A semi-empirical equation to predict filling wall pressures on oblique conical hoppers
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Buildings, Infrastructures and Projects for Rural and Environmental Engineering (BIPREE), ETSIAAB, Universidad Politécnica de Madrid, Spain
Final revision date: 2022-07-22
Acceptance date: 2022-08-08
Publication date: 2022-09-26
Corresponding author
Francisco Ayuga   

Buildings, Infrastructures and Projects for Rural and Environmental Engineering (BIPREE), ETSIAAB, Universidad Politécnica de Madrid, ETSIAAB Ciudad Universitaria, 28040, Madrid, Spain
Int. Agrophys. 2022, 36(4): 285–295
  • Finite Element Model to predict the wall pressures on oblique hoppers
  • Outlet circumferential location and eccentricity are the pressure main factors
  • A semi-empirical equation is proposed to estimate pressures on oblique hoppers
Hoppers are frequently used in steel silos, especially in farm facilities and food industries. These structures occasionally have an oblique hopper with an eccentric outlet to improve the flow of material during discharge. The 2006 version of the European standard EN 1991-4 uses classical Walker theory to predict wall pressures on concentric hoppers, but oblique hoppers are not considered. The authors have developed a Finite Element Model to predict the wall pressures on oblique hoppers and several sensitivity analyses have been made to study the possible influence of different parameters including outlet eccentricity, the outlet circumferential position, the aspect ratio of the silo and hopper, and different stored materials. The results show that the circumferential location and eccentricity of the outlet are the main factors affecting the pressures on oblique hoppers. A semi-empirical equation is proposed to estimate the expected pressures on oblique hoppers which is designed to match with the maximum normal pressure obtained from the simulation, and to provide a good representation for the circumferential distribution of normal pressures. The results of this research may be of interest with regard to the upcoming revised version of the European standard EN 1991-4.
This work was supported by the Spanish Agencia Estatal de Investigación via the research project “Study of the structural behaviour of corrugated wall silos using Discrete Element Models (SILODEM)” [grant number PID2019-107051GB-I00/AEI/10.13039/501100011033], (2020-2023).
All authors declare no conflict of interest.
Ansys, 2012. ANSYS User’s manual. Version 13.0, ANSYS, Canonsburg, PA, USA.
Aoki R. and Tsunakawa H., 1969. The pressure in a granular material at the wall of bins and hoppers. J. Chem. Eng. Japan, 2(1), 126-129,
Ayuga F., Guaita M., Aguado P.J., and Couto A., 2001. Discharge and the eccentricity of the hopper influence on the silo wall pressures. J. Eng. Mech.-ASCE, 127(10), 1067-1074,
Brown C.J., Lahlouh E.H., and Rotter J.M., 2000. Experiments on a square plan form steel silo. Chem. Eng. Sci., 55(20), 4399-4413,
Couto A., Ruiz A., and Aguado P.J., 2012. Design and instrumentation of a mid-size test station for measuring static and dynamic pressures in silos under different conditions - Part I: Description. Comput. Electron. Agric., 85(1), 164-173,
Couto A., Ruiz A., and Aguado P.J., 2013. Experimental study of the pressures exerted by wheat stored in slender cylindrical silos, varying the flow rate of material during discharge. Comparison with Eurocode 1 part 4. Powder Technol., 237(1), 450-467,
Dąbrowski A., 1957. Pressures in bulk solids in hoppers. (In Polish), Arch. Inżynierii Lądowej. 3, 325-334.
Ding S., Ji Y., Ye S., Rotter J.M., and Li Q., 2014. Measurements of pressure and frictional tractions along walls of a large-scale conical shallow hopper and comparison with Eurocode 1991-4:2006. Thin-Walled Struct., 80(1), 231-238,
Ding S., Rotter J.M., Ooi J.Y., and Enstad G., 2011. Development of normal pressure and frictional traction along the walls of a steep conical hopper during filling, Thin-Walled Struct., 49(12), 1246-1250,
Do Nascimento J.W.B., Neto J.P.L., and Montross M.D., 2013. Horizontal pressures in cylindrical metal silos and comparison with different international standards. Eng. Agric., 33(4), 601-611,
Drucker D.C. and Prager W., 1952. Soil mechanics and plastic analysis or limit design. Q. Appl. Math., 10(1), 157-165,
EN 1991-4, 2006, Actions on structures. Part 4: Silos and tanks, European Commitee for Standardization, Brussels, Belgium.
