Jaeger, H., Nagel, S. R., and Behringer, R. P., 1996, “Granular Solids, Liquids, and Gases,” Rev. Mod. Phys.

[CrossRef], 68 , pp. 1259–1273.

Brilliantov, N. V., and Pöschel, T., 2004, "*Kinetic Theory of Granular Gases*", Oxford University Press, New York.

Campbell, C. S., 1990, “Rapid Granular Flows,” Annu. Rev. Fluid Mech.

[CrossRef], 22 , pp. 57–90.

Goldhirsch, I., 2003, “Rapid Granular Flows,” Annu. Rev. Fluid Mech.

[CrossRef], 35 , pp. 267–293.

Goldhirsch, I., and Zanetti, G., 1993, “Clustering Instability in Dissipative Gases,” Phys. Rev. Lett.

[CrossRef], 70 , pp. 1619–1622.

Jenkins, J. T., and Savage, S. B., 1983, “A Theory for the Rapid Flow of Identical, Smooth, Nearly Elastic, Spherical Particles,” J. Fluid Mech.

[CrossRef], 130 , pp. 187–202.

Kadanoff, L. P., 1999, “Built Upon Sand: Theoretical Ideas Inspired by Granular Flows,” Rev. Mod. Phys.

[CrossRef], 71 , pp. 435–444.

Lun, C. K. K., 1991, “Kinetic Theory for Granular Flow of Dense, Slightly Inelastic, Slightly Rough Spheres,” J. Fluid Mech.

[CrossRef], 233 , pp. 539–559.

PöschelT. and BrilliantovN. V., eds., 2003, "*Granular Gas Dynamics*", Springer, New York.

Cleary, P. W., Metcalfe, G., and Liffman, K., 1998, “How Well do Discrete Element Granular Flow Models Capture the Essentials of Mixing Processes?,” Appl. Math. Model.

[CrossRef], 22 , pp. 995–1008.

Langston, P. A., Tüzün, U., and Heyes, D. M., 1995, “Discrete Element Simulation of Granular Flow in 2D and 3D Hoppers: Dependence of Discharge Rate and Wall Stress on Particle Interactions,” Chem. Eng. Sci.

[CrossRef], 50 , pp. 967–987.

Vu-Quoc, L., Zhang, X., and Walton, O. R., 2000, “A 3D Discrete-Element Method for Dry Granular Flows of Ellipsoidal Particles,” Comput. Methods Appl. Mech. Eng.

[CrossRef], 187 , pp. 483–528.

Cundall, P. A., and Strack, O. D. L., 1979, “A Distinct Element Model for Granular Assemblies,” Geotechnique, 29 , pp. 47–65.

Tordesillas, A., 2007, “Force Chain Buckling, Unjamming Transitions and Shear Banding in Dense Granular Assemblies,” Philos. Mag., 87 , pp. 4987–5016.

de Gennes, P. G., 1999, “Granular Matter: A Tentative View,” Rev. Mod. Phys.

[CrossRef], 71 , pp. S374–382.

Kolymbas, D., and Wu, W., 1993, “Introduction to Hypoplasticity,” "*Proceedings of the Modern Approaches to Plasticity*", D.Kolymbas, ed., Elsevier, Amsterdam, pp. 213–223.

Kolymbas, D., 1999, "*Introduction to Hypoplasticity: Advances in Geotechnical Engineering*", Balkema, Rotterdam.

Wu, W., and Kolymbas, D., 2000, “Hypoplasticity, Then and Now,” "*Constitutive Modelling of Granular Materials*", D.Kolymbas, ed., Springer-Verlag, Berlin, pp. 57–105.

Coulomb, C. A., 1776, “Essai sur une Application des règles de maximis & minimis á quelques problèmes de statique, relatifs á l’architecture,” Mémoire de Mathématique & de Physique, présentés àl’Académie Royale des Sciences par divers Savans, & lûs dans ses Assemblées, 7 , pp. 343–382.

