The Mechanics of Rapid Granular Flows

Advances in Applied Mechanics - Tập 24 - Trang 289-366 - 1984
Stuart B. Savage1
1Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, Quebec

Tài liệu tham khảo

Ackermann, 1982, Stresses in rapidly sheared fluid-solid mixtures, J. Eng. Mech. Div., Am. Soc. Civ. Eng., 108, 95 Allen, 1970, The avalanching of granular solids on dune and similar slopes, J. Geol., 78, 326, 10.1086/627520 Augenstein, 1974, Friction factors for powder flow, Powder Technol., 10, 43, 10.1016/0032-5910(74)85030-8 Augenstein, 1978, An experimental study of the flow of dry powders over inclined surfaces, Powder Technol., 19, 205, 10.1016/0032-5910(78)80029-1 Bagnold, 1954, Experiments on a gravity free dispersion of large solid spheres in a newtonian fluid under shear, Proc. R. Soc. London, Ser. A, 225, 49, 10.1098/rspa.1954.0186 Bagnold, 1956, The flow of cohesionless grains in fluids, Phil. Trans. R. Soc. London, Ser. A, 249, 235, 10.1098/rsta.1956.0020 Bagnold, 1966, The shearing and dilation of dry sand and the ‘singing’ mechanism, Proc. R. Soc. London, Ser. A, 295, 219, 10.1098/rspa.1966.0236 Bagnold, 1973, The nature of saltation and of ‘bed-load’ transport in water, Proc. R. Soc., London, Ser. A, 332, 473, 10.1098/rspa.1973.0038 Bailard, 1978 Balmer, 1978, The operation of sand clocks and their medieval development, Technol. Culture., 19, 615, 10.2307/3103761 Batchelor, 1974, Transport properties of two-phase materials with random structure, Annu. Rev. Fluid Mech., 6, 227, 10.1146/annurev.fl.06.010174.001303 Bingham, 1931, The flow of dry sand through capillary tubes, J. Rheol. (NY), 2, 395, 10.1122/1.2116398 Blinowski, 1978, On the dynamic flow of granular media, Arch. Mech., 30, 27 Botterill, 1975 Botterill, 1972, Flow of fluidized solids, Powder Technol., 6, 343, 10.1016/0032-5910(72)83032-8 Botterill, 1979, The open channel flow of fluidized solids, Powder Technol., 23, 67, 10.1016/0032-5910(79)85026-3 Botterill, 1976, The flow properties of fluidized solids, Powder Technol., 14, 131, 10.1016/0032-5910(76)80015-0 C.E. Brennen, K. Sieck, J. Paslaski, (1982). Hydraulic jumps in granular material flow. Submitted to Powder Technol Bridgwater, 1972, Stress-velocity relationships for particulate solids, Am. Soc. Mech. Eng. Pap. Bridgwater, 1980, On the width of failure zones, Geotechnique, 30, 533, 10.1680/geot.1980.30.4.533 Brown, 1970 Buyevich, 1978, Flow of dense suspensions, Prog. Aeronaut. Sci., 18, 121, 10.1016/0376-0421(77)90004-5 Campbell, 1982 Carnahan, 1969, Equations of state for non-attracting rigid spheres, J. Chem. Phys., 51, 635, 10.1063/1.1672048 Carr, 1967, An annular shear cell for granular materials, Powder Technol., 1, 369, 10.1016/0032-5910(68)80019-1 Chapman, 1970 Cheng, 1966, Comments on the paper ‘Rheological Behaviour of Powder in a Rotational Viscometer’ by Hiroshi Kuno and Kozo Kurihara, Rheol. Acta, 5, 53, 10.1007/BF01973580 Cheng, 1978, Some observations on the rheological behaviour of dense suspensions, Rheol. Acta, 17, 446, 10.1007/BF01525960 Choda, 1967, Flow regimes of grains in inclined chutes, Trans. Am. Soc. Agri. Eng., 10, 136, 10.13031/2013.39614 Chong, 1971, Rheology of concentrated suspensions, J. Appl. Polymer Sci., 15, 2007, 10.1002/app.1971.070150818 Cowin, 1974, A theory for the flow of granular materials, Powder Technol., 9, 61, 10.1016/0032-5910(74)85010-2 Cowin, 1974, Constitutive relations that imply a generalized Mohr-Coulomb criterion, Acta Mech., 20, 41, 10.1007/BF01374961 Cox, 1971, Suspended particles in fluid flow through tubes, Annu. Rev. Fluid Mech., 3, 291, 10.1146/annurev.fl.03.010171.001451 Cundall, 