Development of new comprehensive relations to assess rock fragmentation by blasting for different open pit mines using GEP algorithm and MLR procedure

Document Type : Research Paper

Authors

1 Department of Mining Engineering, Faculty of Engineering, University of Urmia, Urmia, Iran.

2 Department of Mining Engineering, Faculty of Engineering, University of Kurdistan, Sanandaj, Iran.

Abstract

The fragment size of blasted rocks considerably affects the mining costs and production efficiency. The larger amount of blasthole diameter (ϕh) indicates the larger blasting pattern parameters, such as spacing (S), burden (B), stemming (St), charge length (Le), bench height (K), and the larger the fragment size.  In this study, the influence of blasthole diameter, blastability index (BI), and powder factor (q) on the fragment size were investigated. First, the relation between each of X20, X50, and X80 with BI, ϕh, and q as the main critical parameters were analyzed by Table curve v.5.0 software to find better input variables with linear and nonlinear forms. Then, the results were analyzed by multivariable linear regression (MLR) procedure using SPSS v.25 software and gene expression programming (GEP) algorithm for prepared datasets of four open-pit mines in Iran. Relations between each of X20, X50, and X80 with the combination of adjusted BI, ϕh, and q were obtained by MLR procedure with good correlations of determination (R2) and less root mean square error (RMSE) values of (0.811, 1.4 cm), (0.874, 2.5 cm) and (0.832, 5.4 cm) respectively. Moreover, new models were developed to predict X20, X50, and X80 by the GEP algorithm with better correlations of R2 and RMSE values (0.860, 1.3 cm), (0.913, 2.49 cm), and (0.885, 5.6 cm) respectively and good agreement with actual field results. The developed GEP models can be used as new relations to estimate the fragment sizes of blasted rocks.

