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A spherical discrete element model: calibration procedure and incremental response. (English) Zbl 1258.74213

Summary: When using spherical elements within the discrete element method, computational costs can be kept low even for large numbers of elements. However, this oversimplification of the granular geometry has drawbacks when quantitatively assessing the model even for frictional geomaterials. To overcome this limitation, the local constitutive law must at least take into account the transfer of a moment between elements. This moment, which is added to normal and shear local interaction forces, increases the number of local parameters. Moreover, when local plastic thresholds are considered, the calibration of the model becomes tricky. With such a set of local parameters, a calibration procedure is proposed, which attempts to define the respective role of each parameter in the macroscopic behavior. A series of numerical simulations of triaxial compression tests has been performed to check the capability of this model to get good quantitative results and the incremental behavior of the numerical medium is studied by performing a series of axisymmetric stress probes with varying directions. The corresponding strain responses are measured. From different initial stress states, the results indicate that the incremental response is well described by elastoplasticity with a single mechanism, and a non-associative flow rule.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74E10 Anisotropy in solid mechanics
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[1] Thornton C.: Numerical simulations of deviatoric shear deformation in granular media. Géotechnique 50(4), 43–53 (2000) · doi:10.1680/geot.2000.50.1.43
[2] Donzé F.V., Bernasconi P.: Simulation of the blasting patterns in shaft sinking using a discrete element method. Electronic. J. Geotech. Eng. 9(B), 1–44 (2004)
[3] Sibille L., Nicot F., Donze F.V., Darve F.: Material instability in granular assemblies from fundamentally different models. Int. J. Numer. Anal. Methods Geomech. 31(3), 457–481 (2007) · Zbl 1196.74055 · doi:10.1002/nag.591
[4] Shiu, W., Donze, F.V., Magnier, S.A.: Numerical study of rockfalls on covered galleries by the discrete elements method. Electronic. J. Geotech. Eng. 11(D) (2006)
[5] Mahboubi A., Ghaouti A., Cambou B.: La simulation numérique discrète du comportement des matériaux granulaires. Rev. Franç. Geot. 76, 45–61 (1996)
[6] Calvetti F., Viggiani G., Tamagnini C.: A numerical investigation of the incremental behavior of granular soils. Riv. Ital. Geotec. 3, 11–29 (2003)
[7] Oda M., Konishi J., Nemat-Nasser S.: Experimental micromechanical evaluation of strength of granular materials: effects of particles rolling. Mech. Mater. 1, 267–283 (1982)
[8] Iwashita K., Oda M.: Rolling resistance at contacts in simulation of shear band development by DEM. J. Eng. Mech. 124, 285–292 (1998) · doi:10.1061/(ASCE)0733-9399(1998)124:3(285)
[9] Plassiard, J.P.: Modélisation discrète d’impacts de blocs rocheux sur structures de protection type merlons. PhD Thesis, Joseph Fourier University, Grenoble (2007)
[10] Belheine N., Plassiard J.P., Donze F.V., Darve F., Seridi A.: Numerical simulation of drained triaxial test using 3D discrete element modeling. Comput. Geotech. 36(1–2), 320–331 (2008) · doi:10.1016/j.compgeo.2008.02.003
[11] Hill R.: The Mathematical Theory of Plasticity. Oxford University Press, New york (1950) · Zbl 0041.10802
[12] Drucker D.C., Prager W.: Soil Mechanics and plastic Analysis or Limit Design. Quart. Appl. Mech. 10, 157–165 (1952) · Zbl 0047.43202
[13] Mandel J.: Generalisation de la théorie de la palsticité de W.T. Koiter. Int. J. Solids. Struct. 1(3), 273–295 (1965) · doi:10.1016/0020-7683(65)90034-X
