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Patterns of shear zones in granular bodies within a polar hypoplastic continuum

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Summary

The paper deals with numerical investigations on the patterning of shear zones in granular bodies. The behavior of dry sand during plane strain compression tests was numerically modelled with a finite element method using a hypoplastic constitutive relation within a polar (Cosserat) continuum. The constitutive relation was obtained through an extension of a non-polar one by polar quantities, viz. rotations, curvatures, couple stresses using the mean grain diameter as a characteristic length. This relation can reproduce the essential features of granular bodies during shear localisation. During FE-calculations, the attention was laid on the influence of boundary conditions and the distribution of imperfections in the granular specimen on the formation of patterns of shear zones.

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References

  1. Vardoulakis, I.: Shear band inclination and shear modulus in biaxial tests. Int. J. Num. Anal. Meth. Geomech.4, 103–119 (1980).

    Google Scholar 

  2. Gudehus, G.: Einige Beiträge der Bodenmechanik zur Entstehung und Auswirkung von Diskontinuitäten. Felsbau4, 190–195 (1986).

    Google Scholar 

  3. Han, C., Vardoulakis, I.: Plane strain compression experiments on water saturated fine-grained sand. Géotechn.41, 49–78 (1991).

    Google Scholar 

  4. Tejchman, J.: Modelling of shear localisation and autogeneous dynamic effects in granular bodies. Publication Series of the Institute of Soil and Rock Mechanics, University Karlsruhe140, 1–353, 1997.

    Google Scholar 

  5. Scarpelli, G., Wood, D. M.: Experimental observations of shear band patterns in direct shear tests. Proc. IUTAM Conference on Deformation and Failure of Granular Materials 1982, pp. 473–483.

  6. Desrues, J., Chambon, R., Mokni, M., Mazerolle, F.: Void ratio evolution inside shear bands in triaxial sand specimens studied by computed tomography. Géotechn.46, 3, 529–546 (1996).

    Google Scholar 

  7. Tatsuoka, F., Okahara, M., Tanaka, T., Tani, K., Morimoto, T., Siddiquee, M. S.: Progressive failure and particle size effect in bearing capacity of footing on sand. Proc. of the ASCE Geotechnical Engineering Congress27, 788–802 (1991).

    Google Scholar 

  8. Tatsuoka, F., Goto, S., Tanaka, T., Tani, K., Kimura, Y.: Particle size effects on bearing capacity of footing on granular material. In: Deformation and progressive failure in geomechanics (Asaoka, A., Adachi, T., Oka, F., eds.), pp. 133–139, Gifu: Pergamon 1997.

    Google Scholar 

  9. Stazhevskii, S. B., Revushenko, A. F.: Localisation in granular materials. Lecture at the Karlsruhe University, Germany 1992.

  10. Bransby, P. L., Milligan, G. W. E.: Soil deformations near cantilever sheet pile walls, Géotechn.25, 175–195 (1975).

    Google Scholar 

  11. Gudehus, G., Nübel, K.: Entstehen und Vergehen von Scherfugenmustern. Special Research Programme, Institute for Rock and Soil Mechanics, Karlsruhe University, 1999.

  12. Schwing, E.: Standsicherheit historischer Stützwände. Publication Series of the Institute of Soil and Rock Mechanics University Karlsruhe121, 1–182, 1991.

    Google Scholar 

  13. Vardoulakis, I., Graf, B., Gudehus, G.: Trap-door problem with dry sand: a statical approach based upon model test kinematics. Int. J. Num. Anal. Meth. Geomech5, 57–78, (1981).

    Google Scholar 

  14. Mróz, Z., Maciejewski, J.: Post-critical response of soils and shear band evolution. Localisation and bifurcation theory for soils and rocks (Chambon, R., Desrues, J., Vardoulakis, I., eds.), pp. 19–32. Rotterdam: Balkema 1994.

    Google Scholar 

  15. Baxter, G. W., Behringer, R. P.: Pattern formation and time-dependence in flowing sand. In: Two phase flows and waves, pp. 1–29, New York: Springer 1990.

    Google Scholar 

  16. Drescher, A., Cousens, T. W., Bransby, P. L.: Kinematics of the mass flow of granular material through a plane hopper. Géotechn.32, 291–303 (1982).

    Google Scholar 

  17. Michalowski, R. L.: Flow of granular material through a plane hopper. Powder Technology39, 29–40 (1984).

    Google Scholar 

  18. Tejchman, J.: Scherzonenbildung und Verspannungseffekte in Granulaten unter Berücksichtigung von Korndrehungen. Publication Series of the Institute of Soil and Rock Mechanics, University Karlsruhe117, 1–236, 1989.

    Google Scholar 

  19. Hassan, A. H.: Etude experimentale et numerique du comportement local et global d'une interface sol granulaire structure. Dissertation Grenoble University, 1995.

