Technical Papers
May 21, 2020

DEM Investigation on the Evolution of Fabric under True Triaxial Conditions in Granular Materials

Publication: International Journal of Geomechanics
Volume 20, Issue 8

Abstract

The evolution of fabric under loading plays an important role in the micromechanical analysis of granular materials. This paper addressed this issue from the perspective of the discrete element method (DEM) simulation. A series of drained tests were performed under true triaxial stress conditions. Isotropic assemblies with different densities were sheared to the critical state under three kinds of loading paths. The evolution of three-dimensional fabric under general stress conditions was investigated by analyzing the influences of density, shear mode, and loading path on the fabric anisotropy. Numerical results revealed some evolution patterns of fabric with strain and stress. The evolutions of fabric components and deviatoric fabric were dependent on shear mode. An ultimate fabric anisotropic state was achieved at a relatively large strain for a given shear mode, which agreed with the theoretical expectation of anisotropic critical state theory. Noncoaxialities between fabric, stress, and strain tensors were also observed in simulations and these noncoaxialities needed to be rationally incorporated into fabric evolution laws.

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Acknowledgments

The authors appreciate the financial support of the National Natural Science Foundation of China (No. 51178044), Beijing Excellent Talent Training Program (2013D009006000005), and the China National Key Research and Development Plan (2017YFC0805300).

