical approach to granular materials.” Int. J. Eng. Sci., 30(10), 1525–1533.
Sibille, L., Donzé, F.-V., Nicot, F., and Chareyre, B. (2008). “From bifurcation to failure in a granular material: A DEM analysis.” Acta Geotech., 3(1), 15–24.
Sibille, L., Nicot, F., Donzé, F.-V., and Darve, F. (2007). “Material instability in granular assemblies from fundamental different models.” Int. J. Num. Anal. Methods Geomech., 31(3), 457–481.
Sibille, L., Prunier, F., Nicot, F., and Darve, F. (2011). “Discrete numerical analysis of failure modes in granular materials.” Particle-based methods, Springer, Dordrecht, Netherlands, 187–210.
Singer I., and Pollock H., eds. (1992). Fundamentals of friction, macroscopic and microscopic processes, Springer, Dordrecht, Netherlands.
Šmilauer, V., et al. (2015). “Dem formulation.” Yade documentation, 2nd Ed., The Yade Project.
Ting, J., Corkum, B., Kauffman, C., and Greco, C. (1989). “Discrete numerical model for soil mechanics.” J. Geotech. Eng., 379–398.
Tordesillas, A., and Muthuswamy, M. (2009). “On the modelling of confined buckling of force chains.” J. Mech. Phys. Solids, 57(4), 706–727.
Welker, P., and McNamara, S. (2009). “What triggers failure in frictional granular assemblies?” Phys. Rev. E, 79(6), 061305.
Yang, Z., Yang, J., and Wang, L. (2012). “On the influence of interdilatancy friction and dilatancy in granular soils: A numerical analysis.” Granular Matter, 14(3), 433–447.
Yoshimine, M., Ishihara, K., and Vargas, W. (1998). “Effects of principal stress direction and intermediate principal stress on undrained shear behaviour of sand.” Soils Found., 38(3), 179–188.
Zhu, H., Nicot, F., and Darve, F. (2016). “Meso-structure evolution in a 2D granular material during biaxial loading.” Granular Matter, 18(1), 3.
Zhu, H., Veylon, G., Nicot, F., and Darve, F. (2017). “On the mechanics of meso-scale structures in two-dimensional granular materials.” Eur. J. Environ. Civ. Eng., 21(7–8), 912–935.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 144 • Issue 6 • June 2018
Copyright
©2018 American Society of Civil Engineers.
History
Received: Jul 9, 2016
Accepted: Nov 9, 2017
Published online: Mar 28, 2018
Published in print: Jun 1, 2018
Discussion open until: Aug 28, 2018
Authors
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.