A generalization of Reiner's mathematical model for wet sand

Abstract In this paper we modify the constitutive relation derived by Reiner (1945) , to describe dilatancy in wet sand, by suggesting that the shear viscosity would depend on the shear rate and the volume fraction. We then look at the flow of a saturated densely packed bed of particles (with liquid in the pores) between two horizontal flat plates. We obtain exact solutions for a very special case.

[1]  G. Ahmadi.  On mechanics of saturated granular materials , 1980 .

[2]  Gabriel I. Tardos,et al.  A fluid mechanistic approach to slow, frictional flow of powders , 1997 .

[3]  R. L. Braun,et al.  Stress calculations for assemblies of inelastic speres in uniform shear , 1986 .

[4]  S. Cowin.  A theory for the flow of granular materials , 1974 .

[5]  E. Andrade,et al.  The Mechanism of Dilatancy , 1949 .

[6]  P. Lagrée,et al.  The Couette flow of dense and fluid-saturated granular media , 2006 .

[7]  G. Gudehus.  A COMPREHENSIVE CONSTITUTIVE EQUATION FOR GRANULAR MATERIALS , 1996 .

[8]  C. Truesdell.  The rational mechanics of materials , 1965 .

[9]  P. W. Rowe.  The stress-dilatancy relation for static equilibrium of an assembly of particles in contact , 1962, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[10]  S. Elaskar,et al.  Constitutive relations for compressible granular materials using non-Newtonian fluid mechanics , 1998 .

[11]  R. Bagnold.  Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear , 1954, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[12]  R. Rivlin,et al.  Hydrodynamics of Non-Newtonian Fluids , 1947, Nature.

[13]  Olivier Pouliquen,et al.  A constitutive law for dense granular flows , 2006, Nature.

[14]  M. Massoudi,et al.  A method for measuring the material moduli of granular materials: Flow in an orthogonal rheometer , 1990 .

[15]  Yulong Ding,et al.  Constitutive modelling of flowing granular materials: A continuum approach , 2004 .

[16]  Hans J. Herrmann,et al.  Statistical models for granular materials , 1999 .

[17]  M. Reiner,et al.  A Mathematical Theory of Dilatancy , 1945 .

[18]  M. Bolton.  THE STRENGTH AND DILATANCY OF SANDS , 1986 .

[19]  J. Duran,et al.  Sands, Powders, and Grains , 2000 .

[20]  M. De.  Handbuch der Physik , 1957 .

[21]  A. Wineman,et al.  Flow of granular materials between rotating disks , 1994 .

[22]  C. Truesdell,et al.  The Non-Linear Field Theories Of Mechanics , 1992 .

[23]  D. C. Drucker,et al.  Soil mechanics and plastic analysis or limit design , 1952 .

[24]  M. Massoudi,et al.  A continuum–kinetic theory approach to the rapid flow of granular materials: the effects of volume fraction gradient , 2001 .

[25]  Dimitrios Kolymbas,et al.  An outline of hypoplasticity , 1991, Archive of Applied Mechanics.

[26]  I. Goldhirsch,et al.  RAPID GRANULAR FLOWS , 2003 .

[27]  Christophe Ancey,et al.  Plasticity and geophysical flows: A review , 2007 .

[28]  R. Bagnold,et al.  The flow of cohesionless grains in fluids , 1956, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[29]  Hans J. Herrmann,et al.  Modeling granular media on the computer , 1998 .

[30]  J. Serrin.  The Derivation of Stress-Deformation Relations for a Stokesian Fluid , 1959 .

[31]  Yongqi Wang,et al.  A constitutive theory of fluid-saturated granular materials and its application in gravitational flows , 1999 .

[32]  Mehrdad Massoudi,et al.  A Mixture Theory formulation for hydraulic or pneumatic transport of solid particles , 2010 .

[33]  S. Savage,et al.  Gravity flow of cohesionless granular materials in chutes and channels , 1979, Journal of Fluid Mechanics.

[34]  R. Rivlin,et al.  Stress-Deformation Relations for Isotropic Materials , 1955 .

[35]  Osborne Reynolds Ll.D. F.R.S..  LVII. On the dilatancy of media composed of rigid particles in contact. With experimental illustrations , 1885 .

[36]  Mehrdad Massoudi,et al.  A continuum model for granular materials: Considering dilatancy and the Mohr-Coulomb criterion , 2001 .

[37]  M. Reiner.  Elasticity Beyond the Elastic Limit , 1948 .

[38]  Mehrdad Massoudi,et al.  On the flow of granular materials with variable material properties , 2001 .

[39]  C. Jenkin.  The Pressure Exerted by Granular Material: An Application of the Principles of Dilatancy , 1931 .

[40]  Y. P. Vaid,et al.  The strength and dilatancy of sand , 1992 .

[41]  Yulong Ding,et al.  Granular Materials: Fundamentals and Applications , 2007 .