Gallego E., Rombach G.A., Neumann F., and Ayuga F., 2010. Simulations of granular flow in silos with different finite element programs: ANSYS vs. SILO. Trans. ASABE., 53(3), 819-829,
Guaita M., Couto A., and Ayuga F., 2003. Numerical simulation of wall pressure during discharge of granular material from cylindrical silos with eccentric hoppers. Biosyst. Eng., 85(1), 101-109,
Kibar H., 2017. Patterns between wall pressures and stresses with grain moisture on cylindrical silo. Struct. Eng. Mech., 62(4), 487-496,
Kibar H. and Ozturk T., 2014. The evaluation with ANSYS of stresses in hazelnut silos using Eurocode 1. Struct. Eng. Mech., 51(1), 15-37,
Keiter T.W.R. and Rombach G.A., 2001. Numerical aspects of FE simulations of granular flow in silos. J. Eng. Mech., 127(10), 1044-1050,
Kumar R., Patel C.M., Jana A.K., and Gopireddy S.R., 2018. Prediction of hopper discharge rate using combined discrete element method and artificial neural network. Adv. Powder Technol., 29(11), 2822-2834,
Matchett A.J., O’Neill J.A., and Shaw P., 2009. Stresses in bulk solids in wedge hoppers: A flexible formulation of the co-ordinate specific, Lame-Maxwell equations for circular arc, principal stress systems. Powder Technol., 194 (3), 166-180,
Michalowski R.L., 1983. Approximate theory of loads in plane asymmetrical converging hoppers. Powder Technol., 36(1), 5-11,
Molenda M., Montross M.D., Thompson S.A., and Horabik J., 2009. Asymmetry of model bin wall loads and lateral pressure induced from two- and three-dimensional obstructions attached to the wall. Trans. ASABE., 52(1), 225-233,
Moya M., Aguado P.J., and Ayuga F., 2013. Mechanical properties of some granular agricultural materials used in silo design. Int. Agrophys., 27(2), 181-193,
Moya M., Ayuga F., Guaita M., and Aguado P., 2002. Mechanical properties of granular agricultural materials. Trans. Am. Soc. Agric. Eng., 45(5), 1569-1577,
Munch-Andersen J., Askegaard V., and Brink A., 1992. Silo model tests with sand. Bull. Danish Build. Res. Inst. 91.
Ramírez A., Nielsen J., and Ayuga F., 2010. Pressure measurements in steel silos with eccentric hoppers. Powder Technol., 201(1), 7-20,
Rotter J.M., 2001. Guide for the economic design of circular metal silos. CRC Press, London, UK,
Rotter J.M., 2009. Silo and hopper design for strength, in: Bulk Solids Handl. Equip. Sel. Oper., Wiley,
Rotter J.M., Goodey R.J., and Brown C.J., 2019. Towards design rules for rectangular silo filling pressures. Eng. Struct., 198(1), 109547,
Vidal P., Gallego E., Guaita M., and Ayuga F., 2008. Finite element analysis under different boundary conditions of the filling of cylindrical steel silos having an eccentric hopper. J. Constr. Steel Res., 64(4), 480-492,
Vidal P., Gallego E., Guaita M., and Ayuga F., 2006a. Simulation of the filling pressures of cylindrical steel silos with concentric and eccentric hoppers using 3-dimensional finite element models. Trans. ASABE., 49(6), 1881-1895,
Vidal P., Couto A., Ayuga F., and Guaita M., 2006b. Influence of hopper eccentricity on discharge of cylindrical mass flow silos with rigid walls. J. Eng. Mech.-ASCE., 132 (9), 1026-1033,
Walker D.M., 1966. An approximate theory for pressures and arching in hoppers. Chem. Eng. Sci., 21(11), 975-997,
Wang Y., Lu Y., and Ooi J.Y., 2013. Numerical modelling of dynamic pressure and flow in hopper discharge using the Arbitrary Lagrangian-Eulerian formulation. Eng. Struct. 56(1), 1308-1320,
Xiao H., Fan Y., Jacob KV., Umbanhowar P.B., Kodam M., Koch J.F., and Lueptow R.M., 2019. Continuum modelling of granular segregation during hopper discharge. Chem. Eng. Sci., 193(1), 188-204,
Zhang Y., Jia F., Zeng Y., Han Y., and Xiao Y., 2018. DEM study in the critical height of flow mechanism transition in a conical silo. Powder Technol., 331(1), 98-106,
Zheng Q.J. and Yu A.B., 2015. Finite element investigation of the flow and stress patterns in conical hopper during discharge. Chem. Eng. Sci., 129(1), 49-57,
Zheng Q.J., Xia B.S., Pan R.H., and Yu A.B., 2017. Prediction of mass discharge rate in conical hoppers using elastoplastic model. Powder Technol., 307(1), 63-72,