Sokolovskii, V. V., 1965, "*Statics of Granular Materials*", Pergamon, Oxford.

Nedderman, R. M., 1992, "*Statics and Kinematics of Granular Materials*", Cambridge University Press, Cambridge.

Spencer, A. J. M., 1987, "*Continuum Models of Discrete Systems*", Balkema, Rotterdam.

Matsuoka, H., and Nakai, T., 1974, “Stress-Deformation and Strength Characteristics of Soils Under Three Different Principal Stresses,” "*Proceedings of the JSCE*", Vol. No. 232 , pp. 59–70.

Collins, I. F., 2003, “A Systematic Procedure for Constructing Critical State Models in Three Dimensions,” Int. J. Solids Struct., 40 , pp. 4379–4397.

Jenike, A. W., 1987, “A Theory of Flow of Particulate Solids in Converging and Diverging Channels Based on a Conical Yield Function,” Powder Technol., 50 , pp. 229–236.

Farley, R., and Valentin, F. H. H., 1967, “Effect of Particle Size Upon the Strength of Powders,” Powder Technol., 1 , pp. 334–354.

Hill, R., 1998, "*The Mathematical Theory of Plasticity*", Clarendon, Oxford.

Drescher, A., and de Josselin de Jong, G., 1972, “Photoelastic Verification of a Mechanical Model for the Flow of a Granular Material,” J. Mech. Phys. Solids

[CrossRef], 20 , pp. 337–351.

Ishihara, K., and Towhata, I., 1983, “Sand Response to Cyclic Rotation of Principal Stress Directions as Induced by Wave Loads,” Soils Found., 23 , pp. 11–26.

Symes, M. J. P. R., Gens, A., and Hight, D. W., 1984, “Undrained Anisotropy and Principal Stress Rotation in Saturated Sand,” Geotechnique, 34 , pp. 11–27.

Miura, K., Miura, S., and Toki, S., 1986, “Deformation Behaviour of Sand Under Principal Axes Rotation,” Soils Found., 26 , pp. 36–52.

Wong, R. K. S., and Arthur, J. R. F., 1986, “Sand Sheared by Stresses With Cyclic Variations in Directions,” Geotechnique, 36 , pp. 215–226.

Gutierrez, M., Ishihara, K., and Towhata, I., 1991, “Flow Theory for Sand During Rotation of Principal Stress Directions,” Soils Found., 31 , pp. 121–132.

Drucker, D. C., and Prager, W., 1952, “Soil Mechanics and Plastic Analysis or Limit Design,” Q. Appl. Math., 10 , pp. 157–165.

De Josselin de Jong, G., 1959, “Statics and Kinematics of the Failable Zone of a Granular Material,” Ph.D. thesis, Uitgeverij Waltman, Delft.

De Josselin de Jong, G., 1977, “Mathematical Elaboration of the Double-Sliding, Free Rotating Model,” Arch. Mech., 29 , pp. 561–591.

Spencer, A. J. M., 1964, “A Theory of the Kinematics of Ideal Soils Under Plane Strain Conditions,” J. Mech. Phys. Solids, 12 , pp. 337–351.

Spencer, A. J. M., 1982, “Deformation of Ideal Granular Materials,” "*Mechanics of Solids: The Rodney Hill 60th Anniversary Volume*", H.G.Hopkins and M.J.Sewell, eds., Pergamon, Oxford, pp. 607–652.

Mehrabadi, M. M., and Cowin, S. C., 1978, “Initial Planar Deformation of Dilatant Granular Materials,” J. Mech. Phys. Solids, 26 , pp. 269–284.

Harris, D., 1997, “Modelling Mathematically the Flow of Granular Materials,” "*Mechanics of Granular and Porous Materials*", N.A.Fleck and A.C. F.Cocks, eds., Kluwer, Dordrecht, pp. 239–250.

