Gipronickel Institute, Saint-Petersburg, Russia:

A. V. Yavarov, Leading Researcher at Geotechnique Laboratory, Candidate of Engineering Sciences
A. E. Rumyantsev, Chief Specialist at Geotechnique Laboratory, Candidate of Engineering Sciences, rumyantsevae@nornik.ru

Geodynamic Safety Center, Norilsk Nickel’s Polar Division, Norilsk, Russia:

M. P. Sergunin, Head of Department for Engineering Supervision of Mining

Polar Construction Company, Norilsk, Russia:
A. V. Bylkov, CEO

A critical safety factor of ore pass walls is the correct evaluation of rock flow pressure on the walls at the design stage. This study uses the discrete element method to determine load of rock flow on the ore pass walls. This method is the most effective in modeling ore flow through a trapdoor. On the other hand, modeling of each discrete particle can create an illusion that the model automatically takes into account all typical phenomena of granular medium. From this point of view, the method of discrete elements can be discredited in practice. Therefore, it is necessary to describe the methodology of constructing and correcting the discrete element and finite element models of ore passes. At the first stage, the grain size distribution of rock flow is analyzed, and the representative sample volume is determined. At the second stage, the shear tests are performed at the particle–particle and particle–ore pass wall contacts. It is required to implement both tests as the difference between internal and external friction angles can be assumed to be the cause of bridging (a silo phenomenon). At the third stage, due to essentially different kinematics of shearing andconical pile formation, the calibration criterion is chosen to be the angle of repose. The fourth stage is the bridging modeling and comparison of the model data with the analytical results. This stage is only limited to the numerical modeling as there are yet no fully developed techniques to reconstruct bridging in ore passes on a laboratory scale. At the fifth stage, the numerical experiments on filling an ore pass and on ore outflow from it are carried out. The results are transferred to a finite element method program.