  20. Tatsuoka, F., Siddiquee, M. S., Yoshida, T., Park, C. S. Kamegai, Y., Goto, S., Kohata, Y.: Testing methods and results of element tests and testing conditions of plane strain model bearing capacity tests using air-dried dense Silver Buzzard sand. Internal Report, University of Tokyo, pp. 1–129, 1994.

  21. Yoshida, T., Tatsuoka, F., Siddiquee, M.: Shear banding in sands observed in plane strain compression. In: Localisation and bifurcation theory for solis and rocks (Chambon, R., Desrues, J., Vardoulakis, I., eds.), pp. 165181, Rotterdam: Balkema 1994.

    Google Scholar 

  22. Desrues, J., Hammad, W.: Shear banding dependency on mean pressure level in sand. Lecture at Int. Workshop on Numerical Methods for Localization and Bifurcation of Granular Bodies, Gdansk, Poland, 1989.

  23. Löffelmann, F.: Theoretische und experimentelle Untersuchungen zur Schüttgut-Wand-Wechselwirkung und zum Mischen und Entmischen von Granulaten. PhD Thesis, Karlsruhe University, 1989.

  24. Nedderman, R. M., Laohakul, C.: The thickness of the shear zone of flowing granular materials. Powder Technology25, 91–100 (1980).

    Google Scholar 

  25. Poliakov, A., Herrmann, H., Podladchikov, Y., Roux, S.: Fractal plastic shear bands. Fractals2, 567–581 (1994).

    Google Scholar 

  26. Lade, P. V.: Localisation effects in triaxial tests on sand. Proc. IUTAM Conference on Deformation and Failure of Granular Materials, pp. 461–470, 1982.

  27. Oda, M., Konishi, J., Nemat-Nasser, S.: Experimental micro-mechanical evaluation of strength of granular materials, effects of particle rolling. Mech. Materials1, 269–283 (1982).

    Google Scholar 

  28. Oda, M.: Micro-fabric and couple stress in shear bands of granular materials. In: Powders and grains (Thornton, C., ed.) 161–167, Rotterdam: Balkema, 1993.

    Google Scholar 

  29. Oda, M., Tatsuoka, F., Yoshida, T.: Void ratio in shear band of dense granular soils. In: Deformation and progressive failure in geomechanics, (Asaoka, A., Addchi, T., Oka, F., eds.) 157–163, Gifu: Pergamon, 1997.

    Google Scholar 

  30. Oda, M., Kazama, H.: Micro-structure of shear band and its relation to the mechanism of dilatancy and failure of granular soils. Géotechn.48, 465–481 (1998).

    Google Scholar 

  31. Bathe, K. J.: Finite element procedures in engineering analysis. Englewood Cliffs Prentice-Hall 1982.

    Google Scholar 

  32. Hobbs, B. E., Ord, A.: Numerical simulation of shear band formation in frictional-dilational material. Ingenieur-Archiv59, 209–220 (1989).

    Google Scholar 

  33. Cundall, P. A.: Numerical experiments on localisation in frictional materials. Ingenieur-Archiv59, 148–159 (1989).

    Google Scholar 

  34. Belytschko, T., Chiang, H., Plaskacz, E.: High resolution two dimensional shear band computations: imperfections and mesh dependence. Com. Meth. Appl. Mech. Engng119, 1–15 (1994).

    Google Scholar 

  35. Needleman, A., Tvergaard, V.: Analysis of plastic flow localisation in metals. Appl. Mech. Rev.45, 3–18 (1992).

    Google Scholar 

  36. Shuttle, D. A., Smith, I. M.: Numerical simulation of shear band formation in soils. Int. J. Num. Anal. Meth. Geomech.12, 611–626 (1988).

    Google Scholar 

  37. Hicks, M. A.: Error estimation and mesh refinement for computations of localisation in geomaterials. In: Localisation and bifurcation theory for soils and rocks (Adachi, T., Oka, F., Yashima, A., eds.) pp. 271–281. Rotterdam: Balkema 1998.

    Google Scholar 

  38. Ramakrshnan, N., Atluri, S. N.: Simulations of shear band formations in plane strain tension and compression using FEM. Mech. Materials17, 307–317 (1994).

    Google Scholar 

  39. Leroy, Y., Ortiz, M.: Finite element analysis of strain localisation in frictional materials. Int. J. Num. Anal. Meth. Geom.13, 53–74 (1989).

    Google Scholar 

  40. Pastor, M., Peraire, J.: Capturing shear bands via adaptive remeshing techniques. Euromech 248: Non-linear soil-structure interaction, 1989.

  41. Yatomi, C., Yashima, A., Izuka, A., Sano, I.: Shear bands formation numerically simulated by a non-coaxial cam-clay model Soil and Foudations29, 1–13 (1989).