Harris, D., 1997, “Discrete and Continuum Models in the Mechanics of Granular Materials,” "*Powders and Grains 97*", R.P.Behringer and J.T.Jenkins, eds., Balkema, Rotterdam.

Harris, D., and Grekova, E. F., 2005, “A Hyperbolic Well-Posed Model for the Flow of Granular Materials,” J. Eng. Math., 52 , pp. 107–135.

Jiang, M. J., Harris, D., and Yu, H. S., 2005, “Kinematic Models for Non-Coaxial Granular Materialism—Part I: Theory,” Int. J. Numer. Analyt. Meth. Geomech., 29 , pp. 643–661.

Jiang, M. J., Harris, D., and Yu, H. S., 2005, “Kinematic Models for Non-Coaxial Granular Materials—Part II: Evaluation,” Int. J. Numer. Analyt. Meth. Geomech., 29 , pp. 663–689.

Yu, H. S., and Yuan, X., 2006, “On a Class of Non-Coaxial Plasticity Models for Granular Soils,” Proc. R. Soc. London, Ser. A, 462 , pp. 725–748.

Butterfield, R., and Harkness, R. M., 1972, “The Kinematics of Mohr-Coulomb Materials,” "*Stress-Strain Behaviour of Soils*", R.H. G.Parry, ed., Foulis, Henley, pp. 220–281.

Spencer, A. J. M., 1997, “Remarks on Coaxiality in Fully Developed Gravity Flows of Dry Granular Materials, in: Mechanics of Granular and Porous Materials,” "*Mechanics of Granular and Porous Materials*", N.A.Fleck and A.C. F.Cocks, eds., Kluwer, Dordrecht, pp. 227–238.

Spencer, A. J. M., and Bradley, N. J., 1996, “Gravity Flow of Granular Materials in Converging Wedges and Cones,” "*Proceedings of the Eighth International Symposium on Continuum Models and Discrete Systems*", Varna, Bulgaria, Jun. 11–16, 1995, K.Z.Markov, ed., World Scientific, Singapore, pp. 581–590.

Spencer, A. J. M., and Bradley, N. J., 2002, “Gravity Flow of Granular Materials in Contracting Cylinders and Tapered Tubes,” Int. J. Eng. Sci., 40 , pp. 1529–1552.

Savage, J. C., and Lockner, D. A., 1997, “A Test of the Double-Shearing Model of Flow for Granular Materials,” J. Geophys. Res., 102 , pp. 12287–12294.

Cox, A. D., Eason, G., and Hopkins, H. G., 1961, “Axially Symmetric Plastic Deformations in Soils,” Philos. Trans. R. Soc. London, Ser. A, 254 , pp. 1–45.

Spencer, A. J. M., 1983, “Kinematically Determined Axially Symmetric Deformations of Granular Materials,” "*Mechanics of Granular Media, New Models and Constitutive Relations*", J.T.Jenkins and M.Satake, eds., Elsevier, Amsterdam, pp. 245–253.

Spencer, A. J. M., 1986, “Axially Symmetric Flows of Granular Materials,” Solid Mechanics Archives, 11 , pp. 185–198.

Shield, R. T., 1955, “On the Plastic Flow of Metals Under Conditions of Axial Symmetry,” Proc. R. Soc. London, Ser. A, 233 , pp. 267–287.

Lippmann, H., 1962, “Principal Line Theory of Axially-Symmetric Plastic Deformation,” J. Mech. Phys. Solids, 10 , pp. 111–122.

Lippmann, H., 1965, “Statics and Dynamics of Axially-Symmetric Plastic Flow,” J. Mech. Phys. Solids, 13 , pp. 29–39.

Parker, D. F., 1990, “Some Generalized Similarity Solutions for Plastic Flow,” Acta Mech., 81 , pp. 163–180.

Spencer, A. J. M., 1984, “Plastic Flow Past a Smooth Cone,” Acta Mech., 54 , pp. 63–74.

