The characteristic state

References

• Agnolin , I. and Roux , J. 2008 . On the elastic moduli of three-dimensional assemblies of spheres: Charactrisation and modeling of fluctuations in the particle displacement en rotation . International Journal of Solids and Structures , 45 : 1101 – 1123 .
   Google Scholar
• Azema , E. and Radjai , F. 2010 . Stress-strain behavior and geometrical properties of packings of elongated particles . Physical Review E , 81 ( 051304 ) : 1 – 17 .
   Google Scholar
• Azema , E. , Radjai , F. , Peyroux , R. and Saussine , G. 2007 . Force transmission in a packing of pentagonal particles . Physical Review E , 76 ( 0111301 ) : 1 – 13 .
   Google Scholar
• Been , K. and Jefferies , M.G. 1985 . A state parameter for sands . Géotechnique , 35 ( 1 ) : 127 – 132 .
   Google Scholar
• Casagrande , A. 1936 . Characteristics of cohesionless soils affecting the stability of slopes and earth fills . Journal of the Boston Society of Civil Engineering , : 13 – 32 .
   Google Scholar
• Chang , C.S. and Hicher , P.Y. 2005 . An elasto-plastic model for granular materials with microstructural consideration . International Journal of Solids and Structures , 42 : 4258 – 4277 .
   Web of Science ®Google Scholar
• Cundall , P. and Strack , O. 1979 . A discrete numerical model for granular assemblies . Géotechnique , 29 : 47 – 75 .
   Web of Science ®Google Scholar
• Fang , H.L. 2003 . A state dependent multi-mechanism model for sands . Géotechnique , 53 ( 4 ) : 407 – 420 .
   Google Scholar
• Gajo , A. and Wood , D.M. 1999 . A kimematic hardening constitutive model for sands: the multiaxial formulation . International Journal for Numerical and Analytical Methods in Geomechanics , 23 : 925 – 965 .
   Web of Science ®Google Scholar
• GdR-Midi . 2004 . On dense granular flows . European Physical Journal E , 14 : 341 – 365 .
   Google Scholar
• Hujeux , J.C. 1985 . “ Une loi de comportement pour le chargement cyclique de sols ” . In Génie parasimique , Edited by: Davidovici , V. 287 – 302 . Paris : Presses Ponts et Chaussées .
   Google Scholar
• Ishihara , K. , Tatsuoka , F. and Yasuda , S. 1975 . Undrained deformation and liquefaction of sand under cyclic stress . Soils and Foundations , 15 ( 1 ) : 29 – 44 .
   Google Scholar
• Jean , M. 1999 . The non-smooth contact dynamics method . Computer Methods in Applied Mechanics and Engineering , 109 : 192 – 205 .
   Google Scholar
• Kabilamany , K. and Ishihara , K. 1990 . Stress dilatancy and hardening laws for rigid granular model of sand . Soil Dynamics and Earthquake Engineering , 9 ( 2 ) : 66 – 77 .
   Google Scholar
• Li , X.S. and Dafalias , Y.F. 2000 . Dilatancy for cohesionless soils . Géotechnique , 50 ( 4 ) : 449 – 460 .
   Web of Science ®Google Scholar
• Luong , M.P. 1980 . Phénomènes cycliques dans les sols pulvérulents . Revue Française de Géotechnique , 10 : 39 – 53 .
   Google Scholar
• Maleki , M. , Cambou , B. and Dubujet , P. 2000 . Hierarchical modelling of soils behaviour (in French) . Revue Française de Génie Civil , 4 ( 7 ) : 895 – 928 .
   Google Scholar
• Manzari , M.T. and Dafalias , Y.F. 1997 . A critical state two-surface plasticity model for sands . Géotechnique , 47 ( 2 ) : 255 – 272 .
   Web of Science ®Google Scholar
• Mirghasemi , A.A. , Rothenburg , L. and Matyas , E.L. 1997 . Numerical simulations of assemblies of two-dimensional polygon-shaped particles and effects of confining pressure on shear strength . Soils and Foundations , 37 ( 3 ) : 43 – 52 .
