Abstract
The mechanical behaviors of granular materials are dominated by internal structure, which are related to fabric evolution during loading. This study investigated the fabric evolution of granular materials with different densities and stress paths under true triaxial conditions. A series of discrete element numerical simulations with different intermediate principal stress coefficient b were carried out along the constant mean stress p and the constant minor principal stress σ3 stress paths for both loose and dense specimens. The results indicated that the constant-p stress path produced a faster increase in stress ratio than the constant-σ3 stress path at the same b. The effects of specimen density on the peak friction angle are greater than that of stress path. The microscopic analyses revealed that the constant-p stress path facilitates a much more preferential distribution of normal contact force network along the major principal direction. The discrepancies in the peak stress ratio under two stress paths were thus interpreted. The dense specimen will rapidly form a higher anisotropic distribution of the normal contact force network upon shearing, and its anisotropic intensity was almost twice that of the loose specimen at the peak stress state. In addition, a unique relationship between the strong deviatoric fabric ratio and stress ratio was presented. The ratio of the two was approximately 1.0 regardless of stress path, density and b value. Finally, an underlying relationship between the stress components and the whole fabric components at the critical state was confirmed by introducing a new stress tensor. The three principal components (F1, F2 and F3) of the whole fabric tensor can be quantitatively represented with the imposed three principal stress components (σ1, σ2 and σ3) by employing a relationship of F1:F2:F3 = σ10.27:σ20.27:σ30.27. It provides a more comprehensive perspective to analyze the macro-micro performances of granular materials at the critical state.
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References
Aboul Hosn R, Sibille L, Benahmed N, Chareyre B (2017) Discrete numerical modeling of loose soil with spherical particles and interparticle rolling friction. Granular Matter 19(4), DOI: https://doi.org/10.1007/s10035-016-0687-0
Antony SJ, Momoh RO, Kuhn MR (2004) Micromechanical modelling of oval particulates subjected to bi-axial compression. Computational Materials Science 29(4):494–498, DOI: https://doi.org/10.1016/j.commatsci.2003.12.007
Bardet JP (1994) Observations on the effects of particle rotations on the failure of idealized granular materials. Mechanics of materials 18(2):159–182, DOI: https://doi.org/10.1016/0167-6636(94)00006-9
Barreto D, O Sullivan C, Zdravkovic L, Nakagawa M, Luding S (2009) Quantifying the evolution of soil fabric under different stress paths. AIP Conf Proc 1145(1):181–184, DOI: https://doi.org/10.1063/1.3179881
Belheine N, Plassiard JP, Donzé FV, Darve F, Seridi A (2009) Numerical simulation of drained triaxial test using 3D discrete element modeling. Computers and Geotechnics 36(1–2):320–331, DOI: https://doi.org/10.1016/j.compgeo.2008.02.003
Chantawarangul K (1993) Numerical simulations of three dimensional granular assemblies. PhD thesis, University of waterloo, Waterloo, Ontario, Canada
Chowdhury EQ, Nakai T (1998) Consequences of the tij-concept and a new modeling approach. Computers and Geotechnics 23(3):131–164, DOI: https://doi.org/10.1016/S0266-352X(98)00017-2
Cundall PA, Strack OD (1979) A discrete numerical model for granular assemblies. Géotechnique 29(1):47–65, DOI: https://doi.org/10.1680/geot.1979.29.1.47
Gu XQ, Zhang JC, Huang X (2020) DEM analysis of monotonic and cyclic behaviors of sand based on critical state soil mechanics framework. Computers and Geotechnics 128:103787, DOI: https://doi.org/10.1016/j.compgeo.2020.103787
Guo N (2014) Multiscale characterization of the shear behavior of granular media. PhD Thesis, Hong Kong University of Science and Technology, Hong Kong, China
Guo N, Zhao JD (2013) The signature of shear-induced anisotropy in granular media. Computers and Geotechnics 47:1–15, DOI: https://doi.org/10.1016/j.compgeo.2012.07.002
Habib P (1953) Influence of the variation of the average principal stress upon the shearing strength of soils. Proceedings of the 3rd International Conference on Soil Mechanics and Foundation Engineering 1:131–136
Jop P, Forterre Y, Pouliquen O (2006) A constitutive law for dense granular flows. Nature 441:727–730, DOI: https://doi.org/10.1038/nature04801
Kim BS, Sakakibara T, Park SW, Kato S (2021) Effects of grain shape on mechanical behavior of granular materials using DEM analysis. KSCE Journal of Civil Engineering 25(6):1939–1950, DOI: https://doi.org/10.1007/s12205-021-0582-z
Lade PV (2006) Assessment of test data for selection of 3-D failure criterion for sand. International Journal for Numerical and Analytical Methods in Geomechanics 30:307–333, DOI: https://doi.org/10.1002/nag.471