Hill, J. M., and Wu, Y.-H., 1991, “Kinematically Determined Axially-Symmetric Plastic Flows of Metals and Granular Materials,” Q. J. Mech. Appl. Math., 44 , pp. 451–469.

Hill, J. M., and Katoanga, T. L., 1997, “The Velocity Equations for Dilatant Granular Flow and a New Exact Solution,” Rev. Mod. Phys.

[CrossRef], 48 , pp. 1–8.

Hill, J. M., and Katoanga, T. L., 1997, “On a Family of Axially Symmetric Kinematically Determined Plastic Flows,” Math. Mech. Solids, 2 , pp. 275–290.

Australian Standard: Loads on Bulk Solids Containers, 1996, Standards Association of Australia, ISBN 0733707335, AS 3774, p. 23.

Sture, S., 1999, “Constitutive Issues in Soil Liquefaction,” "*Proceedings of the Physics and Mechanics of Soil Liquefaction*", P.V.Lade and J.A.Yamamuro, eds., Balkema, Rotterdam, pp. 133–143.

Perkins, S. W., 1994, “Non-Linear Limit Analysis for the Bearing Capacity of Highly Frictional Soils,” "*Proceedings of the Second Congress on Computing in Civil Engineering*", Jun. 4, 1995, ASCE, Atlanta, Vol. 1 , pp. 629–636.

Perkins, S. W., 1995, “Bearing Capacity of Highly Frictional Material,” Geotech. Test. J., 18 , pp. 450–462.

Perkins, S. W., and Gui, D., 1994, “Mechanical Properties of Lunar Regolith and Their Effect on Bearing Capacity,” "*Computer Methods and Advances in Geomechanics*", H.J.Siriwardane and M.M.Zaman, eds., Balkema, Rotterdam, pp. 1521–1526.

Thamwattana, N., and Hill, J. M., 2003, “Analytical Stress and Velocity Fields for Gravity Flow of Highly Frictional Granular Materials,” Acta Mech., 164 , pp. 91–112.

Cox, G. M., McCue, S. W., Thamwattana, N., and Hill, J. M., 2005, “Perturbation Solutions for Flow Through Symmetrical Hoppers With Inserts and Asymmetrical Wedge Hoppers,” J. Eng. Math., 52 , pp. 63–91.

McCue, S. W., Johnpillai, I. K., and Hill, J. M., 2005, “New Stress and Velocity Fields for Highly Frictional Granular Materials,” IMA J. Appl. Math., 70 , pp. 92–118.

Hill, J. M., and Cox, G. M., 2001, “An Exact Parametric Solution for Granular Flow in a Converging Wedge,” ZAMP, 52 , pp. 657–668.

Thamwattana, N., and Hill, J. M., 2003, “Analytical Solutions for Tapering Quadratic and Cubic Rat-Holes in Highly Frictional Granular Solids,” Int. J. Solids Struct., 40 , pp. 5923–5948.

Abramowitz, M., and Stegun, A., 1974, "*Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables*", Dover, New York, pp. 505–506.

Johnpillai, I. K., McCue, S. W., and Hill, J. M., 2005, “Lie Group Symmetry Analysis for Granular Media Stress Equations,” J. Math. Anal. Appl., 301 , pp. 135–157.

Jenike, A. W., 1964, “Steady Gravity Flow of Frictional-Cohesive Solids in Converging Channels,” ASME J. Appl. Mech., 31 , pp. 5–11.

Jenike, A. W., 1965, “Gravity Flow of Frictional-Cohesive Solids: Convergence to Radial Stress Fields,” ASME J. Appl. Mech., 32 , pp. 205–207.

Johanson, J. R., 1964, “Stress and Velocity Fields in the Gravity Flow of Bulk Solids,” ASME J. Appl. Mech., 31 , pp. 499–506.

Gremaud, P. A., 2004, “Numerical Issues in Plasticity Models for Granular Materials,” J. Volcanol. Geotherm. Res., 137 , pp. 1–9.