    Google Scholar 

  42. de Borst, R.: Bifurcations in finite element models with a non-associated flow rule. Int. J. Num. Anal. Meth. Geomech.12, 99–116 (1988).

    Google Scholar 

  43. Ehlers, W., Volk, W.: On shear band localisation phenomena of liquid saturated granular elastoplastic porous solid materials accounting for fluid viscosity and micropolar solid rotations. Mechanics of Cohesive-Frictional Materials2, 301–320 (1997).

    Google Scholar 

  44. Gutierrez, M. A., de Borst, R.: Numerical analysis of localisation using a viscoplastic regularization: influence of stochastic material defects. Int. J. Num Meth. Eng44, 1823–1841 (1999).

    Google Scholar 

  45. Loret, B., Prevost, J. H.: Dynamic strain localization in fluid-saturated porous media. ASCE J. Engng Mech.117, 907–922 (1991).

    Google Scholar 

  46. Sluys, L. J.: Wave propagation, localisation and dispersion in softening solids. PhD Thesis, Delft University of Technology, 1992.

  47. Brinkgreve, R.: Geomaterial models and numerical analysis of softening. PhD Thesis, Delft University, 1994.

  48. de Borst, R., Mühlhaus, H. B., Pamin, J., Sluys, L. Y.: Computational modelling of localization of deformation. Proc. of the 3rd Int. Conf. Comp. Plasticity (Owen, D. R. J., Onate, E., Hinton, E., eds.), pp. 483–508. Swansea: Pineridge Press 1992.

    Google Scholar 

  49. Pamin, J.: Gradient-dependent plasticity in numerical simulation of localisation phenomena. PhD Thesis, Delft University, 1994.

  50. de Borst, R.: Simulation of strain localization: a reappraisal of the Cosserat continuum. Engng. Computations8, 317–322 (1991).

    Google Scholar 

  51. Murakami, A., Yoshida, N.: Cosserat continuum and finite element analysis. In: Deformation and progressive failure in geomechanics (Asaoka, A., Adachi, T., Oka, F., eds.), pp. 871–876, Gifu: Pergamon, 1997.

    Google Scholar 

  52. Mühlhaus, H. B.: Berücksichtigung von Inhomogenitäten im Gebirge in Rahmen einer Kontinuumstheorie. Publication Series of the Institute of Soil and Rock Mechanics, University Karlsruhe106, 1–70, 1989.

    Google Scholar 

  53. Tejchman, J., Wu, W.: Numerical study on shear band patterning in a Cosserat continuum. Acta Mech.99, 61–74 (1993).

    Google Scholar 

  54. Nübel, K., Karcher, Ch.: FE simulations of granular material with a given frequency distribution of voids as initial condition. Granular Matter1, 105–112 (1998).

    Google Scholar 

  55. Tejchman, J., Herle, I., Wehr, J.: FE-studies on the influence of initial void ratio, pressure level and mean grain diameter on shear localisation. Int. J. Num. Anal. Meth. Geomech.23, 2045–2074, (1999).

    Google Scholar 

  56. Tejchman, J., Herle, I.: A class A prediction of the bearing capacity of plane strain footings on granular material. Soils and Foundations39, 47–60 (1999).

    Google Scholar 

  57. Tejchman, J.: Behaviour of granular bodies in induced shear zones. Granular Matter22, 77–96. (2000).

    Google Scholar 

  58. Tejchman, J., Ummenhofer, T.: Bedding effects in bulk solids in silos-experiments and a polar hypoplastic approach. Thin-Walled Structures37, 333–361 (2000).

    Google Scholar 

  59. Tejchman, J., Gudehus, G.: Shearing of a narrow granular strip with polar quantities. J. Num. and Anal. Meth. Geomech.25, 1–28, (2001).

    Google Scholar 

  60. Tejchman, J.: Grain size effects in bearing capacity of a strip foundation., In: Numerical Models in Geomechanics, NUMOG, Davos (Pande, G. N., Pietruszcak, S., ed.), pp. 571–576, 1995.

  61. Benallal, A., Billardon, R. Geymonat, G.: Localization phenomena at the boundaries and interfaces of solids. Proc. of the 3rd Int. Conf. Constitutive Laws for Engineering Materials: Theory and Applications, Tucson, Arizona (Desai, C. S. et al., eds.), pp. 387–390, 1987.

  62. Tejchman, J., Wu, W.: Dynamic patterning of shear bands in a Cosserat continuum. Int. J. Engng. Mech. ASCE123, 123–134 (1997).

    Google Scholar 

  63. Leśniewska, D., Mróz, Z.: Limit equilibrium approach to study the evolution of shear band systems in soil. Geotechnique (in print).

