DEM investigation of strength and critical state behaviours of sand under axisymmetric stress paths with different shearing modes

Abstract

This paper investigates the strength and critical state (CS) behaviours of sand under axisymmetric stress paths with different shearing modes using discrete element method (DEM). The stress paths include axial compression (AC) and axial extension (AE), and the shearing modes include conventional triaxial (CT) mode and constant mean pressure (CP) mode. A series of dense and loose sand samples are generated for this purpose with confining pressures ranging from 100 kPa to 900 kPa. The CS is achieved for all samples after an axial strain (absolute value) of about 45%. The CS value of deviator stress is unique and independent of the initial packing densities for the samples with a given confining pressure, but the unique deviator stress under AC is generally larger than that under AE. The CS values of the stress ratio are independent of the shearing modes and the confining pressures, but are dependent on the stress paths. The CS friction angle for a given confining pressure is found to be unique and independent of the shearing modes, stress paths and initial packing densities, indicating that Mohr-Coulomb criterion (for axisymmetric conditions, equivalent to Matsuoka criterion) is an appropriate CS strength criterion. The CS value of void ratio is independent of the initial packing densities for a given confining pressure and shearing mode under a given stress path. The differences among the CS values of the mechanical coordination number are found to be attributed to changes in the effective mean pressures.

Keywords

discrete element method / axisymmetric stress path / shearing mode / sand / critical state / failure criterion

References

[1] RoscoeK H, SchofieldA N, WrothC P. On the yielding of soils [J]. Géotechnique, 1958, 8(1): 22-53

[2] SchofieldA, WrothPCritical state soil mechanics, 1968, New York, McGraw-Hill[M]

[3] LiX S, DafaliasY F. Anisotropic critical state theory: Role of fabric [J]. Journal of Engineering Mechanics, 2012, 138(3): 263-275

[4] OdaM, KonishiJ, Nemat-NasserS. Experimental micromechanical evaluation of strength of granular materials: Effects of particle rolling [J]. Mechanics of Materials, 1982, 1(4): 269-283

[5] ChuJ. An experimental examination of the critical state and other similar concepts for granular soils [J]. Canadian Geotechnical Journal, 1995, 32(6): 1065-1075

[6] RahmanZ A, TollD G, GallipoliD. Critical state behaviour of weakly bonded soil in drained state [J]. Geomechanics and Geoengineering, 2018, 13(4): 233-245

[7] ThorntonC, ZhangL. On the evolution of stress and microstructure during general 3D deviatoric straining of granular media [J]. Géotechnique, 2010, 60(5): 333-341

[8] HuangX, HanleyK J, O’SullivanC, et al. . Exploring the influence of interparticle friction on critical state behavior using DEM [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2014, 38(12): 1276-1297

[9] ZhouW, LiuJ-y, MaG, et al. . Three-dimensional DEM investigation of critical state and dilatancy behaviours of granular materials [J]. Acta Geotechnica, 2017, 12: 527-540

[10] KodicherlaS P K, GongG-b, FanL, et al. . Discrete element modelling of strength and critical state characteristics of granular materials under axial compression and axial extension stress path tests [J]. Particuology, 2021, 56: 152-162

[11] BeenK, JefferiesM G, HacheyJ E. The critical state of sands [J]. Géotechnique, 1991, 41(3): 365-381

[12] EshtehardA ATriaxial testing on very loose sands for flow liquefaction analyses, 1996, Edmonton, Canada, University of Alberta[D]

[13] ZhaoJ-d, GuoNing. Unique critical state characteristics in granular media considering fabric anisotropy [J]. Géotechnique, 2013, 63(8): 695-704

[14] YangZ-x, WuYu. Critical state for anisotropic granular materials: A discrete element perspective [J]. International Journal of Geomechanics, 2017, 17(2): 04016054

[15] LiXiaMicro-scale investigation on the quasi-static behaviour of granular material, 2006, Hong Kong, China, Hong Kong University of Science and Technology[D]