Cleaver, J. A. S., and Nedderman, R. M., 1993, “Measurement of Velocity Profiles in Conical Hoppers,” Chem. Eng. Sci., 48 , pp. 3703–3712.

Horne, R. M., and Nedderman, R. M., 1978, “Stress Distribution in Hoppers,” Powder Technol., 19 , pp. 243–254.

Moreea, S. B. M., and Nedderman, R. M., 1996, “Exact Stress and Velocity Distributions in a Cohesionless Material Discharging From a Conical Hopper,” Chem. Eng. Sci., 51 , pp. 3931–3942.

Wu, Y.-H., and Collinson, R., 2000, “Determination of Velocity and Stress Discontinuities in Quasi-Static Granular Flows,” ANZIAM J., 42 , pp. C1556–C1579.

Savage, S. B., 1965, “The Mass Flow of Granular Materials Derived From Coupled Velocity-Stress Fields,” Br. J. Appl. Phys., 16 , pp. 1885–1888.

Savage, S. B., 1967, “Gravity Flow of a Cohesionless Bulk Solid in a Converging Conical Channel,” Int. J. Mech. Sci., 9 , pp. 651–659.

Davidson, J. F., and Nedderman, R. M., 1973, “The Hour-Glass Theory of Hopper Flow,” Trans. Inst. Chem. Eng., 51 , pp. 29–35.

Brennen, C., and Pearce, J. C., 1978, “Granular Material Flow in Two-Dimensional Hoppers,” ASME J. Appl. Mech., 45 , pp. 43–50.

Nguyen, T. V., Brennen, C., and Pearce, J. C., 1979, “Gravity Flow of Granular Materials in Conical Hoppers,” ASME J. Appl. Mech., 46 , pp. 529–535.

Kaza, K. R., and Jackson, R., 1982, “The Rate of Discharge of Coarse Granular Material From a Wedge-Shaped Mass Flow Hopper,” Powder Technol., 33 , pp. 223–237.

Weir, G. J., 2005, “Incompressible Granular Flow From Wedge-Shaped Hoppers,” J. Eng. Math., 52 , pp. 293–305.

Prakash, J. R., and Rao, K. K., 1991, “Steady Compressible Flow of Cohesionless Granular Materials Through a Wedge-Shaped Bunker,” J. Fluid Mech., 225 , pp. 21–80.

Choi, J., Kudrolli, A., and Bazant, M. Z., 2005, “Velocity Profile of Granular Flows Inside Silos and Hoppers,” J. Phys.: Condens. Matter, 17 , pp. S2533–2548.

Samadani, A., Pradhan, A., and Kudrolli, A., 1999, “Size Segregation of Granular Matter in Silo Discharges,” Phys. Rev. E

[CrossRef], 60 , pp. 7203–7209.

Thamwattana, N., and Hill, J. M., 2005, “Perturbation Solutions for Highly Frictional Granular Media,” Proc. R. Soc. London, Ser. A, 461 , pp. 21–42.

Cox, G. M., and Hill, J. M., 2005, “Some Exact Velocity Profiles for Granular Flow in Converging Hoppers,” ZAMP, 56 , pp. 92–106.

Cox, G. M., and Hill, J. M., 2003, “Some Exact Mathematical Solutions for Granular Stock Piles and Granular Flow in Hoppers,” Math. Mech. Solids, 8 , pp. 21–50.

Drescher, A., 1991, "*Analytical Methods in Bin-Load Analysis*", Elsevier, Amsterdam.

McCue, S. W., and Hill, J. M., 2005, “Free Surface Problems for Static Coulomb-Mohr Granular Solids,” Math. Mech. Solids, 10 , pp. 651–672.

Gremaud, P. A., Matthews, J. V., and Schaeffer, D. G., 2003, “Secondary Circulation in Granular Flow Through Nonaxisymmetric Hoppers,” SIAM J. Appl. Math., 64 , pp. 583–600.