Keywords

Main Subjects


[1] Jimeno, C.L., Jimeno, E.L. & Carcedo, F.J.A. (1995). Drilling and Blasting of Rocks. A.A.Balkema, Rotterdam.
[2] An, H.M., Liu, H.Y., Han, H., Zheng, X. &Wang, X. (2017). Hybrid finite-discrete element modelling of dynamic fracture and resultant fragment casting and muck-piling by rock blast. Computers and Geotechnics, 81,322-345. https://doi.org/
10.1016/j.compgeo.2016.09.007.
[3] Sastry, V.R. (2016). Rock blasting technology: The way forward. Proceedings of the conference on Recent Advances in Rock Engineering (RARE 2016), 606 – 611. https://doi.org/10.2991/
rare-16.2016.97.
[4] Faradonbeh, R. S., Armaghani, D. J., Amnieh, H. B., & Mohamad, E. T. (2018). Prediction and minimization of blast-induced flyrock using gene expression programming and firefly algorithm. Neural Computing and Applications, 29(6), 269-281.
[5] Monjezi, M., Dehghani, H., Shakeri, J., & Mehrdanesh, A. (2021). Optimization of prediction of flyrock using linear multivariate regression (LMR) and gene expression programming (GEP)—Topal Novin mine, Iran. Arabian Journal of Geosciences, 14(15), 1-12.
[6] Faradonbeh, R.S. & Monjezi, M. (2017). Prediction and minimization of blast-induced ground vibration using two robust meta-heuristic algorithms. Engineering with Computers. 33, 835–851. https://doi.org/10.1007/s00366-017-0501-6.
[7] Hasanipanah, M., Faradonbeh, R.S., Amnieh, H.B. et al. (2017). Forecasting blast-induced ground vibration developing a CART model. Engineering with Computers 33, 307–316. https://doi.org/10.1007/s00366-016-0475-9
[8] Şenyur, M. G. (1998). A statistical analysis of fragmentation after single hole bench blasting. Rock Mechanics and Rock Engineering, 31(3), 181-196. https://doi.org/10.1007/s006030050018.
[9] Ozkahraman, H.T. (2006). Fragmentation assessment and design of blast pattern at Goltas Limestone Quarry, Turkey. International Journal of Rock Mechanics and Mining Sciences, 43(4), 628-633. https://doi.org/10.1016/j.ijrmms.2005.09.004.
[10] Kuznetsov, V.M. (1973). The mean diameter of the fragments formed by blasting rock. Journal of Mining Science, 9,144–148.
[11] Cunningham, C.V.B. (1983). The Kuz-Ram Model for Prediction of Fragmentation from Blasting. In: First International Symposium on Rock Fragmentation by Blasting, Luleå University of Technology, Lulea 2:439-453.
[12] Nourian, A. & Moomivand, H. (2020). Development of a new model to predict uniformity index of fragment size distribution based on the blasthole parameters and blastability index, Journal of Mining Science, 56(1),47–58. https://doi.org/ 10.1134/S1062739120016478.
[13] Monjezi, M., Amini khoshalan, H. & Yazdian, A. (2011). Optimization of Blast Parameters Using Genetic Algorithms. International Journal of Rock Mechanics and Mining Sciences, 48,864–869. https://doi.org/10.1007/s12517-010-0185-3.
[14] Mojtahedi, S.F.F., Ebtehaj, I., Hasanipanah, M., et al. (2019). Proposing a novel hybrid intelligent model for the simulation of particle size distribution resulting from blasting. Engineering with Computers, 35,47–56. https://doi.org/ 10.1007/s00366-018-0582-x.
[15] Zhang., S., Bui, X. N., Trung, N.T., Nguyen, H. & Bui, H.B. (2020). Prediction of rock size distribution in mine bench blasting using a novel ant colony optimization-based boosted regression tree technique. Natural Resources Research, 29(2), 867-886. https://doi.org/10.1007/s11053-019-09603-4.
[16] Akyildiz, O. & Hudaverdi, T. (2020). ANFIS modelling for blast fragmentation and blast-induced vibrations considering stiffness ratio. Arabian Journal of Geoscience, 13,1162. https://doi.org/10.1007/s12517-020-06189-7.
[17] Faramarzi, F., Mansouri, H. & Ebrahimi Farsangi, M.A. (2013). A Rock Engineering systems-based model to predict rock fragmentation by blasting. International Journal of Rock Mechanics and Mining Sciences, 60, 82–94. https://doi.org/10.1016/j.ijrmms.2012.12.045.
[18] Azadmehr, A., Jalali, S.M.E. & Pourrahimian, Y. (2019). An application of rock engineering system for assessment of the rock mass fragmentation: A hybrid approach and case study. Rock Mechanics and Rock Engineering, 52, 4403–4419. https://doi.org/10.1007/s00603-019-01848-y.
[19] Kulatilake, P.H.S.W., Qiong, W., Hudaverd, T. & Kuzu, C. (2010). Median particle size prediction in rock blast fragmentation using neural networks. Engineering Geology, 114:298–311.
[20] Moomivand, H. & Vandyousefi, H. (2020). Development of a new empirical fragmentation model using rock mass properties, blasthole parameters, and powder factor. Arabian Journal of Geoscience, 13, 1173. https://doi.org/10.1007/s12517- 20-06110-2.
