Critical length of force chains and shear band thickness in dense granular materials

Acta Geotechnica

Volumn 7, Issue 1, 2012, Pages 41-55

  Guo, Peijun ^a  

^a MCMASTER UNIVERSITY   (Canada)

Author keywords

Buckling; Force chains; Granular material; Shear band

Indexed keywords

EID: 84857648726     PISSN: 18611125     EISSN: 18611133     Source Type: Journal    
DOI: 10.1007/s11440-011-0154-3     Document Type: Article

References (73)

1. Aharonov E, Sparks DW (2002) Shear profiles in granular layers. Phys Rev E65 051302: 1-12.
2. Alonso-Marroquin F, Vardoulakis I (2005) Micromechanics of shear bands in granular media. In: Garcia-Rojo R, Herrmann HJ, MacNamara S (eds), Powders and grains 2005, pp 701-704.
3. Alshibli KA, Hasan A (2008) Spatial variation of void ratio and shear band thickness in sand using X-ray computed tomography. Géotechnique 58(4): 249-257.
4. Bardet JP, Huang Q (1993) Rotational stiffness of cylindrical particle contacts. Proceeding on 2nd International Conference on Micromechanics of Granular Media, pp 39-43.
5. Bardet JP, Proubet J (1992) The structure of shear bands in idealized granular materials. Appl Mech Rev 3(2): 118-122.
6. Bardet JP, Shiv A (1995) Plane-strain instability of saturated porous material. J Eng Mech 121(6): 717-724.
7. Bauer E, Huang W, Wu W (2004) Investigations of shear banding in an anisotropic hypoplastic material. Int J Solids Struct 41: 5903-5919.
8. Bazant Z, Lin F, Pijaudier-Cabot G (1987) Yield limit degradation: Non-local continuum model with local strain. Proceeding of International Conference on Computational Plasticity, Barcelona, pp 1757-1780.
9. Behringer RP, Daniels KE, Majmudar TS, Sperl M (2008) Fluctuations, correlations and transitions in granular materials: Statistical mechanics for a non-conventional system. Philos Trans R Soc A 366: 493-504.
10. Cates ME, Wittmer JP, Bouchaud J-P, Claudin P (1999) Jamming and static stress transmission in granular materials. Chaos 9(3): 511-522.
11. Chambon R, Crochepeyre S, Desrues J (2000) Localization criteria for non linear constitutive equations of geomaterials. Mech Cohes-Frict Mater 5: 561-582.
12. Cho G-C, Dodds J, Santamarina JC (2006) Particle shape effects on packing density, stiffness, and strength: Natural and crushed sands. J Geotech Geoenviron Eng 132(5): 591-602.
13. Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Géotechnique 29: 47-65.
14. de Borst R (1991) Simulation of strain localization: A reappraisal of the Cosserat continuum. Eng Comput 8: 317-332.
15. de Borst R, Mühlhaus H-B (1992) Gradient dependent plasticity: Formulation and algorithmic aspects. Int J Numer Methods Eng 35: 521-539.
16. Desrues J, Chambon R (1989) Shear band analysis for granular materials-the question of incremental non-linearity. Ingenieur Arch 59: 187-196.
17. Desrues J, Viggiani G (2004) Strain localization in sand: An overview of the experimental results obtained in Grenoble using stereophotogrammetry. Int J Numer Anal Methods Geomech 28: 279-321.
18. Finno R, Harris W, Mooney M, Viggiani G (1997) Shear bands in plane strain compression of loose sand. Géotechnique 47(1): 149-165.
19. Gardiner BS, Tordesillas A (2004) Micromechanics of shear bands. Int J Solids Struct 41: 5885-5901.
20. Gudehus G, Nübel K (2004) Evolution of shear bands in sand. Géotechnique 54(3): 187-201.
21. Guo P, Su X (2007) Effect of dilatancy on instability, pre-instability strain softening of sand along proportional strain paths. Soils Found 47(4): 757-770.
22. Hamadi K, Razavi AM-F, Darve F (2008) Bifurcation and instability modelling by a multimechanism elasto-plastic model. Int J Numer Anal Methods Geomech 32: 461-492.
23. Harr ME (1977) Mechanics of Particulate Media: a Probabilistic approach. McGraw-Hill, New York.
24. Howell D, Behringer RP, Veje C (1999) Stress fluctuations in a 2D granular Couette experiment: A continuous transition. Phys Rev Lett 82: 5241-5244.