   Google Scholar
• Moreau , J. 1994 . Some numerical methods in multibody dynamics: application to granular materials . European Journal of Mechanics, A/Solids , 13 ( 4-suppl ) : 93 – 114 .
   Google Scholar
• Moreau , J. 1999 . “ Some basics of unilateral dynamics ” . In Unilateral multibody contacts , Edited by: Pfeiffer , F. and Glocker , C. 1 – 14 . Dordrecht : Kluwer .
   Google Scholar
• Negussey , D. , Wijewickreme , W.K.D. and Vaid , Y.P. 1988 . Constant-volume friction angle of granular materials . Canadian Geotechnical Journal , 25 : 50 – 55 .
   Web of Science ®Google Scholar
• Nishi , K. and Kanatan , M. 1990 . Constitutive relations for sands under cyclic loading based on elasto-plasticity theory . Soils and Foundations , 30 ( 2 ) : 43 – 59 .
   Google Scholar
• Nouguier-Lehon , C. , Cambou , B. and Vincens , E. 2003 . Influence of particle shape and angularity on the behaviour of granular materials: a numerical analysis . International Journal for Numerical and Analytical Methods in Geomechanics , 27 : 1207 – 1226 .
   Web of Science ®Google Scholar
• Nouguier-Lehon , C. , Vincens , E. and Cambou , B. 2005 . Structural changes in granular materials: The case of irregular polygonal particles . International Journal of Solids and Structures , 42 ( 24–25 ) : 6356 – 6375 .
   Google Scholar
• Poulos , S.J. 1981 . The steady state of deformation . Journal of the Geotechnical Engineering Division, ASCE , 105 ( 2 ) : 201 – 255 .
   Google Scholar
• Pradhan , B.S. and Tatsuoka , F. 1989 . On stress-dilatancy equations of sand subjected to cyclic loading . Soils and Foundations , 29 ( 1 ) : 65 – 81 .
   Google Scholar
• Radjai , F. and Wolf , D.E. 1998 . Features of static pressure in dense granular media . Granular Matter , 1 ( 1 ) : 3 – 8 .
   Google Scholar
• Roscoe , K.H. , Schofield , A.N. and Thurairajah , A. 1963 . Yielding of clays in states wetter than critical . Géotechnique , 13 ( 3 ) : 211 – 240 .
   Google Scholar
• Roscoe , K.H. , Schofield , A.N. and Wroth , C.P. 1958 . On the yielding of soils . Géotechnique , 8 ( 1 ) : 22 – 53 .
   Google Scholar
• Rothenburg , L. and Bathurst , R.J. 1989 . Analytical study of induced anisotropy in idealized granular materials . Géotechnique , 39 ( 4 ) : 601 – 614 .
   Web of Science ®Google Scholar
• Rothenburg , L. and Kruyt , N.P. 2004 . Critical state and evolution of coordination number in simulated granular materials . International Journal of Solids and Structures , 41 : 5763 – 5774 .
   Web of Science ®Google Scholar
• Shahnazari , H. and Towhata , I. 2002 . Torsion shear tests on cyclic stress–dilatancy relationship of sand . Soils and Foundations , 42 ( 1 ) : 105 – 119 .
   Web of Science ®Google Scholar
• Sitharam , T.G. 2003 . Discrete element modelling of cyclic behaviour of granular materials . Geotechnical and Geological Engineering , 21 : 297 – 329 .
   Google Scholar
• Thornton , C. 2000 . Numerical simulations of deviatoric shear deformation of granular media . Géotechnique , 50 ( 1 ) : 43 – 53 .
   Web of Science ®Google Scholar
• Verdugo , R. and Ishihara , K. 1996 . The steady state of sandy soils . Soils and Foundations , 36 ( 2 ) : 81 – 91 .
   Google Scholar
• Wan , R.G. and Guo , P.J. 1998 . A simple constitutive model for granular soils: modified stress–dilatancy approach . Computers and Geotechnics , 22 ( 2 ) : 109 – 133 .
   Web of Science ®Google Scholar
• Wood , D.M. , Belkheir , K. and Liu , D.F. 1994 . Strain softening and state parameter for sand modelling . Géotechnique , 44 ( 2 ) : 335 – 339 .
   Web of Science ®Google Scholar