[14] Roscoe K.H., Burland J.B.: On the generalized stress-train behavior of ”wet” clay. In: Heyman, J., Leckie, F.A. (eds) Engineering Plasticity, pp. 535–609. Cambridge University Press, Cambridge (1968) · Zbl 0233.73047
[15] Gudehus G., Darve F., Vardoulakis I.: Constitutive relations of soils, pp. 5–12. Balkema, Rotterdam (1984)
[16] Anandarajah A., Sobhan K., Kuganenthira N.: Incremental stress-strain behavior of a granular soil. J. Geotech. Eng. 121(1), 57–68 (1995) · doi:10.1061/(ASCE)0733-9410(1995)121:1(57)
[17] Royis P., Doanh T.: Theoretical analysis of strain response envelopes using incrementally non-linear constitutive equations. Int. J. Numer. Anal. Methods. Geomech. 22(2), 97–132 (1998) · Zbl 0912.73046 · doi:10.1002/(SICI)1096-9853(199802)22:2<97::AID-NAG911>3.0.CO;2-Z
[18] Bardet J.P.: Numerical simulations of the incremental responses of idealized granular materials. Int. J. Plast. 10(8), 879–908 (1994) · Zbl 0820.73020 · doi:10.1016/0749-6419(94)90019-1
[19] Calvetti, F., Viggiani, G., Tamagnini, C.: On the incremental behavior of granular soils. In: Proceedings of NUMOG VIII, Rome, Swets &amp; Zeitlinger, pp. 3–9 (2002) · Zbl 1079.74046
[20] Kishino Y.: On the incremental nonlinearity observed in a numerical model for granular media. Ital. Geotech. J. 3, 3–12 (2003)
[21] Plassiard, J.P., Donze, F.V., Lorentz, J.: Simulation of Rockfall impact on embankments: general results and application, Interdisciplinary Workshop on Rockfall Protection, 23–25 June, Morschach, Switzerland (2008)
[22] Donze F.V., Magnier S.A.: Formulation of a three dimensional numerical model of brittle behaviour. Int. J. Geophys. 22, 790–802 (1995) · doi:10.1111/j.1365-246X.1995.tb06838.x
[23] Weitz D.A.: Packing in the spheres. Science 303, 968–969 (2004) · doi:10.1126/science.1094581
[24] Lubachevsky B.D., Stillinger F.H.: Geometric properties of random disk packings. J. Stat. Phys. 60, 561–583 (2004) · Zbl 1086.82569 · doi:10.1007/BF01025983
[25] Sherwood J.D.: Packing of spheroids in three-dimensional space by random sequential add. J. Phys. A Math. Gen. 30(24), L839–L843 (1997) · doi:10.1088/0305-4470/30/24/004
[26] Hentz S., Daudeville L., Donzé F.V.: Identification and validation of a discrete element model for concrete. ASCE J. Eng. Mech. 130(6), 709–719 (2004) · doi:10.1061/(ASCE)0733-9399(2004)130:6(709)
[27] Villard P., Chareyre B.: Design methods for geosynthetic anchor trenches on the basis of true scale experiments and discrete element modelling. Can. Geotech. J. 41(6), 1193–1205 (2004) · doi:10.1139/t04-063
[28] Sibille L., Nicot F., Donze F.V., Darve F.: Material instability in granular assemblies from fundamentally different models. Int. J. Numer. Anal. Meth. Geomech. 31, 457–481 (2007) · Zbl 1196.74055 · doi:10.1002/nag.591
[29] Lorentz J., Donze F.V., Perrotin P., Plotto P.: Experimental study of the dissipative efficiency of a multilayered protective structure against rockfall impact. Rev. Eur. Génie Civ. 10(3), 295–308 (2006)
[30] Bardet J.P.: Observation on the effects of particle rotation on the failure of idealized granular materials. Mech. Mater. 18, 159–182 (1994) · doi:10.1016/0167-6636(94)00006-9
[31] Gudehus G.: A comparaison of some constitutive laws for soils under radially symmetric loading and unloading. Ing. Can. Geotech. J. 20, 502–516 (1979)
[32] Bardet, J.P., Proubet, J. (eds.): Application of micro-mechanics to incrementally nonlinear constitutive equations for granular media. Powders and Grains, pp. 265–273. Balkema, Rotterdam (1989)
[33] Darve F.: The expression of reological laws in incremental form and the main classes of constitutive equations. In: Darve, F. (eds) Geomaterials: Constitutive Equations and Modelling, pp. 123–148. Elsevier, London (1991)
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