25. Huang W, Nübel K, Bauer E (2002) A polar extension of hypoplastic model for granular material with shear localization. Mech Mater 34: 563-576.
26. Hunt GW, Tordesillas A, Green SC, Shi J (2010) Force-chain buckling in granular media: A structural mechanics perspective. Philos Trans R Soc A 368: 249-262.
27. Imposimato S, Nova R (1998) An investigation on the uniqueness of the incremental response of elastoplastic models for virgin sand. Mech Cohes-Frict Mater 3: 65-87.
28. Itasca (2006) PFC2D Manual. Itasca Consulting Group Inc, Minneapolis.
29. Iwashita K, Oda M (1998) Rolling resistance at contacts in the simulation of shear band development by DEM. J Eng Mech 124(3): 285-292.
30. Kuhl E, Ramm E (2000) Simulation of strain localization with gradient enhanced damage models. Comp Mater Sci 16: 176-185.
31. Loret B, Prevost JH (1990) Dynamic strain localisation in elasto-viscoplastic solids, Part 1. General formulation and 1D examples. Comp Appl Mech Eng 83: 247-273.
32. Marcher T, Vermeer PA (2001) Macromodelling of softening in non-cohesive soils. In: Vermeer PA, Diebels S, Ehlers W, Herrmann HJ, Luding S, Ramm E (eds) Continuous and discontinuous modelling of cohesive frictional materials. Lecture series in physics, vol 568, Springer, Berlin, pp 89-110.
33. Mahmood Z, Iwashita K (2010) A simulation study of microstructure evolution inside the shear band in biaxial compression test. Int J Numer Anal Methods Geomech. Published online in Wiley InterScience (www.interscience.wiley.com). doi: 10.1002/nag. 917.
34. Majmudar TS, Behringer RP (2005) Contact force measurements and stress induced anisotropy in granular materials. Nature 435(23): 1079-1082.
35. Masson S, Martinez J (2001) Micromechanical analysis of the shear behaviour of a granular material. J Eng Mech 127(10): 1007-1016.
36. Mitchell JK, Soga K (2005) Fundamentals of soil behaviour, 3rd edn. Wiley, New Jersey.
37. Mokni M, Desrues J (1999) Strain localisation measurements in undrained plane-strain biaxial tests on Hostun RF sand. Mech Cohes-Frict Mater 4(4): 419-441.
38. Muhlhaus HB, Vardoulakis I (1987) The thickness of shear bands in granular materials. Géotechnique 37(3): 271-283.
39. Muthuswamy M, Peters J, Tordesillas A (2006) Uncovering the secretes to relieving stress: Discrete element analysis of force chains in particular media. ANZIAM J 47: C355-C372.
40. Ni Q, Powrie W, Zhang X, Harkness R (2000) Effect of particle properties on soil behaviour: 3-D numerical modelling of shear box tests. ASCE Geotech Special Publ 96: 58-70.
41. Oda M (1993) Micro-fabric and couple stress in shear bands of granular materials. In: Thornton C (ed) Powders and grains. Proceedings of Second International Conference on Micromechanics of Granular Media, Birmingham, Balkema, Rotterdam, Netherlands, pp 161-166.
42. Oda M, Kazama H (1998) Microstructure of shear bands and its relation to the mechanisms of dilatancy and failure of dense granular soils. Géotechnique 48(4): 465-481.
43. Oda M, Iwashita K (2000) Micro-deformation mechanism of shear banding process based on modified distinct element method. Powder Technol 109: 192-205.
44. Oda M, Kazama H, Konish J (1998) Effects of induced anisotropy on the development of shear bands in granular materials. Mech Mater 28(1-4): 103-111.
45. Oda M, Iwashita K (2000) Study on couple stress and shear band development in granular media based on numerical simulation analyses. Int J Eng Sci 38(15): 1713-1740.
46. Peters JF, Muthuswamy M, Wibowo J, Tordesillas A (2005) Characterization of force chains in granular material. Phys Rev E 72: 0413071-0413078.
47. Pradhan TBS (1997) Characteristics of shear band in plane strain compression tests of sands. In: Asaoka A, Adachi T, Oka F (eds), Deformation and progressive failure in geomechanics. Proceedings of IS-NAGOYA'97, Pergamon, pp 241-246.
48. Radjai F, Wolf DE, Jean M, Moreau JJ (1998) Bimodal character of stress transmission in granular packings. Phys Rev Lett 80(1): 61-64.
49. Radjai F (2008). Particle-scale origins of shear strength in granular media. arXiv: 0801. 4722v1 [cond-mat. soft].