Gremaud, P. A., Matthews, J. V., and O’Mally, M., 2004, “On the Computation of Steady Hopper Flows II: Von Mises Materials in Various Geometries,” J. Comput. Phys., 200 , pp. 639–653.

Gremaud, P. A., Matthews, J. V., and Schaeffer, D. G., 2006, “On the Computation of Steady Hopper Flows III: Model Comparisons,” J. Comput. Phys., 219 , pp. 443–454.

Hummel, F. H., and Finnan, E. J., 1920, “The Distribution of Pressure on Surfaces Supporting a Mass of Granular Material,” Minutes of Proceedings of the Institution of Civil Engineers , Session 1920–1921, Part II, Selected Papers, Vol. 212 , pp. 369–392.

Smid, J., and Novosad, J., 1981, “Pressure Distribution Under Heaped Bulk Solids,” Inst. Chem. Eng. Symp. Ser., 63 , p. D3/V/1-12.

Watson, A., 1991, “The Perplexing Puzzle Posed by a Pile of Apples,” New Sci., 1799 , p. 19.

Watson, A., 1996, “Searching for the Sand-Pile Pressure Dip,” Science, 273 , pp. 579–580.

Trollope, D. H., and Burman, B. C., 1980, “Physical and Numerical Experiments With Granular Wedges,” Geotechnique, 30 (2), pp. 137–157.

Michalowski, R. L., and Park, N., 2004, “Admissible Stress Fields and Arching in Piles of Sand,” Geotechnique, 54 (8), pp. 529–538.

Wittmer, J. P., Claudin, P., Cates, M. E., and Bouchaud, J.-P., 1996, “An Explanation for the Central Stress Minimum in Sand Piles,” Nature (London), 382 , pp. 336–338.

Wittmer, J. P., Cates, M. E. and Claudin, P., 1997, “Stress Propagation and Arching in Static Sandpiles,” J. Phys. I

[CrossRef], 7 , pp. 39–80.

Cates, M. E., Wittmer, J. P., Bouchaud, J.-P., and Claudin, P., 1999, “Jamming and Static Stress Transmission in Granular Materials,” Chaos, 9 (3), pp. 511–522.

Cates, M. E., Wittmer, J. P., Bouchaud, J.-P., and Claudin, P., 1999, “Jamming and Static Stress Transmission in Particle Matter,” Physica A, 263 , pp. 354–361.

Cates, M. E., Wittmer, J. P., Bouchaud, J.-P., and Claudin, P., 1998, “Development of Stresses in Cohesionless Poured Sand,” Philos. Trans. R. Soc. London, Ser. A, 356 , pp. 2535–2560.

Geng, F., Longhi, E., Behringer, R. P., and Howell, D. W., 2001, “Memory in Two-Dimensional Heap Experiments,” Phys. Rev. E

[CrossRef], 64 , p. 060301.

Baxter, J., Tüzün, U., Burnell, J., and Heyes, D. M., 1997, “Granular Dynamics Simulations of Two-Dimensional Heap Formation,” Phys. Rev. E

[CrossRef], 55 (3), pp. 3546–3554.

Atman, A. P. F., Brunet, O., Geng, J., Reydellet, G., Combe, G., Claudin, P., Behringer, R. P., and Clément, E., 2005, “Sensitivity of the Stress Response Function to Packing Preparation,” J. Phys.: Condens. Matter, 17 , pp. S2391–2403.

Goldenberg, C., Atman, A. P. F., Claudin, P., Combe, G., and Goldhirsch, I., 2006, “Scale Separation in Granular Packings: Stress Plateaus and Fluctuations,” Phys. Rev. Lett.

[CrossRef], 96 , p. 168001.

Gland, N., Wang, P., and Makse, H. A., 2006, “Numerical Study of the Stress Response of Two-Dimensional Dense Granular Packings,” Eur. Phys. J. E, 20 , pp. 179–184.