1. Janssen H. Versuche über Getreidedruck in Silozellen. Zeitschrift des Vereines Deutscher Ingenieure. 1895. Vol. 39. pp. 1045–1049.
2. Sokolovskiy V. V. Statics of granular medium. 3^rd enlarged and revised edition. Moscow : Fizmatlit, 1960. 239 p.
3. Zenkov R. L. Mechanics of bulkloads. 2^nd enlarged and revised edition. Moscow : Mashinostroenie, 1964. 251 p.
4. Kleyn G. K. Construction mechanics of granular bodies. 2^nd enlarged and revised edition. Moscow : Stroyizdat, 1977. 256 p.
5. Geniev G. A., Estrin M. I. Dynamics of plastic and granular media. Moscow : Stroyizdat, 1972. 216 p.
6. Dikteruk M. G., Kravchuk V. T., Zasluzennyi A. S., Chovnyuk Yu. V. Investigation of free-flowing bulk material’s movement laws at vertical vessels (silos/hoppers): monitoring of static stress state and analysis of efflux by the second form at the general definition of a problem. Vestnik Khersonskogo natsionalnogo tekhnicheskogo universiteta. 2018. No. 3(66). pp. 55–73.
7. Ooi J. Y., Chen J. F., Lohnest R. A., Rotter J. M. Prediction of static wall pressures in coal silos. Construction and Building Maferials. 1996. Vol. 10, Iss. 2. pp. 109–116.
8. Rotter J. M., Holst J. M. F. G., Ooi J. Y., Sanad A. M. Silo pressure predictions using discrete–element and finite–element analyses. Philosophical Transactions of the Royal Society A. Mathematical, Physical and Engineering Sciences. 1998. Vol. 356, Iss. 1747. pp. 2685–2712.
9. Gallego E., Goodey R. J., Ayuga F., Brown C. J. Some Practical Features in Modelling Silos with Finite Elements : Presentation. 2004 ASAE/CSAE Annual International Meeting. Ontario, 2004.
10. Artoni R., Santomaso A., Canu P. Simulation of dense granular flows: Dynamics of wall stress in silos. Chemical Engineering Science. 2009. Vol. 64, Iss. 18. pp. 4040–4050.
11. Widisinghe S., Sivakugan N. Vertical Stresses within Granular Materials in Silos. Proceedings of the 11^th Australia-New Zealand Conference on Geomechanics. Melbourne, 2012. pp. 590–595.
12. Cundall P. A. A computer model for simulating progressive, large-scale movements in blocky rock system. Proceedings of the International Symposium on Rock Mechanics. Nancy, 1971. pp. 129–136.
13. Cundall P. A., Strack O. D. L. A discrete numerical model for granular assemblies. Géotechnique. 1979. Vol. 29, Iss. 1. pp. 47–65.
14. Landry J. W., Grest G. S., Plimpton S. J. Discrete element simulations of stress distributions in silos: crossover from two to three dimensions. Powder Technology. 2004. Vol. 139. pp. 233–239.
15. Hadjigeorgiou J., Lessard J. F. Numerical investigations of ore pass hang-up phenomena. International Journal of Rock Mechanics and Mining Sciences. 2007. Vol. 44, Iss. 6. pp. 820–834.
16. Feoktistov A. Yu., Kamenetskiy A. A., Blekhman L. I., Vasilkov V. B., Skryabin I. N. et al. The application of discrete element method to mining and metallurgy process modeling. Journal of Mining Institute. 2011. Vol. 192. pp. 145–149.
17. Lanis A. L., Han G. N. Modification of geoenvironment model for solving the problem of soil mechanics by discrete element method. Vestnik of Tomsk State University of Architecture and Building. 2013. No. 1. pp. 273–281.
18. Klishin S. V., Revuzhenko A. F. 3D discrete element approach to Janssen’s problem. Journal of Mining Science. 2014. Vol. 50, Iss. 3. pp. 417–422.
19. Goda T. J., Ebert F. Three-dimensional discrete element simulations in hoppers and silos. Powder Technology. 2005. Vol. 158(1-3). pp. 58–68.
20. Klishin S. V., Kosykh V. P., Revuzhenko A. F. Experimental and theoretical research of deformation localizations in granular medium. Naukoemkie tekhnologii razrabotki i ispolzovaniya mineralnykh resursov. 2019. No. 5. pp. 268–272.
21. Kokoev S. G., Yusupov G. A., Feoktistov A. Yu., Trofimov A. V., Rumyantsev A. E. et al. Substantiation of the main ore pass parameters based on discrete-element modeling. GIAB. 2019. Special issue 37. Digital technologies in mining. pp. 158–167.
22. Laptev V. V. Numerical modelling of fragmented mined rock flow during ore drawing using the ROCKY DEM programme. Vestnik MGTU. Trudy Murmanskogo gosudarstvennogo tekhnicheskogo universiteta. 2019. Vol. 22, No. 1. pp. 149–157.
23. Marcinowski J. Effect on horizontal pressure in steel silos evoked by a sudden change in the ambient temperature. Heliyon. 2019. Vol. 5, Iss. 5. e01611. DOI: 10.1016/j.heliyon.2019.e01611
24. Sato A., Tang H. Analysis of Ore Pass Hang-Ups in Long Vertical Ore Passes by 3-D DEM. International Journal of Mining Engineering and Mineral Processing. 2020. Vol. 9, No. 1. pp. 1–11.
25. Klishin S. V. Discrete-Element Modeling of Strain Localization in Granular Medium at Passive Pressure Application to a Retaining Wall. Journal of Mining Science. 2021. Vol. 57, Iss. 5. pp. 740–748.
26. Gudehus G., Tejchman J. Some Mechanisms of a Granular Mass in a Silo – Model Tests and a Numerical Cosserat Approach. Advances in Continuum Mechanics. Berlin : Springer, 1991. pp. 178–193.
27. Shashenko A. N., Pustovoytenko V. P., Sdvizhkova E. A. Geomechanics : Textbook. Kiev, 2015. 560 p.
28. Derakhshani S. M., Schott D. L., Lodewijks G. Micro–macro properties of quartz sand: Experimental investigation and DEM simulation. Powder Technology. 2015. Vol. 269. pp. 127–138.
29. Yanjie Li, Yong Xu, Thornton C. A comparison of discrete element simulations and experiments for ‘sandpiles’ composed of spherical particles. Powder Technology. 2005. Vol. 160, Iss. 3. pp. 219–228.
30. Coetzee C. J. Review: Calibration of the discrete element method. Powder Technology. 2017. Vol. 310. pp. 104–142.
31. Grabowski A., Nitka M., Tejchman J. Comparative 3D DEM simulations of sand–structure interfaces with similarly shaped clumps versus spheres with contact moments. Acta Geotechnica. 2021. Vol. 16, Iss. 11. pp. 3533–3554.
32. Li С., Yin H., Wu C., Zhang Y., Zhang J. et al. Calibration of the Discrete Element Method and Modeling of Shortening Experiments. Frontiers in Earth Science. 2021. Vol. 9. 636512. DOI: 10.3389/feart.2021.636512
33. Cornforth D. H. Some experiments on the influence of strain conditions on the strength of sand. Géotechnique. 1964. Vol. 14, Iss. 2. pp. 143–167.
34. Zhou Y. C., Xu B. H., Yu A. B., Zulli P. An experimental and numerical study of the angle of repose of coarse spheres. Powder Technology. 2002. Vol. 125, Iss. 1. pp. 45–54.
35. Castro R. L., Fuenzalida M. A., Lund F. Experimental study of gravity flow under confined conditions. International Journal of Rock Mechanics and Mining Sciences. 2014. Vol. 67. pp. 164–169.
36. Ahmadi A., Hosseininia E. S. An Experimental Investigation on the Generation of a Stable Arch in Granular Materials Using a Developed Trapdoor Apparatus. Powders & Grains 2017 : 8^th International Conference on Micromechanics on Granular Media. 2017. EPJ Web of Conferences. 2017. Vol. 140. 10002. DOI: 10.1051/epjconf/201714010002