50. Rice JR (1975) On the stability of dilatant hardening of saturated rock mass. J Geophys Res 80: 1531-1536.
51. Rudnicki JW (2000) Diffusive instabilities in dilating and compacting geomaterials. In: Chuang T-J, Rudnicki JW (eds) Multiscale deformation and fracture in materials and structures. Kluwer, The Netherlands, pp 159-182.
52. Rudnicki JW, Rice JR (1975) Conditions for the localization of deformation in pressure sensitive dilatant materials. J Mech Phys Solids 23: 371-394.
53. Sadrekarimi A, Olson SM (2010) Shear band formation observed in ring shear tests on sandy soils. J Geotech Geoenviron Eng 136(2): 366-375.
54. Satake M (1998) Finite difference approach to the shear band formation from the viewpoint of particle column buckling. In: Proceedings of 13th Southeast Asian Geotechical Conference, pp 815-818.
55. Tejchman J (2004) Influence of a characteristic length on shear zone thickness in hypoplasticity with different enhancements. Comput Geotech 31(8): 595-611.
56. Tejchman J, Niemunis A (2006) FE-studies on shear localization in an anisotropic micro-polar hypoplastic granular material. Granular Matter 8: 205-220.
57. Tejchman J, Bauer E, Wu W (2007) Effect of fabric anisotropy on shear localization in sand during plane strain compression. Acta Mech 189: 23-51.
58. Tejchman J, Wu W (1993) Numerical study on shear band patterning in a Cosserat continuum. Acta Mech 99: 61-74.
59. Tordesillas A, Hunt A, Shi J (2011) A characteristic length scale in confined elastic buckling of a force chain. Granular Matter 13: 215-218.
60. Tordesillas A, Lin Q, Zhang J, Behringer RP, Shi J (2011) Structural stability and jamming of self-organized cluster conformations in dense granular materials. J Mech Phys Solids 59: 265-296.
61. Tordesillas A, Muthuswamy M (2009) On the modeling of confined buckling of force chains. J Mech Phys Solids 57(4): 706-727.
62. Tordesillas A, Muthuswamy M, Walsh SDC (2008) Mesoscale measures of nonaffine deformation in dense granular assemblies. J Eng Mech 134(12): 1095-1113.
63. Tordesillas A, Walker DM, Lin Q (2010) Force cycles and force chains. Phys Rev E 81: 0113021-0113029.
64. Tordesillas A, Zhang J, Behringer R (2009) Buckling force chains in dense granular assemblies: Physical and numerical experiments. Geomech Geoeng 4(1): 3-16.
65. Vardoulakis I, Georgopoulos IO (2005) The "stress-dilatancy" hypothesis revisited: Shear-banding related instabilities. Soils Found 45(2): 61-76.
66. Vardoulakis I, Graf B (1985) Calibration of constitutive models for granular materials using data from biaxial experiments. Géotechnique 35(3): 299-317.
67. Vardoulakis I, Sulem J (1995) Bifurcation analysis in geomechanics. Chapman & Hall, London.
68. Viggiani G, Kuntz M, Desrues J (2001) An experimental investigation of the relationships between grain size distribution and shear banding in sand. In: Vermeer PA, Diebels S, Ehlers W, Hermann HJ, Luding S, Ramm E (eds) Continuous and discontinuous modeling of cohesive-frictional materials. Lecture Notes in Physics vol 568. Springer, New York, pp 111-127.
69. Wan RG, Guo P, Al-Mamun M (2005) Behaviour of granular materials in relation to their fabric dependence. Soils Found 45(2): 77-86.
70. Yoshida T, Tatsuoka F, Siddiquee MSA, Kamegai Y, Park C-S (1994) Shear banding in sands observed in plane strain compression. In: Chambon R, Desrues J, Vardouylakis I (eds) Localization and bifurcation theory for soils and rocks. A. A. Balkema, Rotterdam, pp 165-179.
71. Zhang HW, Schrefler BA (2000) Gradient dependent plasticity model and dynamic strain localisation analysis of saturated and partially saturated porous media: 1D model. Eur J Mech A/Solids 19: 503-524.
72. Zhang L, Thornton C (2007) A numerical examination of the direct shear test. Géotechnique 57(4): 343-354.
73. Zbib HM, Aifantis EC (1988) On the localization and post localisation behaviour of plastic deformation. Res Mechanica Int J Strut Mech Mater Sci 23: 261-277.