Snyder, R. E., and Ball, R. C., 1994, “Self-Organised Criticality in Computer Models of Settling Powders,” Phys. Rev. E

[CrossRef], 49 (1), pp. 104–109.

Bagster, D. F., 1982, “A Randomised Model of Granular Material in an Ore Heap,” Rev. Mod. Phys.

[CrossRef], 6 , pp. 1–3.

Bagster, D. F., 1989, “The Development of a Microscopic Model of Granular Material Behaviour in a Heap,” "*Proceedings of the Third International Conference Bulk Materials, Storage, Handling and Transportation*", Newcastle, Australia, Jun. 27–29, pp. 24–32.

Bagster, D. F., and Kirk, R., 1985, “Computer Generation of a Model to Simulate Granular Material Behaviour,” J. Powder Bulk Solids Technol., 9 , pp. 19–24.

Liffman, K., Nguyen, M., and Cleary, P., 1999, “Stress in Sandpiles,” "*Proceedings of the Second International Conference on CFD in the Materials and Process Industries*", Dec. 6–8, CSIRO, Melbourne, Australia, pp. 83–87.

Vanel, L., Howell, D., Clark, D., Behringer, R. P., and Clement, E., 1999, “Memories in Sand: Experimental Tests of Construction History on Stress Distributions Under Sandpiles,” Phys. Rev. E

[CrossRef], 60 , pp. R5040–R5043.

Savage, S. B., 1997, “Problems in the Statics and Dynamics of Granular Materials,” "*Proceedings of the Powders and Grains ’97*", R.P.Behringer and J.T.Jenkins, eds., Balkema, Rotterdam, pp. 185–194.

Didwania, A. K., Cantelaube, F., and Goddard, J. D., 2000, “Static Multiplicity of Stress States in Granular Heaps,” Proc. R. Soc. London, Ser. A

[CrossRef], 456 , pp. 2569–2588.

Hill, J. M., and Cox, G. M., 2000, “The Force Distribution at the Base of Sand-Piles,” "*Development in Theoretical Geomechanics*", The John Booker Memorial Symposium , D.W.Smith and J.P.Carter, pp. 43–61.

Thamwattana, N., Cox, G. M., and Hill, J. M., 2004, “Stress Distributions in Highly Frictional Granular Heaps,” ZAMP, 55 , pp. 330–356.

Thamwattana, N., and Hill, J. M., 2004, “Stress Distributions Within Curved Highly Frictional Granular Stockpiles,” Q. J. Mech. Appl. Math., 57 , pp. 447–466.

Jeschar, R., Potke, W., Petersen, V., and Polthier, K., 1975, “Blast Furnace Aerodynamics,” "*Proceedings of the Symposium on Blast Furnace Aerodynamics*", N.Standish, ed., Sept. 25–27, The Australian Institute of Mining & Metallurgy, Wollongong, pp. 136–147.

Grasselli, Y., Herrmann, H. J., Oron, G., and Zapperi, S., 2000, “Effect of Impact Energy on the Shape of Granualr Heaps,” Granular Matter, 2 , pp. 97–100.

Hill, J. M., and Cox, G. M., 2002, “On the Problem of the Determination of Force Distributions in Granular Heaps Using Continuum Theory,” Q. J. Mech. Appl. Math., 55 , pp. 655–668.

Cantelaube, F., and Goddard, J. D., 1997, “Elastoplastic Arching in 2D Heaps,” "*Powders and Grains*", Proceedings of the Third International Conference , Durham, NC, May 18–23, R.P.Behringer and J.T.Jenkins, eds., Balkema, Rotterdam, pp. 231–234.

Cantelaube, F., Didwania, A. K., and Goddard, J. D., 1998, “Elasto-Plastic Arching in Two Dimensional Granular Heaps,” "*Physics of Dry Granular Media*", Proceedings of the NATO ASI , Cargese, France, Sept. 15–26, 1997, H.J.Herrmann, J.P.Hovi, and S.Luding, eds., Kluwer, Dordrecht, pp. 123–127.