1979, A discrete numerical model for granular assemblies, Geotech., 29, 47, 10.1680/geot.1979.29.1.47 Davidson, 1963 Davis, 1977, A discrete probabilistic model for mechanical response of a granular medium, Acta Mech., 26, 69, 10.1007/BF01180077 de Jong, 1969, Vertical air-controlled particle flow from a bunker through a circular orifice, Powder Technol., 3, 279, 10.1016/0032-5910(69)80095-1 de Josselin de Jong, 1959 de Josselin de Jong, 1971, The double-sliding, free-rotating model for granular assemblies, Geotechnique, 21, 155, 10.1680/geot.1971.21.2.155 de Josselin de Jong, 1977, Mathematical elaboration of the double-sliding, free-rotating model, Arch. Mech., 29, 561 Delaplaine, 1956, Forces acting on flowing beds of solids, AIChE J., 2, 127, 10.1002/aic.690020125 Dresher, 1972, Photoelastic verification of a mechanical model for the flow of a granular material, J. Mech. Phys. Solids, 20, 337, 10.1016/0022-5096(72)90029-4 Erismann, 1979, Mechanisms of large landslides, Rock Mech., 12, 15, 10.1007/BF01241087 Faber, 1972 Gadala-Maria, 1979 Goddard, 1977, A review of recent developments in the constitutive theory of particulate dispersions Goodman, 1971, Two problems in the gravity flow of granular materials, J. Fluid. Mech., 45, 321, 10.1017/S0022112071000065 Goodman, 1972, A continuum theory for granular materials, Arch. Ration. Mech. Anal., 44, 249, 10.1007/BF00284326 Green, 1956, Steady flow of non-Newtonian fluids through tubes, Quart. Appl. Math., 14, 299, 10.1090/qam/90335 Hagen, 1852, Druck und Bewegung des Trockenen Sandes, Berl. Monatsb. Akad. d. Wiss., S35 Hansen, 1976 Herczyński, 1980, Towards a statistical theory of suspension, Annu. Rev. Fluid Mech., 12, 237, 10.1146/annurev.fl.12.010180.001321 Hill, 1966, Bed forms due to a fluid stream, J. Hydraul. Div., Am. Soc. Civ. Eng., 92, 127 Hoffman, 1972, Discontinuous and dilatant viscosity behavior in concentrated suspensions. I. Observation of a flow instability, Trans. Soc. Rheol., 16, 155, 10.1122/1.549250 Hopfinger, 1983, Snow avalanche motion and related phenomena, Annu. Rev. Fluid Mech., 15, 47, 10.1146/annurev.fl.15.010183.000403 Hsu, 1975, Catastrophic debris streams generated by rock falls, Geol. Soc. Amer. Bull., 86, 129, 10.1130/0016-7606(1975)86<129:CDSSGB>2.0.CO;2 Hvorslev, 1936, A ring shearing apparatus for the determination of the shearing resistance and plastic flow of soil, Proc. Int. Conf. Soil Mech. Found. Engl., 2, 125 Hvorslev, 1939, Torsion shear tests and their place in the determination of the shearing resistance of soils, Proc. ASTM, 39, 999 Ishida, 1979, Velocity distributions in the flow of solid particles in an inclined open channel, J. Chem. Eng. Jpn., 12, 46, 10.1252/jcej.12.46 Ishida, 1980, Measurement of the velocity and directions of flow of solid particles in a fluidized bed, Powder Technol., 27, 1, 10.1016/0032-5910(80)85034-0 Ishida, 1980, The flow of solid particles in an aerated inclined channel, Powder Technol., 27, 7, 10.1016/0032-5910(80)85035-2 Janssen, 1895, Tests on grain pressure silos, Z. Ver. Dtsch. Ing., 39, 1045 Jeffrey, 1976, The rheological properties of suspensions in rigid particles, AIChE J., 22, 417, 10.1002/aic.690220303 Jenike, 1960, Flow properties of bulk solids, Proc. ASTM, 60, 1 Jenkins, 1979, Theories for flowing granular materials, 79 Jenkins, 1981, The mean stress resulting from interparticle collisions in a rapid granular shear flow, 4, 365 Jenkins, 1982, A theory for the rapid flow of identical smooth, nearly elastic particles, J. Fluid Mech. Kanatani, 1979, A micropolar continuum theory for the flow of granular materials, Int. J. Eng. Sci., 17, 