  64. Kolymbas, D.: A novel constitutive law for soils. Proc. Int. Conf. on Constitutive Laws, Tucson, (Desai, C.S. et al., eds.), pp. 319–323, 1987.

  65. Gudehus, G.: Localisation in granular bodies-position and objectives. In: Localisation and bifurcation theory for soils and rocks, (Chambon, R., Desrues, J., Vardoulakis, I., eds.), pp. 1–15, Rotterdam: Balkema 1994.

    Google Scholar 

  66. Gudehus, G.: A comprehensive constitutive equation for granular materials. Soils and Foundations36, 1–12 (1996).

    Google Scholar 

  67. Bauer, E.: Calibration of a comprehensive hypoplastic model for granular materials. Soils and Foundations36, 13–26 (1996).

    Google Scholar 

  68. von Wolffersdorff, P. A.: A hypoplastic relation for granular materials with a predefined limit state surface. Mechanics of Cohesive-Frictional Materials1, 251–271 (1996).

    Google Scholar 

  69. Wu, W., Bauer, E., Kolymbas, D.: Hypoplastic constitutive model with critical state for granular materials. Mech. Materials23, 45–69 (1996).

    Google Scholar 

  70. Wu, W., Niemunis, A.: Failure criterion, flow rule and dissipation function derived from hypoplasticity. Mechanics of Cohesive-Frictional Materials1, 145–163 (1996).

    Google Scholar 

  71. Herle, I.: Hypoplastiziät und Granulometrie einfacher Korngerüste. Publication Series of the Institute of Soil and Rock Mechanics, University Karlsruhe142, 1997.

  72. Gudehus, G.: Shear localization in simple grain skeletons with polar effects. In: Localisation and bifurcation theory for soils and rocks (Adachi, T., Oka, F., Yashima, A., eds.), pp. 3–11, Rotterdam: Balkema 1998.

    Google Scholar 

  73. Herle, I.: A relation between parameters of a hypoplastic constitutive model and grain properties. In: Localisation and bifurcation theory for soils and rocks (Adachi, T., Oka, F., Yashima, A., eds.), pp. 91–99, Rotterdam: Balkema 1998.

    Google Scholar 

  74. Herle, I., Gudehus, G.: Determination of parameters of a hypoplastic constitutive model from grain properties. Mechanics of Cohesive-Frictional Materials4, 461–486 (1999).

    Google Scholar 

  75. Schäfer, H.: Versuch einer Elastizitätstheorie des zweidimensionalen ebenen Cosserat-Kontinuums. Miszellancen der Angewandten Mechanik, Festschrift Tolmien, W, Berlin: Akademie-Verlag 1962.

    Google Scholar 

  76. Mühlhaus, H. B.: Application of Cosserat theory in numerial solutions of limit load problems. Ing. Arch.59, 124–137 (1989).

    Google Scholar 

  77. Mühlhaus, H. B.: Continuum models for layered and blocky rock. In: Comprehensive rock engineering (Hudson, J. A., Fairhurt, C., eds.),2, Oxford: Pergamon, 1990.

    Google Scholar 

  78. Tejchman, J., Bauer, E.: Numerical simulation of shear band formation with a polar hypoplastic model. Computers and Geotechnics19, 221–244 (1996).

    Google Scholar 

  79. Bauer, E., Huang, W.: Numerical study of polar effects in shear zones. In: Numerical models in geomechanics (Pande, G. N., Pietruszczak, S., Schweiger, H. F., eds.), pp. 133–141, Rotterdam: Balkema 1999.

    Google Scholar 

  80. Wehr, J., Tejchman, J.: Sand anchors in rock and granular soils-experiments and a polar hypolastic approach. Proc. World Civil and Environmental Engineering Conference, Thailand, 8–12 XI 1999 (Balasubramaniam et al., A. S., eds.)2, VII 1–10, 1999.

    Google Scholar 

  81. Nübel, K., Gudehus, G.: Evolution of localised shearing: dilation and polarization in grainskeleton. Powder and Grains (in print).

  82. Groen, A. E.: Three-dimensional elasto-plastic analysis of soils. PhD Thesis, Delft University, 1997.

  83. Nagtegaal, J. C., Parks, D. M., Rice, J. R.: On numerically accurate finite element solutions in fully plastic range. Comp. Meth. Appl. Mech. Engng4, 153–177 (1974).

    Google Scholar 

  84. Vermeer, P. A., van Langen, H.: Soil collapse computations with finite elements. Ing. Arch.59, 221–236 (1989).

    Google Scholar 

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  1. J. Tejchman

    Present address: Civil Engineering Department, Technical University of Gdańsk, Narutowicza 11/12, PL-80952, Gdańsk, Poland

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    Tejchman, J. Patterns of shear zones in granular bodies within a polar hypoplastic continuum. Acta Mechanica 155, 71–94 (2002). https://doi.org/10.1007/BF01170841

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