Lade PV, Duncan JM (1973) Cubical triaxial tests on cohesionless soil. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 11(3):50, DOI: https://doi.org/10.1016/0148-9062(74)91579-4
Li XS, Dafalias YF (2011) Anisotropic critical state theory: Role of fabric. Journal of Engineering Mechanics 138(3):263–275, DOI: https://doi.org/10.1061/(ASCE)EM.1943-7889.0000324
Liu YM, Liu HB, Mao HJ (2018) The influence of rolling resistance on the stress-dilatancy and fabric anisotropy of granular materials. Granular Matter 20:12, DOI: https://doi.org/10.1007/s10035-017-0780-z
Liu YM, Xu CM, Xu GF, Mao HJ, Xiao ZQ (2021) Macro-micro mechanical behavior of crushable granular materials under generalized stress conditions. KSCE Journal of Civil Engineering 25(5):1634–1644, DOI: https://doi.org/10.1007/s12205-021-1035-4
Liu Y, Zhang D, Wu SC, Yu PQ (2020) DEM investigation on the evolution of fabric under true triaxial conditions in granular materials. International Journal of Geomechanics 20(8):04020110, DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0001740
Lopera Perez JC, Kwok CY, O’Sullivan C, Huang X, Hanley KJ (2016) Assessing the quasi-static conditions for shearing in granular media within the critical state soil mechanics framework. Soils and Foundations 56(1):152–159, DOI: https://doi.org/10.1016/j.sandf.2016.01.013
Mair K, Hazzard J (2007) Nature of stress accommodation in sheared granular material: Insights from 3D numerical modeling. Earth and Planetary Science Letters 259(3–4):469–485, DOI: https://doi.org/10.1016/j.epsl.2007.05.006
Matsuoka H, Nakai T (1974) Stress-deformation and strength characteristics of soil under three different principal stresses. Proceedings of the Japan Society of Civil Engineers 232:59–70, DOI: https://doi.org/10.2208/jscej1969.1974.232_59
Oda M (1982) Fabric tensor for discontinuous geological materials. Soils and Foundations 22(4):96–108, DOI: https://doi.org/10.3208/sandf1972.22.4_96
Phusing D, Suzuki K, Zaman M (2016) Mechanical behavior of granular materials under continuously varying b values using DEM. International Journal of Geomechanics 16(1):04015027, DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0000506
Radjai F, Jean M, Moreau JJ, Roux S (1996) Force distributions in dense two-dimensional granular systems. Physical Review Letters 77(2): 274–277, DOI: https://doi.org/10.1103/PhysRevLett.77.274
Rodriguez NM, Lade PV (2013) True triaxial tests on cross-anisotropic deposits of fine Nevada sand. International Journal of Geomechanics 13(6):779–793, DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0000282
Rothenburg L, Bathurst RJ (1989) Analytical study of induced anisotropy in idealised granular materials. Géotechnique 39(4):601–614, DOI: https://doi.org/10.1680/geot.1989.39.4.601
Satake M (1978) Constitution of mechanics of granular materials through the graph theory. Proceedings of US-Japan Seminar on Continuum-Mechanical and Statistical Approaches in the Mechanics of Granular Materials, 47–62
Satake M (1982) Fabric tensor in granular materials. Proceeding of IUTAM Symposium on Deformation and Failure of Granular Materials 63–68, Amsterdam, Netherland: A.A. Balkema
Sazzad MM, Azad MS, Ghosh A (2022) Macro- and micro-mechanical responses of granular materials under different stress paths using DEM. In: Arthur, S., Saitoh, M., Pal, S.K. (eds) Advances in Civil Engineering. Lecture Notes in Civil Engineering 184. Springer, Singapore, DOI: https://doi.org/10.1007/978-981-16-5547-0_9
Sazzad MM, Suzuki K (2013) Density dependent macro-micro behavior of granular materials in general triaxial loading for varying intermediate principal stress using DEM. Granular Matter 15:583–593, DOI: https://doi.org/10.1007/s10035-013-0422-z
Sazzad MM, Suzuki K, Modaressi-Farahmand-Razavi A (2012) Macromicro responses of granular materials under different b values using DEM. International Journal of Geomechanics 12(3):220–228, DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0000133
Shi JS, Guo PJ (2018) Fabric evolution of granular materials along imposed stress paths. Acta Geotechnica 13:1341–1354, DOI: https://doi.org/10.1007/s11440-018-0665-2
Sibille L, Benahmed N, Darve F (2021) Constitutive response predictions of both dense and loose soils with a discrete element model. Computers and Geotechnics 135:104161, DOI: https://doi.org/10.1016/j.compgeo.2021.104161
Sitharam TG, Dinesh SV, Shimizu N (2002) Micromechanical modeling of monotonic shear behaviour of granular media using three dimensional DEM. International Journal for Numerical and Analytical Methods in Geomechanics 26(12):1167–1189, DOI: https://doi.org/10.1002/nag.240
Sitharam TG, Vinod JS, Ravishankar BV (2009) Post-liquefaction undrained monotonic behaviour of sands: Experiments and DEM simulations. Géotechnique 59(9):739–749, DOI: https://doi.org/10.1680/geot.7.00040s