419, 10.1016/0020-7225(79)90078-8 Kanatani, 1979, A continuum theory for the flow of granular materials. In “Theoretical and Applied Mechanics”, Japan Natl. Comm. Theor. and Appl. Mech., 27, 571 Kanatani, 1980, A continuum theory for the flow of granular materials (II). In “Theoretical and Applied Mechanics”, Japan Natl. Comm. Theor. and Appl. Mech., 28, 485 Knight, 1983, The role of particle collisions in determining high strain rate flow behaviour, Proc. Int. Symp. Role Particle Interactions Powder Mech. Komar, 1976 Krasheninnikov, 1967, Sharp growth of viscosity with increasing deformation rate in some disperse systems, Dokl. Phys. Chem., 174, 360 Kuno, 1965, Rheological behaviour of powder in a rotational viscometer, Rheol. Acta, 4, 73, 10.1007/BF01968739 Leal, 1980, Particle motions in a viscous fluid, Annu. Rev. Fluid Mech., 12, 435, 10.1146/annurev.fl.12.010180.002251 Lees, 1959 Leung, 1978, Flow of gas-solid mixtures in standpipes. A review, Powder Technol., 20, 145, 10.1016/0032-5910(78)80044-8 Leung, 1978, An analysis of moving bed flow of solids down standpipes and slide valves, Powder Technol., 19, 7, 10.1016/0032-5910(78)80069-2 Lun, 1982, Kinetic theories for granular flow: Inelastic particles in Couette flow and slightly inelastic particles in a general flow field, J. Fluid Mech. Mandel, 1966, Sur les Équations à Écoulement des Sols Indeaux en Déformation Plane et le Concept de Double Glissement, J. Mech. Phys. Solids, 14, 303, 10.1016/0022-5096(66)90006-8 Mandl, 1970, Fully developed plastic shear flow of granular materials, Geotech., 20, 277, 10.1680/geot.1970.20.3.277 Mandl, 1977, Shear zones in granular material, Rock Mech., 9, 95, 10.1007/BF01237876 Marble, 1964, Mechanism of particle collision in the one-dimensional dynamics of gas-particle mixtures, Phys. Fluids, 7, 1270, 10.1063/1.1711372 McDougall, 1969, Gravity flow of solids down vertical pipes, Trans. Inst. Mech. Eng., 184, 1 McDougall, 1973, The effect on solids mass flowrate of an expansion chamber between a hopper outlet and a vertical standpipe, Powder Technol., 8, 231, 10.1016/0032-5910(73)80088-9 D.F. McTigue, (1978). A model for stresses in shear flow of granular material. Proc. U.S. Japan Seminar on Continuum-Mechanical and Statistical Approaches in the Mechanics of Granular Materials, pp. 266–271 McTigue, 1979 Mellor, 1978, Dynamics of snow avalanches, 753 Metzner, 1958, Flow behavior of concentrated (dilatant) suspensions, Trans. Soc. Rheol., 2, 239, 10.1122/1.548831 Middleton, 1970, Experimental studies related to problems of flysch sedimentation, 253 Middleton, 1976, Subaqueous sediment transport and deposition by sediment gravity flows, 197 Morrison, 1976, Application of Spencer's ideal soil model to granular materials flow, Trans. ASME, Ser. E, 43, 49, 10.1115/1.3423794 Z. Mroz, (1980). Deformation and flow of granular materials. Proc. 15th Int. Congr. Theor. Appl. Mech. (F.P. J. Rimrott, B. Tabarrok, pp. 119–132 Nedderman, 1980, The flow of granular materials round obstacles, Powder Technol., 25, 215, 10.1016/0032-5910(80)87032-X Nedderman, 1980, The thickness of the shear zone of flowing granular materials, Powder Technol., 25, 91, 10.1016/0032-5910(80)87014-8 Nedderman, 1982, The flow of granular materials, I—discharge rates from hoppers, Chem. Eng. Sci., 37, 1597, 10.1016/0009-2509(82)80029-8 Nguyen, 1979 Novosad, 1964, Apparatus for measuring the dynamic angle of internal friction and external friction of a granular material, Collect. Czech. Chem. Comm., 29, 2697, 10.1135/cccc19642697 Nunziato, 1980, Gravitational flows of granular materials with incompressible grains, J. Rheol., 24, 395, 10.1122/1.549601 S. Ogawa, (1978). Multi-temperature theory of granular materials. Proc. U.S.