Summary
The non-dilatant double-shearing theory for granular flow is applied to the problem of dynamical chute flow down an inclined slope. Four distinct families of solutions are examined and a number of simple exact solutions are determined which apply to the special case of a granular material with an angle of internal friction equal to ninety degrees. Some of the solutions obtained are illustrated graphically.
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Hill, J. M.: Similarity ‘hot-spot’ solutions for a hypoplastic granular material. Proc. R. Soc. London. A.456, 2653–2671 (2000).
Hill, J. M.: Dynamical uniaxial and radial flow for hypoplastic granular materials. In: International Workshop on Bifurcation and Localisation in Geomaterials. Perth, Balkema 2001, pp. 239–248.
Hill, J. M., Williams, K. A.: Dynamical uniaxial compaction of a hypoplastic granular material. Mech. Mat.32, 679–691 (2000).
Spencer, A. J. M.: A theory of the kinematics of ideal soils under plane strain conditions. J. Mech. Phy. Solids.12, 337–351 (1964).
Spencer, A. J. M.: Deformation of ideal granular materials. In: Mechanics of Solids (H. G. Hopkins and M. J. Sewell, eds). Oxford: Pergamon Press 1982, pp. 607–652.
Hill, J. M., Spencer, A. J. M.: Some dynamic shear flow problems for granular materials. Q. J. Appl. Math.52, 253–267 (1999).
Spencer, A. J. M.: Dynamic analysis of shear flow of granular materials. In: Advances in engineering plasticity and its applications-AEPA '96 (Abe, T., Tsuta, T., Eds), pp. 3–7. Oxford: Pergamon Press 1996.
Spencer, A. J. M.: Remarks on coaxiality in fully developed gravity flows of dry granular materials. In: IUTAM symposium on mechanics of granular and porous materials (Fleck, N. A., Cocks, A. C. F., eds), pp. 227–238. Dordrecht: Kluwer 1997.
Spencer, A. J. M.: A model for granular material mechanics combining double-shearing and critical state concepts. In: Proc. 9th Int. Symp. Continuum Models and Discrete Systems (Inan, E., Markov, K. Z., eds), pp. 803–810, Singapore: World Scientific 1998.
Spencer, A. J. M., Bradley, N. J.: Gravity flow of granular materials in converging wedges and cones. In: Continuum models and discrete systems: Proc. 8th Int. Symposium (Markov, K. Z., ed.), pp. 581–590. Singapore: World Scientific 1996.
Spencer, A. J. M., Hill, J. M.: Non-dilatant double-shearing theory applied to granular funnel-flow in hoppers. J. Eng. Math.41, 55–73 (2001).
Zheng, X. M., Hill, J. M.: Molecular dynamics modelling of granular chute flow: Density and velocity profiles. Powder Technol.86, 219–227 (1996).
Hill, J. M., Zheng, X. M.: Dilatant double shearing theory applied to granular chute flow. Acta Mech.118, 97–108 (1996).
Hutter, K.: Two- and three-dimensional evolution of granular avalanche flow—theory and experiments revisited. Acta Mech. [Suppl]1, 167–181 (1991).
Savage, S. B., Hutter, K.: The motion of a finite mass of granular material down a rough incline. J. Fluid Mech.199, 177–215 (1989).
Savage, S. B., Hutter, K.: The dynamics of avalanches of granular materials from initiation to runout. Part I: Analysis. Acta Mech.86, 201–223 (1991).
Hutter, K., Koch, T.: Motion of a granular avalanche in an exponentially curved chute: Experiments and theoretical predictions. Phil. Trans. R. Soc. Lond. A.334, 93–138 (1991).
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Cox, G.M., Hill, J.M. Non-dilatant double-shearing theory applied to dynamical granular chute flow. Acta Mechanica 159, 125–142 (2002). https://doi.org/10.1007/BF01171451
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DOI: https://doi.org/10.1007/BF01171451