Šmilauer V, Catalano E, Chareyre B, Dorofeenko S, Duriez J, Gladky A, Kozicki J, Modenese C, Scholtes L, Sibille L, Stransky J (2015) Yade Documentation. The Yade Project (http://yade-dem.org/doc/)
Suzuki K, Yanagisawa E (2006) Principal deviatoric strain increment ratios for sand having inherent transverse isotropy. International Journal of Geomechanics 6(5):356–366, DOI: https://doi.org/10.1061/(ASCE)1532-3641(2006)6:5(356)
Thornton C, Zhang L (2010) On the evolution of stress and microstructure during general 3D deviatoric straining of granular media. Géotechnique 60(5):333–341, DOI: https://doi.org/10.1680/geot.2010.60.5.333
Tian Y, Yao YP (2018) Constitutive modeling of principal stress rotation by considering inherent and induced anisotropy of soils. Acta Geotechnica 13:1299–1311, DOI: https://doi.org/10.1007/s11440-018-0680-3
Tong AT, Catalano E, Chareyre B (2012) Pore-scale flow simulations: Model predictions compared with experiments on bi-dispersed granular assemblies. Oil & Gas Science and Technology-Revue d IFP Energies nouvelles 67(5):743–752, DOI: https://doi.org/10.2516/OGST/2012032
Wang XL, Li JC (2014) Simulation of triaxial response of granular materials by modified DEM. Science China-Physics Mechanics & Astronomy 57:2297–2308, DOI: https://doi.org/10.1007/s11433-014-5605-z
Wu QX, Yang ZX (2022) Undrained responses of anisotropic granular material under rotational shear by DEM. Journal of Geotechnical and Geoenvironmental Engineering 148(12):04022112, DOI: https://doi.org/10.1061/(ASCE)GT.1943-5606.0002913
Xiao Y, Sun YF, Liu H, Yin F (2016) Critical state behaviors of a coarse granular soil under generalized stress conditions. Granular Matter 18:17, DOI: https://doi.org/10.1007/s10035-016-0623-3
Xie YH, Yang ZX, Barreto D, Jiang MD (2017) The influence of particle geometry and the intermediate stress ratio on the shear behavior of granular materials. Granular Matter 19:35, DOI: https://doi.org/10.1007/s10035-017-0723-8
Yamada Y, Ishihara K (1979) Anisotropic deformation characteristics of sand under three-dimensional stress conditions. Soils and Foundations 19(2):79–94, DOI: https://doi.org/10.3208/sandf1972.19.2_79
Yang ZX, Wu Y (2017) Critical state for anisotropic granular materials: A discrete element perspective. International Journal of Geomechanics 17(2):04016054, DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0000720
Yang ZX, Yang J, Wang LZ (2012) On the influence of inter-particle friction and dilatancy in granular materials: A numerical analysis. Granular Matter 14:433–447, DOI: https://doi.org/10.1007/s10035-012-0348-x
Zhang LR, Nguyen HNG, Lambert S, Nicot F, Prunier F, Djeran-Maigre I (2017) The role of force chains in granular materials: From statics to dynamics. European Journal of Environmental and Civil Engineering 21(7–8):874–895, DOI: https://doi.org/10.1080/19648189.2016.1194332
Zhang M, Yang YM, Zhang HW, Yu HS (2019) DEM and experimental study of bi-directional simple shear. Granular Matter 21(24), DOI: https://doi.org/10.1007/s10035-019-0870-1
Zhao SW, Evans TM, Zhou XW (2018a) Effects of curvature-related DEM contact model on the macro- and micro-mechanical behaviours of granular soils. Géotechnique 68(12):1085–1098, DOI: https://doi.org/10.1680/jgeot.17.P.158
Zhao SW, Evans TM, Zhou XW (2018b) Shear-induced anisotropy of granular materials with rolling resistance and particle shape effects. International Journal of Solids and Structures 150:268–281, DOI: https://doi.org/10.1016/j.ijsolstr.2018.06.024
Zhao JD, Guo N (2013) Unique critical state characteristics in granular media considering fabric anisotropy. Géotechnique 63(8):695–704, DOI: https://doi.org/10.1680/geot.12.P.040
Zhao CF, Pinzón G, Wiebicke M, Andò E, Kruyt NP, Viggiani G (2021) Evolution of fabric anisotropy of granular soils: x-ray tomography measurements and theoretical modelling. Computers and Geotechnics 133:104046, DOI: https://doi.org/10.1016/j.compgeo.2021.104046
Zhu MY, Gong GB, Xia J, Wilkinson S (2024) DEM investigation of strength and critical state behaviours of granular materials under true triaxial loadings. Particuology 85:198–212, DOI: https://doi.org/10.1016/j.partic.2023.04.004
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This work was supported by the National Natural Science Foundation of China [Grant No.41572255], and Guangdong Provincial Key Laboratory of Modern Civil Engineering Technology [Grant No. 2021B1212040003].
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Wang, H., Sun, H., Ge, X. et al. Macro-micro Performances of Granular Materials Considering the Influences of Density and Stress Path under True Triaxial Conditions: A DEM Investigation. KSCE J Civ Eng 27, 4176–4191 (2023). https://doi.org/10.1007/s12205-023-2159-5
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DOI: https://doi.org/10.1007/s12205-023-2159-5