-Japan Seminar on Continuum-Mechanical and Statistical Approaches in the Mechanics of Granular Materials, pp. 208–217 Ogawa, 1977, A thermomechanical theory of soil-like materials. In “Theoretical and Applied Mechanics”, Japan Natl. Comm. Theor. and Applied Mech., 25, 229 Ogawa, 1980, On the equations of fully fluidized granular materials, J. Appl. Math. Phys. (ZAMP), 31, 483, 10.1007/BF01590859 N. Oshima, (1978). Continuum model of fluidized granular media. Proc. U.S.-Japan Seminar on Continuum-Mechanical and Statistical Approaches in the Mechanics of Granular Materials, pp. 189–202 Oshima, 1980, Dynamics of fluidized granular media. In “Theoretical and Applied Mechanics”, Japan Natl. Comm. Theor. and Applied Mech., 28, 475 W.G. Pariseau, D.E. Nicholson, 1979 Elastic-plastic finite element analysis of hopper filling and flow initiation “Mechanics Applied to the Transport of Bulk Materials.” ASME AMD-31 (S.C. Cowin, pp. 61–77 Parlour, 1971 S.L. Passman, J.T. Jenkins, J.P. Thomas, Jr. (1978). Flow of a granular material in a vertical channel. Proc. U.S.-Japan Seminar on Continuum-Mechanical and Statistical Approaches in the Mechanics of Granular Materials, pp. 171–180 Passman, 1980, Shearing flows of granular materials, J. Eng. Mech. Div., Am. Soc. Civ. Eng., 106, 773 Present, 1958 Raudkivi, 1976 Reisner, 1971 Reynolds, 1885, On the dilatancy of media composed of rigid particles in contact, Philos. Mag. Ser. 5., 20, 469, 10.1080/14786448508627791 Ridgway, 1970, Flow of granular materials down chutes, Chem. Process Eng., 51, 82 Roberts, 1969, An investigation of the gravity flow of noncohesive granular materials through discharge chutes, ASME Trans., J. Eng. Ind., 91, 373, 10.1115/1.3591575 Roberts, 1981, Flow of bulk solids through transfer chutes of variable geometry and profile, Bulk Solids Handling, 1, 715 Roscoe, 1953, An apparatus for the application of simple shear to soil samples, 1, 186 Roscoe, 1970, The influence of strains in soil mechanics, Geotechnique, 20, 129, 10.1680/geot.1970.20.2.129 Roscoe, 1958, On the yielding of soils, Geotechnique, 8, 22, 10.1680/geot.1958.8.1.22 Rothrock, 1975, The mechanical behavior of pack ice, Annu. Rev. Earth Sci., 3, 317, 10.1146/annurev.ea.03.050175.001533 Russel, 1981, Brownian motion of small particles suspended in liquids, Annu. Rev. Fluid Mech., 13, 425, 10.1146/annurev.fl.13.010181.002233 Salencon, 1977 Sanders, 1963, Concepts of fluid mechanics provided by primary sedimentary structures, J. Sediment. Petrol., 33, 173 S.B. Savage, (1978). Experiments on shear flows of cohesionless granular materials. Proc. U.S.-Japan Seminar on Continuum-Mechanical and Statistical Approaches in the Mechanics of Granular Materials, pp. 241–254 Savage, 1979, Gravity flow of cohesionless granular materials in chutes and channels, J. Fluid Mech., 92, 53, 10.1017/S0022112079000525 Savage, 1981, The stress tensor in a granular flow at high shear rates, J. Fluid Mech., 110, 255, 10.1017/S0022112081000736 Savage, 1983, Shear stresses developed during rapid shear of dense concentrations of large spherical particles between concentric cylinders, J. Fluid Mech., 127, 453, 10.1017/S0022112083002827 Savage, 1980 Savage, 1982, Stresses developed by dry cohesionless granular materials sheared in an annular shear cell, J. Fluid Mech. Sayed, 1981 Sayed, 1983, Rapid gravity flow of cohesionless granular materials down inclined chutes, J. Appl. Math. Phys. (ZAMP), 34, 84, 10.1007/BF00962617 Scarlett, 1968, A split ring annular shear cell for determination of