References

Andrade, J. E., K. W. Lim, C. F. Avila, and I. Vlahinić. 2012. “Granular element method for computational particle mechanics.” Comput. Methods Appl. Mech. Eng. 241–244: 262–274. https://doi.org/10.1016/j.cma.2012.06.012.
Arthur, J. R. F., M. A. Koenders, and R. K. S. Wong. 1986. “Anisotropy in particle contacts associated with shearing in granular media.” Acta Mech. 64 (1–2): 19–29. https://doi.org/10.1007/BF01180095.
Chang, C. S. 1993. “Micromechanical modeling of deformation and failure for granulates with frictional contacts.” Mech. Mater. 16 (1–2): 13–24. https://doi.org/10.1016/0167-6636(93)90023-K.
Chang, C. S., and Y. Liu. 2013. “Stress and fabric in granular material.” Theor. Appl. Mech. Lett. 3 (2): 021002. https://doi.org/10.1063/2.1302102.
Cundall, P. A., and O. D. L. Strack. 1979. “A discrete numerical model for granular assemblies.” Géotechnique 29 (1): 47–65. https://doi.org/10.1680/geot.1979.29.1.47.
Fu, P., and Y. F. Dafalias. 2011. “Fabric evolution within shear bands of granular materials and its relation to critical state theory.” Int. J. Numer. Anal. Methods Geomech. 35 (18): 1918–1948. https://doi.org/10.1002/nag.988.
Fu, P., and Y. F. Dafalias. 2015. “Relationship between void- and contact normal-based fabric tensors for 2D idealized granular materials.” Int. J. Solids Struct. 63: 68–81. https://doi.org/10.1016/j.ijsolstr.2015.02.041.
Gao, Z., and J. Zhao. 2017. “A non-coaxial critical-state model for sand accounting for fabric anisotropy and fabric evolution.” Int. J. Solids Struct. 106–107: 200–212. https://doi.org/10.1016/j.ijsolstr.2016.11.019.
Gao, Z., J. Zhao, X. S. Li, and Y. F. Dafalias. 2014. “A critical state sand plasticity model accounting for fabric evolution.” Int. J. Numer. Anal. Methods Geomech. 38 (4): 370–390. https://doi.org/10.1002/nag.2211.
Guo, N., and J. Zhao. 2013. “The signature of shear-induced anisotropy in granular media.” Comput. Geotech. 47: 1–15. https://doi.org/10.1016/j.compgeo.2012.07.002.
Guo, P. 2000. “Modelling granular materials with respect to stress-dilatancy and fabric: A fundamental approach.” Ph.D. thesis, Civil Engineering Dept., Univ. of Calgary.
Guo, P. J., and D. F. E. Stolle. 2005. “On the failure of granular materials with fabric effects.” Soils Found. 45 (4): 1–12. https://doi.org/10.3208/sandf.45.4_1.
Hurley, R. C., S. A. Hall, J. E. Andrade, and J. Wright. 2016. “Quantifying interparticle forces and heterogeneity in 3D granular materials.” Phys. Rev. Lett. 117 (9): 098005. https://doi.org/10.1103/PhysRevLett.117.098005.
Ken-Ichi, K. 1984. “Distribution of directional data and fabric tensors.” Int. J. Eng. Sci. 22 (2): 149–164. https://doi.org/10.1016/0020-7225(84)90090-9.
Konishi, J., and F. Naruse. 1988. “A note on fabric in terms of voids.” In Micromechanics of granular materials, edited by M. Satake, and J. Jenkins, 39–46. Amsterdam, Netherlands: Elsevier.
Kruyt, N. P. 2012. “Micromechanical study of fabric evolution in quasi-static deformation of granular materials.” Mech. Mater. 44: 120–129. https://doi.org/10.1016/j.mechmat.2011.07.008.
Kruyt, N. P., and L. Rothenburg. 2016. “A micromechanical study of dilatancy of granular materials.” J. Mech. Phys. Solids 95: 411–427. https://doi.org/10.1016/j.jmps.2016.01.019.
Kuhn, M. R. 2010. “Micro-mechanics of fabric and failure in granular materials.” Mech. Mater. 42 (9): 827–840. https://doi.org/10.1016/j.mechmat.2010.07.004.
Kuhn, M. R., and C. S. Chang. 2006. “Stability, bifurcation, and softening in discrete systems: A conceptual approach for granular materials.” Int. J. Solids Struct. 43 (20): 6026–6051. https://doi.org/10.1016/j.ijsolstr.2005.10.012.
Lade, P. V., and J. M. Duncan. 1973. “Cubical triaxial tests on cohesionless soil.” J. Soil Mech. Found. Div. 99 (10): 793–812.
Lade, P. V., and J. M. Duncan. 1975. “Elastoplastic stress-strain theory for cohesionless soil.” J. Geotech. Eng. Div. 101 (10): 1037–1053.
Li, X. 2016. “Internal structure quantification for granular constitutive modeling.” J. Eng. Mech. 143 (4): C4016001. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001118.
Li, X., and X. S. Li. 2009. “Micro-macro quantification of the internal structure of granular materials.” J. Eng. Mech. 135 (7): 641–656. https://doi.org/10.1061/(ASCE)0733-9399(2009)135:7(641).
Li, X. S., and Y. F. Dafalias. 2002. “Constitutive modeling of inherently anisotropic sand behavior.” J. Geotech. Geoenviron. Eng. 128 (10): 868–880. https://doi.org/10.1061/(ASCE)1090-0241(2002)128:10(868).
Li, X. S., and Y. F. Dafalias. 2012. “Anisotropic critical state theory: Role of fabric.” J. Eng. Mech. 138 (3): 263–275. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000324.
Li, X. S., and Y. F. Dafalias. 2015. “Dissipation consistent fabric tensor definition from DEM to continuum for granular media.” J. Mech. Phys. Solids 78: 141–153. https://doi.org/10.1016/j.jmps.2015.02.003.