Dantion, B., Hossfeld, R., and McAtee, K., 2003, “Converting From Funnel Flow to Mass Flow,” Power, 147 , p. 61.

Roberts, A. W., and Wensrich, C. M., 2002, “Flow Dynamics or ‘Quaking’ in Gravity Discharge From Silos,” Chem. Eng. Sci., 57 , pp. 295–305.

Jenike, A. W., 1962, “Gravity Flow of Bulk Solids,” Utah Engineering Experiment Station, Bulletin No. 108.

Jenike, A. W., 1962, “Gravity Flow of Solids,” Trans. Inst. Chem. Eng., 40 , pp. 264–271.

Jenike, A. W. and Yen, B. C., 1962, “Slope Stability in Axial Symmetry,” Utah Engineering Experimental Station, Bulletin No. 115.

Jenike, A. W., and Yen, B. C., 1963, “Slope Stability in Axial Symmetry,” "*Proceedings of the Fifth Symposium on Rock Mechanics*", University of Minnesota, May 1962, Pergamon, New York, pp. 689–711.

Hill, J. M., and Cox, G. M., 2000, “Cylindrical Cavities and Classical Rat-Hole Theory Occurring in Bulk Materials,” Int. J. Numer. Analyt. Meth. Geomech., 24 , pp. 971–990.

Johanson, K., 2004, “Rathole Stability Analysis for Aerated Powder Materials,” Powder Technol., 141 , pp. 161–170.

Hill, J. M., and Cox, G. M., 2001, “Stress Profiles for Tapered Cylindrical Cavities in Granular Media,” Int. J. Solids Struct., 38 , pp. 3795–3811.

Spencer, A. J. M., and Hill, J. M., 2001, “Non-Dilatant Double-Shearing Theory Applied to Granular Funnel-Flow in Hoppers,” J. Eng. Math., 41 , pp. 55–73.

Spencer, A. J. M., and Bradley, N. J., 1992, “Gravity Flow of a Granular Material in Compression Between Vertical Walls and Through a Tapering Vertical Channel,” Q. J. Mech. Appl. Math., 45 , pp. 733–746.

Hill, J. M., and Cox, G. M., 2002, “Rat-Hole Stress Profiles for Shear-Index Granular Materials,” Acta Mech., 155 , pp. 157–172.

Kozicki, J., and Tejchman, J., 2005, “Application of a Cellular Automaton to Simulations of Granular Flows in Silos,” Granular Matter, 7 , pp. 45–54.

Matchett, A. J., 2006, “Stresses in a Bulk Solid in a Cylindrical Silo, Including an Analysis of Ratholes and an Interpretation of Rathole Stability Criteria,” Chem. Eng. Sci., 61 , pp. 2035–2047.

Matchett, A. J., 2006, “Rotated, Circular Arc Models of Stress in Silos Applied to Core-Flow and Vertical Rat-Holes,” Powder Technol., 162 , pp. 87–99.

Enstad, G., 1975, “On the Theory of Arching in Mass Flow Hoppers,” Chem. Eng. Sci., 30 , pp. 1273–1283.

Li, H., 1994, “Mechanics of Arching in a Moving Bed Standpipe With Interstitial Gas Flow,” Rev. Mod. Phys.

[CrossRef], 78 , pp. 179–187.

Johanson, K., and Barletta, D., 2004, “The Influence of Air Counter-Flow Through Powder Materials as a Means of Reducing Cohesive Flow Problems,” Part. Part. Syst. Charact.

[CrossRef], 21 , pp. 316–325.

Cox, G. M., Hill, J. M., and Thamwattana, N., 2004, “A Formal Exact Mathematical Solution for a Sloping Rat-Hole in a Highly Frictional Granular Solid,” Acta Mech., 170 , pp. 127–147.