[16] NgT T. Shear strength of assemblies of ellipsoidal particles [J]. Géotechnique, 2004, 54: 659-669

[17] GhafghaziM, ShuttleD A, DejongJ T. Particle breakage and the critical state of sand [J]. Soils and Foundations, 2014, 54(3): 451-461

[18] HuangX, HanleyK J, O’SullivanC, et al. . DEM analysis of the influence of the intermediate stress ratio on the critical-state behaviour of granular materials [J]. Granular Matter, 2014, 16641-655

[19] SalvatoreE, ModoniG, AndoE, et al. . Determination of the critical state of granular materials with triaxial test [J]. Soils and Foundations, 2017, 57(5): 733-744

[20] JagodnikV, KrausI, IvandaS, et al. . Behaviour of uniform drava river sand in drained condition—A critical state approach [J]. Applied Sciences, 2020, 10(17): 5733

[21] LashkariA, FalsafizadehS R, ShourijehP T, et al. . Instability of loose sand in constant volume direct simple shear tests in relation to particle shape [J]. Acta Geotechnica, 2020, 15: 2507-2527

[22] da FonsecaA V, CordeiroD, Molina-GómezF. Recommended procedures to assess critical state locus from triaxial tests in cohesionless remoulded samples [J]. Geotechnics, 2021, 1(1): 95-127

[23] NieJ-y, ZhaoJ-d, CuiY-f, et al. . Correlation between grain shape and critical state characteristics of uniformly graded sands: A 3D DEM study [J]. Acta Geotechnica, 2022, 17(7): 2783-2798

[24] RoscoeK H, BurlandJ BOn the generalized stressstrain behaviour of ‘wet’ clay, 1968, Cambridge, Cambridge University Press[M]

[25] CussR J, RutterE H, HollowayR F. The application of critical state soil mechanics to the mechanical behaviour of porous sandstones [J]. International Journal of Rock Mechanics and Mining Sciences, 2003, 40(6): 847-862

[26] ReidD, FourieA, AyalaJ L, et al. . Results of a critical state line testing round robin programme [J]. Géotechnique, 2021, 71(7): 616-630

[27] CundallP A, StrackO D. A discrete numerical model for granular assemblies [J]. Géotechnique, 1979, 29(1): 47-65

[28] CundallP A. A discontinuous future for numerical modelling in geomechanics [J]. Geotechnical Engineering, 2001, 149(1): 41-47

[29] ITASCAParticle flow code in 3 dimensions (PFC^3D) version 5, 2014, USA, Itasca Consulting Group[M]

[30] ThorntonC. Numerical simulations of deviatoric shear deformation of granular media [J]. Géotechnique, 2000, 50(1): 43-53

[31] FlavignyE, DesruesJ, PalayerB. Le sable Hostun RF. Revue Française de [J]. Géotechnique, 1990, 5367-70

[32] Di RenzoA, Di MaioF P. Comparison of contact-force models for the simulation of collisions in DEM-based granular flow codes [J]. Chemical Engineering Science, 2004, 59(3): 525-541

[33] GongJ, LiuJun. Effect of aspect ratio on triaxial compression of multi-sphere ellipsoid assemblies simulated using a discrete element method [J]. Particuology, 2017, 32: 49-62

[34] GoldenbergC, GoldhirschI. Friction enhances elasticity in granular solids [J]. Nature, 2005, 435: 188-191

[35] da CruzF, EmamS, ProchnowM, et al. . Rheophysics of dense granular materials: Discrete simulation of plane shear flows [J]. Physical Review E, 2005, 72(2): 021309

[36] MASE G, MASE G E. Continuum mechanics for engineers [M]. 1st edition. CRC Press, 1999.