Mahmud Sazzad, M., K. Suzuki, and A. Modaressi-Farahmand-Razavi. 2012. “Macro-micro responses of granular materials under different b values using DEM.” Int. J. Geomech. 12 (3): 220–228. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000133.
Matsuoka, H., and T. Nakai. 1974. “Stress-deformation and strength characteristics of soil under three different principal stresses.” Jpn. Soc. Civ. Eng. 1974 (232): 59–70.
Nemat-Nasser, S. 2000. “A micromechanically-based constitutive model for frictional deformation of granular materials.” J. Mech. Phys. Solids 48 (6–7): 1541–1563. https://doi.org/10.1016/S0022-5096(99)00089-7.
Ni, Q., W. Powrie, X. Zhang, and R. Harkness. 2000. “Effect of particle properties on soil behavior: 3-D numerical modeling of shearbox tests.” In Numerical methods in geotechnical engineering, edited by G. M. Filz, and D. V. Griffiths, 58–70. Reston, VA: ASCE. https://doi.org/10.1061/40502(284)5.
Oboudi, M., S. Pietruszczak, and A. G. Razaqpur. 2016. “Description of inherent and induced anisotropy in granular media with particles of high sphericity.” Int. J. Geomech. 16 (4): 04016006. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000635.
Oda, M. 1972. “Initial fabrics and their relations to mechanical properties of granular material.” Soils Found. 12 (1): 17–36. https://doi.org/10.3208/sandf1960.12.17.
Oda, M. 1993. “Inherent and induced anisotropy in plasticity theory of granular soils.” Mech. Mater. 16 (1–2): 35–45. https://doi.org/10.1016/0167-6636(93)90025-M.
Oda, M., and J. Konishi. 1974. “Microscopic deformation mechanism of granular material in simple shear.” Soils Found. 14 (4): 25–38. https://doi.org/10.3208/sandf1972.14.4_25.
Oda, M., and H. Nakayama. 1988. “Introduction of inherent anisotropy of soils in the yield function.” Stud. Appl. Mech. 20: 81–90. https://doi.org/10.1016/B978-0-444-70523-5.50017-5.
Oda, M., and H. Nakayama. 1989. “Yield function for soil with anisotropic fabric.” J. Eng. Mech. 115 (1): 89–104. https://doi.org/10.1061/(ASCE)0733-9399(1989)115:1(89).
Phusing, D., K. Suzuki, and M. Zaman. 2016. “Mechanical behavior of granular materials under continuously varying b values using DEM.” Int. J. Geomech. 16 (1): 04015027. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000506.
Pietruszczak, S., and S. Krucinski. 1989. “Description of anisotropic response of clays using a tensorial measure of structural disorder.” Mech. Mater. 8 (2–3): 237–249. https://doi.org/10.1016/0167-6636(89)90014-8.
Pietruszczak, S., and Z. Mroz. 2000. “Formulation of anisotropic failure criteria incorporating a microstructure tensor.” Comput. Geotech. 26 (2): 105–112. https://doi.org/10.1016/S0266-352X(99)00034-8.
Pouragha, M., and W. Richard. 2016. “Onset of structural evolution in granular materials as a redundancy problem.” Granular Matter 18 (3): 38. https://doi.org/10.1007/s10035-016-0640-2.
Pouragha, M., and W. Richard. 2017. “Non-dissipative structural evolutions in granular materials within the small strain range.” Int. J. Solids Struct. 110–111: 94–105. https://doi.org/10.1016/j.ijsolstr.2017.01.039.
Radjaï, F., D. E. Wolf, M. Jean, and J.-J. Moreau. 1998. “Bimodal character of stress transmission in granular packings.” Phys. Rev. Lett. 80 (1): 61–64. https://doi.org/10.1103/PhysRevLett.80.61.
Rodriguez, N. M., and P. V. Lade. 2013. “True triaxial tests on cross-anisotropic deposits of fine nevada sand.” Int. J. Geomech. 13 (6): 779–793. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000282.
Rothenburg, L., and R. J. Bathurst. 1989. “Analytical study of induced anisotropy in idealized granular materials.” Géotechnique 39 (4): 601–614. https://doi.org/10.1680/geot.1989.39.4.601.
Rothenburg, L., and N. P. Kruyt. 2004. “Critical state and evolution of coordination number in simulated granular materials.” Int. J. Solids Struct. 41 (21): 5763–5774. https://doi.org/10.1016/j.ijsolstr.2004.06.001.
Saadatfar, M., A. P. Sheppard, T. J. Senden, and A. J. Kabla. 2012. “Mapping forces in a 3D elastic assembly of grains.” J. Mech. Phys. Solids 60 (1): 55–66. https://doi.org/10.1016/j.jmps.2011.10.001.
Satake, M. 1978. “Constitution of mechanics of granular materials through graph theory.” In US-Japan seminar on continuum-mechanical and statistica l approaches to granular materials, edited by S. C. Cowin, and M. Satake, 47–62. Amsterdam, Netherlands: Elsevier.
Satake, M. 1982. “Fabric tensor in granular materials.” In Proc., IUTAM Symp. on Deformation and Failure of Granular Materials, edited by P. A. Vermeer, and H. J. Luger, 63–68. Amsterdam, Netherland: A.A. Balkema.
Satake, M. 2004. “Tensorial form definitions of discrete-mechanical quantities for granular assemblies.” Int. J. Solids Struct. 41 (21): 5775–5791. https://doi.org/10.1016/j.ijsolstr.2004.05.046.
Shi, J. S., and P. J. Guo. 2018a. “Induced fabric anisotropy of granular materials in biaxial tests along imposed strain paths.” Soils Found. 58 (2): 249–263. https://doi.org/10.1016/j.sandf.2018.02.001.
