The experience of using the Kuz-Ram model in describing of grain size distribution of blasted rock mass

The article gives an analysis of probabilistic distributions used in mining practice, which describe the granulometric composition of the exploded rock mass. Experimental distributions of fractions of the exploded rock mass were obtained for the conditions of experimental blocks of an ore quarry using the WipFrag software product. The experimental data were compared with the predicted distributions according to the Kuz–Ram model. It is established that the parameters of the initiation of borehole charges affect the actual distribution of the granulated rock mass. Depending on the initiation scheme and deceleration ratings of the cut-in and echelon surface networks, the values of the line of least resistance and the distance between borehole charges during a mass explosion change. The analysis showed that taking into account the isochronous initiation of a mass explosion makes it possible to achieve a better agreement with the experimental grain composition distribution curves in terms of the uniformity of the distribution of pieces. A method for calibrating the Kuz–Ram model to describe the results of explosive rock destruction is proposed. The proposed approach takes into account the actual values of the line of least resistance and the distance between the borehole charges, formed taking into account the isochronous initiation (isoline simultaneity).

Keywords: blasted rock mass, grain size distribution, Kuz-Ram model, parameters of drilling and blasting operations, uniformity index, initiation pattern, blast pattern, delay interval.
For citation:

Marinin M. A., Afanasyev P. I., Sushkova V. I., Ustimenko K. D., Akhmetov A. R. The experience of using the Kuz-Ram model in describing of grain size distribution of blasted rock mass. MIAB. Mining Inf. Anal. Bull. 2023;(9-1):96-109. [In Russ]. DOI: 10.25018/0236_1493_2023_91_0_96.

Issue number: 9
Year: 2023
Page number: 96-109
ISBN: 0236-1493
UDK: 622.22
DOI: 10.25018/0236_1493_2023_91_0_96
Article receipt date: 21.07.2023
Date of review receipt: 16.08.2023
Date of the editorial board′s decision on the article′s publishing: 10.08.2023
About authors:

M.A. Marinin1, Cand. Sci. (Eng.), Assistant Professor, e-mail:, ORCID ID: 0000-0002-5575-9343,
P.I. Afanasyev1, Cand. Sci. (Eng.), Assistant Professor, e-mail:, ORCID ID: 0000-0001-5271-6121,
V.I. Sushkova1, Leading Specialist, e-mail:,
K.D. Ustimenko1, Research Student, e-mail:,
A.R. Akhmetov1, Research Student, e-mail:,
1 Saint-Petersburg Mining University, 199106, Saint-Petersburg, Russia.


For contacts:

M.A. Marinin, e-mail:


1. Marinina O. A., Kirsanova N. Y., Nevskaya M. A. Circular economy models in industry: developing a conceptual framework. Energies. 2022, vol. 15, no. 24, pp. 9376—9386. DOI: 10.3390/en15249376.

2. Fomin S. I., Ovsyannikov M. P. Substantiation of the optimal performance parameters for a quarry during the stage-wise development of steeply dipping ore deposits. Journal of Mining Institute. 2022, vol. 000, pp. 1—10. [In Russ]. DOI: 10.31897/pmi.2022.73.

3. Alenichev I. A., Rakhmanov R. A. Empirical regularities investigation of rock mass discharge by explosion on the free surface of a pit bench. Journal of Mining Institute. 2021, vol. 249, pp. 334—341. [In Russ]. DOI: 10.31897/pmi.2021.3.2.

4. Workman L., Eloranta J. The effects of blasting on crushing and grinding efficiency and energy consumption. Proceedings of the 29th Conference on Explosives and Blasting Techniques. International Society of Explosive Engineers, USA. 2003, vol. 1, pp. 131—140.

5. Yastrebova K., Moldovan D., Chernobay V. Influence of the nature of the outflow of explosion products from blast holes and boreholes on the efficiency of rock destruction. E3S Web of Conferences. 2020, vol. 174, no. 4, article 01017. DOI: 10.1051/e3sconf/202017401017.

6. Dolzhikov V. V., Ryadinsky D. E., Yakovlev A. A. Influence of deceleration intervals on the amplitudes of stress waves during the explosion of a system of borehole charges. MIAB. Mining Inf. Anal. Bull. 2022, no. 6-2, pp. 18—32. [In Russ]. DOI: 10.25018/0236_1493_2022_62_0_18.

7. Khokhlov S. V., Vinogradov Yu. I., Noskov A. P., Bazhenova A. V. Predicting displacements of ore body boundaries in generation of blasted rock pile. MIAB. Mining Inf. Anal. Bull. 2023, no. 3, pp. 40—56. [In Russ]. DOI: 10.25018/0236_1493_2023_3_0_40.

8. Rakhmanov R. A., Loeb J., Kosukhin N. I. Estimation of ore contour movements after the blast using the BMM system. Journal of Mining Institute. 2020, vol. 245, pp. 547—553. [In Russ]. DOI: 10.31897/pmi.2020.5.6

9. Zharikov I. F. Rock fragmentation adjustment in high bench blasting. Explosion technology. 2014, no. 111/68, pp. 93—100. [In Russ].

10. Isheyskiy V. A., Martinyskin E. A., Vasilyev A. S., Smirnov S. A. Data collection features of during the blast wells drilling for the formation of geostructural block models. Sustainable Development of Mountain Territories. 2021, vol. 13, no. 4(50), pp. 608—619. [In Russ]. DOI: 10.21177/1998-4502-2021-13-4-608-619.

11. Vokhmin S. A., Kurchin G. S., Shevnina E. V., Kirsanov A. K., Kostylev S. S. Granulometric composition predicting models after explosion in open-pit mining. Izvestiya vysshikh uchebnykh zavedenii. Gornyi zhurnal. 2020, no. 1, pp. 14—24. [In Russ]. DOI: 10.21440/05361028-2020-1-14-24.

12. Vinogradov Yu. I., Mikhailov V. A., Makaryev V. P., Golovin G. M., Deev E. A. The constancy of the logarithmic dispersion of the size distribution of the pieces during the destruction of rocks. Fizicheskie protsessy gornogo proizvodstva [Physical processes of mining production], Leningrad, 1976, pp. 37—41.

13. Kutepova N. A., Moseykin V. V., Kondakova V. N., Pospehov G. B., Straupnik I. A. Specificity of properties of coal processing waste regarding their storage. MIAB. Mining Inf. Anal. Bull. 2022, no. 12, pp. 77—93. [In Russ]. DOI: 10.25018/0236_1493_2022_12_0_77.

14. Smirnyakov V. V., Rodionov V. A., Smirnyakova V. V., Orlov F. A. The influence of the shape and size of dust fractions on their distribution and accumulation in mine workings when changing the structure of air flow. Journal of Mining Institute. 2022, vol. 253, pp. 71—81. [In Russ]. DOI: 10.31897/pmi.2022.12.

15. Vinogradov Yu. I., Khokhlov S. V., Bazhenova A. V., Sokolov S. T. Methodological principles of measuring granulometric composition. News of the Tula state university. Sciences of Earth. 2020, no. 3, pp. 112—123. [In Russ].

16. Baron L. I., Sirotyuk G. N. Verification of the applicability of the Rozin-Rammler equation for calculating the diameter of an average piece during explosive rock breaking. Explosion technology. 1967, no. 62/19, pp. 111—121. [In Russ].

17. Weibull W. A. A statistical distribution punetion op wide applicability. Journal Application Mechanic. 1951, vol. 18, no. 293, pp. 837—843.

18. Repin N. Ya., Biryukov A. V. On the application of the probabilistic method in th study of lumpiness of rocks. Izvestiya vysshikh uchebnykh zavedenii. Gornyi zhurnal. 1972, no. 7, pp. 11—21. [In Russ].

19. Ouchterlony F. Fragmentation characterization; the Swebrec function and its use in blast engineering. Proceedings of the 9th International Symposium on Rock Fragmentation by Blasting—Fragblast 9. Granada, Spain, 13—17 August, 2009, pp. 3—22.

20. Coello-Velázquez A. L., Arteaga V. Q., Menéndez-Aguado J. M., Pole F. M., Llorente L. Use of the swebrec function to model particle size distribution in an industrial-scale Ni-Co ore grinding circuit. Metals. 2019, vol. 9, no. 8, article 882. DOI: 10.3390/met9080882.

21. Sanchidrián J. A., Segarra P., Ouchterlony F., Gómez S. The influential role of powder factor vs. delay in full-scale blasting: a perspective through the fragment size-energy fan. Rock Mechanics and Rock Engineering. 2022, vol. 55, no. 5, pp. 4209—4236. DOI: 10.1007/ s00603022-02856-1.

22. Zamyshlyaev B. V., Evterev L. S. Modeli dinamicheskogo deformirovaniya i razrusheniya gruntovykh sred [Models of dynamic deformation and destruction of soil media], Moscow, Nauka, 1990. 215 p.

23. Couceiro P., Santos B. The influence of blasting energy factor on the loading performance. International Journal of Engineering Research & Technology. 2019, vol. 8, no. 12, pp. 731—734. DOI: 10.17577/IJERTV8IS120360.

24. Zhang Z. X., Sanchidrián A. J., Ouchterlony F., Luukkanen S. Reduction of fragment size from mining to mineral processing. A review. Rock Mechanics and Rock Engineering. 2023, vol. 56, pp. 747—778. DOI: 10.1007/s00603-022-03068-3.

25. Kolmogorov A. N. On the logarithmically normal law of particle size distribution during crushing. Doklady Akademii nauk SSSR. 1941, vol. 31, no. 2, pp. 103—106. [In Russ].

26. Rodionov V. N. On the similarity of the crushing process in ore-scale explosions.Mekhanizm razrusheniya gornykh porod vzryvom [The mechanism of destruction of rocks by explosion] Kiev, Naukova dumka, 1971, pp. 107—112.

27. Ouchterlony F., Sanchidrián J. A., Moser P. Percentile fragment size predic-tions for blasted rock and the fragmentation—energy fan. Rock Mechanics and Rock Engineering. 2017, vol. 50, no. 4, pp. 751—779. DOI: 10.1007/s00603-016-1094-x.

28. Kuznetsov V. M. Matematicheskie modeli vzryvnogo dela [Mathematical models of explosive business], Novosibirsk, Nauka, 1977, 259 p.

29. Maerz N. H., Palangio T. C., Franklin J. A. WipFrag image based granulometry system. Proceedings of the FRAGBLAST 5 Workshop on Measurement of Blast Fragmentation. Montreal, Quebec, Canada, 1996, pp. 91—99.

30. Marinin M. A., Rakhmanov R. A., Alenichev I. A., Afanasyev P. I., Sushkova V. I. Effect of grain size distribution of blasted rock on WK-35 shovel performance. MIAB. Mining Inf. Anal. Bull. 2023, no. 6, pp. 111—125. [In Russ]. DOI: 10.25018/0236_1493_2023_6_0_111.

31. Cunningham C. V. B. The Kuz-Ram model for predictionof fragmentation from blasting. Proceedings of the 1st International Symposium on Rock Fragmentation by Blasting. Lulea, Sweden, August. 1983, pp. 439—454.

32. Cunningham C. V. B. Fragmentation estimations and the Kuz-Ram model — four years on. Proceedings of the Second International Symposium on Rock Fragmentation by Blasting. Keystone, Colorado. 1987, pp. 475—478.

33. Saadoun A., Fredj M., Boukarm R., Hadji R. Fragmentation analysis using digital image processing and empirical model (KuzRam): a comparative study. Journal of Mining Institute. 2022, vol. 257, pp. 822—832. [In Russ]. DOI: 10.31897/pmi.2022.84.

34. Cunningham C. V. B. The Kuz-Ram Fragmentation Model — 20 Years on. Proceedings of the 3rd European Federation of Explosives Engineers World Conference on Explosives and Blasting. Brighton, 2005, vol. 4, pp. 201—210.

35. Rosin P., Rammler E. The laws governing the fineness of powdered coal. Journal of the Institute of Fuel. 1933, vol. 7, no. 6, pp. 29—36.

Our partners

Подписка на рассылку

Раз в месяц Вы будете получать информацию о новом номере журнала, новых книгах издательства, а также о конференциях, форумах и других профессиональных мероприятиях.