[37] Galindo-TorresS A, PedrosoD M, WilliamsD J, et al. . Strength of non-spherical particles with anisotropic geometries under triaxial and shearing loading configurations [J]. Granular Matter, 2013, 15: 531-542

[38] GongG-b, ZhaX-x, WeiJun. Comparison of granular material behaviour under drained triaxial and plane strain conditions using 3D DEM simulations [J]. Acta Mechanica Solida Sinica, 2012, 25(2): 186-195

[39] YamamuroJ A, LadeP V. Drained sand behaviour in axisymmetric tests at high pressures [J]. Journal of Geotechnical Engineering, 1996, 122(2): 109-119

[40] KodicherlaS P K, GongG-b, FanL, et al. . Investigations of the effects of particle morphology on granular material behaviour using a multi-sphere approach [J]. Journal of Rock Mechanics and Geotechnical Engineering, 2020, 12(6): 1301-1312

[41] JiangM-j, LiL-q, YangQ-jun. Experimental investigation on deformation behaviour of TJ-1 lunar soil simulant subjected to principal stress rotation [J]. Advances in Space Research, 2013, 52(1): 136-146

[42] ZhangJ-j, LoS C R, RahmanM M, et al. . Characterizing monotonic behaviour of pond ash within critical state approach [J]. Journal of Geotechnical and Geoenvironmental Engineering, 2018, 144(1): 04017100

[43] Dolzyk-SzypcioK. Stress-dilatancy relationship of erksak sand under drained triaxial compression [J]. Geosciences, 2020, 109353

[44] RahmanM M, NguyenH B K, FourieA B, et al. . Critical state soil mechanics for cyclic liquefaction and postliquefaction behaviour: DEM study [J]. Journal of Geotechnical and Geoenvironmental Engineering, 2021, 147204020166

[45] GongG-binDEM simulations of drained and undrained behaviour, 2008, Birmingham, UK, University of Birmingham[D]

[46] CornforthD H. Some experiments on the influence of strain conditions on the strength of sand [J]. Géotechnique, 1964, 142143-167

[47] LadeP V, DuncanJ M. Cubical triaxial tests on cohesionless soil [J]. Journal of the Soil Mechanics and Foundations Division, 1973, 99(10): 793-812

[48] MatsuokaH, NakaiT. Stress-deformation and strength characteristics of soil under three different principal stresses [J]. Proceedings of the Japan Society of Civil Engineers, 1974, 23259-70

[49] LabuzJ F, ZangA. Mohr-Coulomb failure criterion [J]. Rock Mechanics and Rock Engineering, 2012, 45: 975-979

[50] XieY H, YangZ X, BarretoD, et al. . The influence of particle geometry and the intermediate stress ratio on the shear behaviour of granular materials [J]. Granular Matter, 2017, 19(2): 1-13

[51] SalimiM J, LashkariA. Undrained true triaxial response of initially anisotropic particulate assemblies using CFM-DEM [J]. Computers and Geotechnics, 2020, 124: 103509

[52] LiX S, WangY. Linear representation of steady-state line for sand [J]. Journal of Geotechnical and Geoenvironmental Engineering, 1998, 1241215-1217

[53] YinZ-y, ChangC S. Non-uniqueness of critical state line in compression and extension conditions [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2009, 33: 1315-1338

[54] BUDHU M. Soil Mechanics and Foundations [M]. 3rd edition. John Wiley & Sons, 2010.

[55] ZhuM-y, GongG-b, XiaJ, et al. . Effects of deviator strain histories on liquefaction of loose sand using DEM [J]. Computers and Geotechnics, 2021, 136: 104213

[56] GongG-b, ZhaX-xiong. DEM simulation of undrained behaviour with preshearing history for saturated granular media [J]. Modelling and Simulation in Materials Science and Engineering, 2013, 21(2): 025001

[57] YimsiriS, SogaK. Effects of soil fabric on behaviours of granular soils: Microscopic modeling [J]. Computers and Geotechnics, 2011, 38861-874

[58] SatakeMFabric tensor in granular materials: The Netherlands, 1982, Rotterdam, Balkema: 63-68[P]

[59] ThorntonC, SunG. Axisymmetric compression of 3D polydisperse systems of spheres [M]. Powers and Grains, 1993, Rotterdam, Balkema