Shi, J. S., and P. J. Guo. 2018b. “Fabric evolution of granular materials along imposed stress paths.” Acta Geotech. 13: 1341–1354. https://doi.org/10.1007/s11440-018-0665-2.
Shi, J. S., P. J. Guo, and D. Stolle. 2018. “Noncoaxiality between fabric and stress in two-dimensional granular materials.” J. Eng. Mech. 144 (9): 04018092. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001511.
Taha, M. R., and H. Shaverdi. 2014. “Evolution of fabric under the rotation of the principal stress axes in the simple shear test.” Mech. Mater. 69 (1): 173–184. https://doi.org/10.1016/j.mechmat.2013.10.003.
Thornton, C., and L. Zhang. 2010. “On the evolution of stress and microstructure during general 3D deviatoric straining of granular media.” Géotechnique 60 (5): 333–341. https://doi.org/10.1680/geot.2010.60.5.333.
Tobita, Y., and E. Yanagisawa. 1992. “Modified stress tensors for anisotropic behavior of granular materials.” Soils Found. 32 (1): 85–99. https://doi.org/10.3208/sandf1972.32.85.
Wan, R. G., and P. J. Guo. 2001a. “Effect of microstructure on undrained behaviour of sands.” Can. Geotech. J. 38 (1): 16–28. https://doi.org/10.1139/t00-088.
Wan, R. G., and P. J. Guo. 2001b. “Drained cyclic behavior of sand with fabric dependence.” J. Eng. Mech. 127 (11): 1106–1116. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:11(1106).
Wang, R., P. C. Fu, J. M. Zhang, and Y. F. Dafalias. 2017. “Evolution of various fabric tensors for granular media toward the critical state.” J. Eng. Mech. 143 (10): 04017117. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001342
Wang, X. L., and J. C. Li. 2014. “Simulation of triaxial response of granular materials by modified DEM.” Sci. China Phys. Mech. Astron. 57 (12): 2297–2308. https://doi.org/10.1007/s11433-014-5605-z.
Yan, W. M., and L. Zhang. 2013. “Fabric and the critical state of idealized granular assemblages subject to biaxial shear.” Comput. Geotech. 49: 43–52. https://doi.org/10.1016/j.compgeo.2012.10.015.
Yang, Z. X., and Y. Wu. 2017. “Critical state for anisotropic granular materials: A discrete element perspective.” Int. J. Geomech. 17 (2): 04016054. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000720.
Yimsiri, S., and K. Soga. 2010. “DEM analysis of soil fabric effects on behaviour of sand.” Géotechnique 60 (6): 483–495. https://doi.org/10.1680/geot.2010.60.6.483.
Yuan, R., H. S. Yu, D. S. Yang, and N. Hu. 2019. “On a fabric evolution law incorporating the effects of b-value.” Comput. Geotech. 105: 142–154. https://doi.org/10.1016/j.compgeo.2018.09.019.
Zhao, J., and N. Guo. 2013. “Unique critical state characteristics in granular media considering fabric anisotropy.” Géotechnique 63 (8): 695–704. https://doi.org/10.1680/geot.12.P.040.
Zhao, J., M. Jiang, K. Soga, and S. Luding. 2016. “Micro origins for macro behavior in granular media.” Granular Matter 18 (3): 59. https://doi.org/10.1007/s10035-016-0662-9.
Zhou, J., S. Long, Q. Wang, and A. D. Dinsmore et al. 2006. “Measurement of forces inside a three-dimensional pile of frictionless droplets.” Science 312 (5780): 1631–1633. https://doi.org/10.1126/science.1125151.
Zhu, H., M. M. Mehrabadi, and M. Massoudi. 2006. “Three-dimensional constitutive relations for granular materials based on the dilatant double shearing mechanism and the concept of fabric.” Int. J. Plast. 22 (5): 826–857. https://doi.org/10.1016/j.ijplas.2005.04.013.
Zhu, H., G. Veylon, F. Nicot, and F. Darve. 2017. “On the mechanics of meso-scale structures in two-dimensional granular materials.” Eur. J. Environ. Civ. Eng. 21 (7–8): 912–935. https://doi.org/10.1080/19648189.2016.1229229.

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International Journal of Geomechanics
Volume 20Issue 8August 2020

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Received: Jan 31, 2019
Accepted: Feb 7, 2020
Published online: May 21, 2020
Published in print: Aug 1, 2020
Discussion open until: Oct 21, 2020

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Professor, Dept. of Civil Engineering, Univ. of Science and Technology Beijing, Beijing 100083, China (corresponding author). ORCID: https://orcid.org/0000-0002-0333-6621. Email: [email protected]
Duo Zhang, Ph.D. [email protected]
Underground Space Engineering Technology Center, Central South Architectural Design Institute Co. Ltd., Wuhan 430071, China; formerly, Dept. of Municipal Branch, Wuhan Institute of Comprehensive Transportation Co. Ltd., Wuhan 430014, China. Email: [email protected]
Shunchuan Wu [email protected]
Professor, Faculty of Land Resource Engineering, Kunming Univ. of Science and Technology, Kunming 650093, China. Email: [email protected]
Pengqiang Yu [email protected]
Ph.D. Candidate, Dept. of Civil Engineering, Univ. of Science and Technology Beijing, Beijing 100083, China. Email: [email protected]

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