the shear strength of a powder, J. Sci. Instr., 1, 655, 10.1088/0022-3735/1/6/318 Scarlett, 1969, The critical porosity of free flowing solids, Trans. ASME, Ser. B., 91, 478, 10.1115/1.3591603 Scarlett, 1969, Application of geometrical probability to particulate systems. Part I. The critical porosity of shear granular systems, Powder Technol., 3, 299, 10.1016/0032-5910(69)80098-7 Schofield, 1968 Schwedes, 1973, Measurements of powder properties for hopper design, Trans. ASME, J. Eng. Ind., 95, 55, 10.1115/1.3438158 Schwedes, 1975, Shearing behavior of slightly compressed cohesive granular materials, Powder Technol., 11, 59, 10.1016/0032-5910(75)80024-6 Scott, 1963 Shahinpoor, 1981, New constitutive equations for the rapid flow of granular materials, J. Non-Newtonian Fluid Mech., 9, 147, 10.1016/0377-0257(87)87012-X Shen, 1982 Shen, 1982, Constitutive relationships for fluid-solid mixtures, J. Eng. Mech. Div., Am. Soc. Civ. Eng., 108, 748 Singh, 1978, Flow of fluidized solids and other fluids in open channels, Powder Technol., 20, 99, 10.1016/0032-5910(78)80014-X Sodhi, 1977 Sokolovski, 1965 Soo, 1967 Spencer, 1964, A theory of the kinematics of ideal soils under plane strain conditions, J. Mech. Phys. Solids., 12, 337, 10.1016/0022-5096(64)90029-8 Spencer, 1981, Deformation of an ideal granular material Stephens, 1978, The mixing and segregation of cohesionless particulate materials, I. Failure zone formation, Powder Technol., 21, 17, 10.1016/0032-5910(78)80104-1 Stephens, 1978, The mixing and segregation of cohesionless particulate materials, II. Microscopic mechanisms for particles differing in size, Powder Technol., 21, 29, 10.1016/0032-5910(78)80105-3 Suzuki, 1971, Measurements of flow properties of powders along an inclined plane, Ind. Eng. Chem. Fundam., 10, 84, 10.1021/i160037a015 Takahashi, 1981, Debris flow, Annu. Rev. Fluid Mech., 13, 57, 10.1146/annurev.fl.13.010181.000421 Takahashi, 1973, Flow profile and void fraction of granular solids in a moving bed, Powder Technol., 7, 205, 10.1016/0032-5910(73)80026-9 Takahasi, 1937, On the dynamical properties of granular mass, Geophys. Mag., 11, 165 Temperley, 1968 Toyama, 1970, The flow of granular materials in moving beds, Powder Technol., 4, 214, 10.1016/0032-5910(71)80037-2 Trees, 1962, A practical investigation of the flow of particulate solids through sloping pipes, Trans. Inst. Chem. Eng., 40, 286 Trevelyan, 1937 Trollope, 1980, Physical and numerical experiments with granular wedges, Geotechnique, 30, 137, 10.1680/geot.1980.30.2.137 Tüzün, 1982, Flow of granular materials, II—velocity distributions in slow flow, Chem. Eng. Sci., 37, 1691, 10.1016/0009-2509(82)80042-0 K. Umeya, (1978). Rheological studies on powder-liquid systems. Proc. U.S.-Japan Seminar on Continuum-Mechanical and Statistical Approaches in the Mechanics of Granular Materials, pp. 222–240 Walton, 1980 Wieghardt, 1975, Experiments in granular flow, Annu. Rev. Fluid Mech., 7, 89, 10.1146/annurev.fl.07.010175.000513 Williams, 1965, The preparation of powder specimens for shear cell testing, Rheol. Acta, 4, 170, 10.1007/BF01969253 Wolf, 1945, Experimental study of the flow of coal in chutes at riverside generating station, ASME Trans., 67, 585 Yoon, 1970, Gas flow and pressure drop through moving beds, Ind. Eng. Chem. Process Des. Dev., 9, 559, 10.1021/i260036a011 Yuasa, 1972, Effects of an efflux tube on the rate of flow of glass beads from a hopper, Powder Technol., 6, 97, 10.1016/0032-5910(72)80063-9 Zagaynov, 1967, Equations of plane steady-state motion of a granular medium (in Russian), Mech. Tverd. Tela, 2, 188 1970, Mechanics of Solids, 2, 130