Skip to main content Accesibility Help

Stresses developed by dry cohesionless granular materials sheared in an annular shear cell

  • S. B. Savage (a1) and M. Sayed (a1)

Experimental results obtained during rapid shearing of several dry, coarse, granular materials in an annular shear cell are described. The main purpose of the tests was to obtain information that could be used to guide the theoretical development of constitutive equations suitable for the rapid flow of cohesionless bulk solids at low stress levels. The shear-cell apparatus consists of two concentric disk assemblies mounted on a fixed shaft. Granular material was contained in an annular trough in the bottom disk and capped by a lipped annular ring on the top disk. The bottom disk can be rotated at specified rates, while the top disk is loaded vertically and is restrained from rotating by a torque arm connected to a force transducer. The apparatus was thus designed to determine the shear and normal stresses as functions of solids volume fraction and shear rate.

Tests were performed with spherical glass and polystyrene beads of nearly uniform diameters, spherical polystyrene beads having a bimodal size distribution and with angular particles of crushed walnut shells. The particles ranged from about ½ to 2 mm in size. At the lower concentrations and high shear rates the stresses are generated primarily by collisional transfer of momentum and energy. Under these conditions, both normal and shear stresses were found to be proportional to the particle density, and the squares of the shear rate and particle diameter. At higher concentrations and lower shear rates, dry friction between particles becomes increasingly important, and the stresses are proportional to the shear rate raised to a power less than two. All tests showed strong increases in stresses with increases in solids concentrations. The ratio of shear to normal stresses showed only a weak dependence upon shear rate, but it increased with decreasing concentration. At the very highest concentrations with narrow shear gaps, finite-particle-size effects became dominant and differences in stresses of as much as an order of magnitude were observed for the same shear rate and solids concentration.

Hide All
Ackermann, N. L. & Shen, H. H. 1982 Stresses in rapidly sheared fluid—solid mixtures. J. Engng Mech. Div. ASCE 108, 95113.
Bagnold, R. A. 1954 Experiments on a gravity free dispersion of large solid spheres in a Newtonian fluid under shear. Proc. R. Soc. Lond. A 225, 4963.
Bagnold, R. A. 1966 The shearing and dilation of dry sand and the ‘singing’ mechanism. Proc. R. Soc. Lond. A 295, 219232.
Bridgwater, J. 1972 Stress-velocity relationships for particulate solids. ASME Paper 72-MH-21.
Campbell, C. S. & Brennen, C. E. 1982a Computer simulation of shear flows of granular materials. In Proc. U.S.—Japan Seminar on New Models and Constitutive Relations in the Mechanics of Granular Materials (ed. J. T. Jenkins & M. Satake). Elsevier.
Campbell, C. S. & Brennen, C. E. 1982b Computer simulation of chute flows of granular materials. In Proc. IUTAM Symp. on Deformation and Failure of Granular Materials, Delft.
Carr, J. F. & Walker, D. M. 1967/68 An annular shear cell for granular materials. Powder Tech. 1, 369373.
Cheng, D. C.-H. & Richmond, R. A. 1978 Some observations on the rheological behaviour of dense suspensions. Rheol. Acta 17, 446453.
Goldsmith, W. 1960 Impact: The theory and physical behaviour of colliding solids. Arnold.
Hawthorne, W. R. 1965 Engineering aspects. In Research Frontiers in Fluid Mechanics (ed. R. J. Seeger & G. Temple), chap. 1, pp. 120. Interscience.
Hoffman, R. L. 1972 Discontinuous and dilatant viscosity behaviour in concentrated suspensions. I. Observation of a flow instability. Trans. Soc. Rheol. 16, 155173.
Hvorslev, M. J. 1936 A ring shearing apparatus for the determination of the shearing resistance and plastic flow of soil. In Proc. Intl Conf. Soil Mech. Found. Engng, Cambridge, Mass., vol. 2, pp. 125129.
Hvorslev, M. J. 1939 Torsion shear tests and their place in the determination of the shearing resistance of soils. Proc. ASTM 39, 9991022.
Jenkins, J. T. & Savage, S. B. 1983 A theory for the rapid flow of identical smooth, nearly elastic particles. J. Fluid Mech. 130, 187202.
Mandl, G., de Jong, L. N. J. & Maltha, A. 1977 Shear zones in granular material. Rock Mech. 9, 95144.
Metzner, A. B. & Whitlock, M. 1958 Flow behaviour of concentrated (dilatant) suspensions. Trans. Soc. Rheol. 2, 239254.
Novosad, J. 1964 Apparatus for measuring the dynamic angles of internal friction and external friction of a granular material. Collection Czech. Chem. Commun. 29, 26972701.
Ogawa, S., Umemura, A. & Oshima, N. 1980 On the equations of fully fluidized granular materials. Z. angew. Math. Phys. 31, 483493.
Savage, S. B. 1978 Experiments on shear flows of cohesionless granular materials. In Proc. U.S.—Japan Seminar on Continuum-Mechanical and Statistical Approaches in the Mechanics of Granular Materials (ed. S. C. Cowin & M. Satake), pp. 24154. Gakujusu Bunken Fukyu-kai.
Savage, S. B. 1979 Gravity flow of cohesionless granular materials in chutes and channels. J. Fluid Mech. 92, 5396.
Savage, S. B. & Jeffrey, D. J. 1981 The stress tensor in a granular flow at high shear rates. J. Fluid Mech. 110, 255272.
Scott, R. F. 1963 Principles of Soil Mechanics. Addison-Wesley.
Scarlett, B., Ackers, R. J., Parkinson, J. S. & Todd, A. C. 1969/70 Application of geometrical probability to particulate systems. Part I. The critical porosity of shear granular systems. Powder Tech. 3, 299308.
Scarlett, B. & Todd, A. C. 1968 A split ring annular shear cell for determination of the shear strength of a powder. J. Sci. Instr. 1, 655656.
Scarlett, B. & Todd, A. C. 1969 The critical porosity of free flowing solids. Trans. ASME B: J. Engng Ind. 91, 478488.
Shen, H. 1982 Constitutive relationships for fluid—solid mixtures. Ph.D. thesis, Clarkson Coll. of Tech.
Stephens, D. J. & Bridgwater, J. 1978a The mixing and segregation of cohesionless particulate materials. Part I. Failure zone formation. Powder Tech. 21, 1728.
Stephens, D. J. & Bridgwater, J. 1978b The mixing and segregation of cohesionless particulate materials. Part II. Microscopic mechanisms for particles differing in size. Powder Tech. 21, 2944.
Umeya, K. 1978 Rheological studies on powder—liquid systems. In Proc. U.S.-Japan Seminar on Continuum-Mechanical and Statistical Approaches in the Mechanics of Granular Materials (ed. S. C. Cowin & M. Satake), pp. 222240. Gakujutsu Bunken Fukyu-kai.
Voight, B. (ed.) 1978 Rockslides and Avalanches, vol. 1. Elsevier.
Voight, B. (ed.) 1979 Rockslides and Avalanches, vol. 2. Elsevier.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed