Evaluation of the Kuz-Ram Model and Its Extensions for Predicting Fragmentation Size Distribution from Blasting: Case Study of the Diack Basalt Quarry (Senegal)

Lamine BAR^1, , Déthié SARR¹, Hamed FALL¹ and Makhtar SOW¹

¹Geotechnical Department, L2M, UFR of Engineering Sciences, Iba Der Thiam University, Thies-Senegal

Cite this paper:
Lamine BAR, Déthié SARR, Hamed FALL and Makhtar SOW. Evaluation of the Kuz-Ram Model and Its Extensions for Predicting Fragmentation Size Distribution from Blasting: Case Study of the Diack Basalt Quarry (Senegal). American Journal of Mining and Metallurgy. 2026; 9(1):7-14. doi: 10.12691/ajmm-9-1-2

Abstract

This study evaluates the predictive performance of the Kuz-Ram model and its extensions (Shifted Kuz-Ram and Extended Kuz-Ram) for blast-induced fragmentation in a hard rock geological context: the Diack basalt quarry in Senegal. Particle size distributions were obtained through WipFrag® image analysis and compared to model predictions. The results show that the original Kuz-Ram model (1987) reproduces the general trend with an R² of 0.91 but underestimates the midsize range. The introduction of the shifting factor (Shifted Kuz-Ram) significantly improves the fit (R² = 0.96). The Extended Kuz-Ram model by Cunningham (2005), after calibration of the C(A) and C(n) coefficients, offers the best performance with an R² of 0.995 and an RMSE of 2.76%, demonstrating the importance of local adaptation of empirical parameters. This study contributes to optimizing blast design in basaltic environments and highlights the necessity of calibrating models with field data.

Keywords:
Blast fragmentation Kuz-Ram model Extended Kuz-Ram Diack quarry WipFrag® image analysis

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References:

[1]	Kinyua, E. M., Jianhua, Z., Kasomo, R. M., Mauti, D., & Mwangangi, J. (2022). A review of the influence of blast fragmentation on downstream processing of metal ores. Minerals Engineering, *186*.
[2]	Zhang, Z. X., Sanchidrián, J. A., Ouchterlony, F., & Luukkanen, S. (2023). Reduction of Fragment Size from Mining to Mineral Processing: A Review. Rock Mechanics and Rock Engineering, *56*(1), 747–778.
[3]	Mutinda, E. K., Alunda, B. O., Ondicho, I. O., & Agyekum, E. (2025). Prediction and measurement of blast induced rock fragmentation − A case study of Kajiado County quarries, Kenya. Journal of the Southern African Institute of Mining and Metallurgy, *125*(2), 113–120.
[4]	Kuznetsov, V. M. (1973). The mean diameter of the fragments formed by blasting rock. Soviet Mining Science, *9*(2), 144–148.
[5]	Rosin, P., & Rammler, E. (1933). The Laws Governing the Fineness of powdered coal. Journal of the Institute of Fuel, *7*, 29–36. https:// www.scirp.org/ reference/ ReferencesPapers? ReferenceID=2167099.
[6]	Cunningham, C. V. B. (1983). The Kuz-Ram Model for Prediction of Fragmentation from Blasting. In R. Holmberg & A. Rustan (Eds.), First International Symposium on Rock Fragmentation by Blasting (pp. 439–453). Luleå University of Technology. https://www.scirp.org/reference/referencespapers?referenceid=2271764.
[7]	Cunningham, C. V. B. (1987). Fragmentation Estimations and the Kuz-Ram Model---Four Years on. In W. L. Fourney & R. D. Dick (Eds.), Second International Symposium on Rock Fragmentation by Blasting (pp. 475–487). https:// www.scirp.org/ reference/ referencespapers? referenceid=2271765.
[8]	Spathis, A. T. (2004). A correction relating to the analysis of the original Kuz-Ram model. Fragblast, *8*(4), 201–205.
[9]	Ouchterlony, F. (2005). The Swebrec© function: Linking fragmentation by blasting and crushing. Institution of Mining and Metallurgy. Transactions. Section A: Mining Technology, *114*(1).
[10]	Cunningham, C.V.B. (2005) The Kuz-Ram Fragmentation Model—20 Years on. Brighton Conference Proceedings, European Federation of Explosives Engineers, Brighton, 13-16 September 2005, 201-210.
[11]	Dia, A. (1982). Contribution à l'étude des caractéristiques pétrographiques, pétrochimiques et géotechniques des granulats basaltiques : de la presqu'île du Cap-Vert et du Plateau de Thiès.
[12]	Bar, L., Sarr, D., A. Sall, O., & Gueye, E. H. M. (2025). Blasting Analysis on the Basalt of Diack (Senegal) Using the Langefors-Kihlstrom Theory. International Journal of Research and Review, *12*(4), 143–152.
[13]	Amin, I., & Salman, S. (2022). Fragmentation Analysis of Blasted Rock using WipFrag Image Analysis Software. Journal of Mines, Metals and Fuels, 263–267.
[14]	Maerz, N. H., Palangio, T. C., & Franklin, J. A. (1996). WipFrag image based granulometry system. Measurement of Blast Fragmentation, 91–99.
[15]	Nanda, S., & Naik, H. K. (2023). A Review of the Blast Fragmentation Analysis Techniques used in Surface Mines. Journal of Mines, Metals and Fuels, 2445–2454.
[16]	Lilly, P. A. (1986). EMPIRICAL METHOD OF ASSESSING ROCK MASS BLASTABILITY. Symposia Series - Australasian Institute of Mining and Metallurgy, 89–92.
[17]	Olofsson, S. O. (1991). Applied explosives technology for construction and mining. 304.
[18]	Ouchterlony, F., & Sanchidrián, J. A. (2019). A review of development of better prediction equations for blast fragmentation. Journal of Rock Mechanics and Geotechnical Engineering, *11*(5), 1094–1109.
[19]	Saldana, M., Gallegos, S., Arias, D., Salazar, I., Castillo, J., Salinas-Rodríguez, E., Navarra, A., Toro, N., & Cisternas, L. A. (2024). Applications of Kuz--Ram Models in Mine-to-Mill Integration and Optimization---A Review. Minerals, *14*(11).
[20]	Marinin, M. A., Afanasyev, P. I., Sushkova, V. I., Ustimenko, K. D., & Akhmetov, A. R. (2023). The experience of using the Kuz-Ram model in describing of grain size distribution of blasted rock mass. Mining Informational and Analytical Bulletin, (91), 96–109.