[21] Monjezi, M., Amiri H., Farrokhi, A. & Goshtasbi, K. (2010). Prediction of rock fragmentation due to blasting in Sarcheshmeh copper mine using artificial neural networks. Geotechnical and Geological Engineering, 28(4), 423-430. https://doi.org/10.1007/s10706-010-9302-z.
[22] Amini, H., Gholami, R., Monjezi, M., Torabi, S.R. & Zadhesh, J. (2011). Evaluation of flyrock phenomenon due to blasting operation by Support Vector Machine. Neural Computing and Applications, 21, 2077-2085. https://doi.org/10.1007/S00521-011-0631-5.
[23] Karami A. & Afiuni-Zadeh, S. (2013). Sizing of rock fragmentation modeling due to bench blasting using adaptive neuro-fuzzy inference system (ANFIS). International Journal of Mining Science and Technology, 23 (6), 809-813. https://doi.org/10.1016/ j.ijmst. 2013.10.005.
[24] Monjezi, M., Mohamadi, H.A., Barati, B. & Khandelwal, M. (2014). Application of soft computing in predicting rock fragmentation to reduce environmental blasting side effects. Arabian Journal of Geoscience, 7(2), 505-511. https://doi.org/10.1007/s12517-012-0770-8.
[25] Shams, S., Monjezi, M., Majd, V.J., et al. (2015). Application of fuzzy inference system for prediction of rock fragmentation induced by blasting. Arabian Journal of Geosciences, 8,10819–10832.  https://doi.org/10.1007/s12517-015-1952-y.
[26] Gao, W., Karbasi, M., Hasanipanah, M. & Zhang Guo, J. (2018). Developing GPR model for forecasting the rock fragmentation in surface mines. Engineering with Computers, 34(2), 339-345.
[27] Mehrdanesh, A., Monjezi, M. & Sayadi, A.R. (2018). Evaluation of effect of rock mass properties on fragmentation using robust techniques. Engineering with Computers, 253–260.
[28] Hasanipanah, M., Amnieh, H.B., Arab, H. & Zamzam, M.S. (2018). Feasibility of PSO–ANFIS model to estimate rock fragmentation produced by mine blasting. Neural Computing and Applications, 30(4), 1015-1024. https://doi.org/ 10.1007/s00521-016-2746-1.
[29] Fang, Q., Nguyen, H., Bui, X.N., Nguyen-Thoi, T. & Zhou, J. (2021). Modeling of rock fragmentation by firefly optimization algorithm and boosted generalized additive model. Neural Computing and Applications, 33, 3503–3519.
[30] Shirani Faradonbeh, R., Taheri, A. & Karakus, M. (2022). The propensity of the over-stressed rock masses to different failure mechanisms based on a hybrid probabilistic approach, Tunnelling and Underground Space Technology, 119,  https:
//doi.org/10.1016/j.tust.2021.104214.
[31] Shirani Faradonbeh, R., Shaffiee Haghshenas, S., Taheri, A. et al. Application of self-organizing map and fuzzy c-mean techniques for rockburst clustering in deep underground projects. Neural Comput & Applic 32, 8545–8559 (2020). https://doi.org/10.1007/s00521-019-04353-z
[32] Shakeri, J., Amini Khoshalan, H., Dehghani, H., Onyelowe, K., Bascompta, M. (2022). Developing new models for flyrock distance assessment in open-pit mines. Journal of Mining and Environment, -. doi: 10.22044/jme.2022.11805.2170
[33] Shirani Faradonbeh, R., Taheri, A., Ribeiro e Sousa, L. & Karakus, M. (2020). Rockburst assessment in deep geotechnical conditions using true-triaxial tests and data-driven approaches, International Journal of Rock Mechanics and Mining Sciences,128: 104279, https://doi.org/10.1016/j.ijrmms.2020.104
279.
[34] Shaffiee Haghshenas, S., Shirani Faradonbeh, R., Mikaeil, R., et al. (2019). A new conventional criterion for the performance evaluation of gang saw machines, Measurement, 146: 159-170, https://doi.org/10.1016/j.measurement.2019.06.031.
[35] Shirani Faradonbeh, R., Taheri, A. & Karakus, M. (2022). Fatigue Failure Characteristics of Sandstone Under Different Confining Pressures. Rock Mechanics Rock Engineering, 55, 1227–1252 https://doi.org/10.1007/s00603-021-02726-2
[36] Monjezi, M., Rezaei, M. & Yazdian Varjani, A. (2009). Prediction of Rock Fragmentation due to Blasting in Gol-E-Gohar Iron Mine Using Fuzzy Logic. International Journal of Rock Mechanics and Mining Sciences, 46 (8), 1273–1280. https://doi.org/10.1016/j.ijrmms.2009.05.005.
[37] Ebrahimi, E., Monjezi, M., Khalesi, M.R. & Jahed Armaghani, D. (2016). Prediction and optimization of back-break and rock fragmentation using an artificial neural network and a bee colony algorithm. Bulletin of Engineering Geology and the Environment, 75(1), 27-36.
[38] Faraji Asl, P., Monjezi, M., Hamidi, J.K. et al. (2018). Optimization of flyrock and rock fragmentation in the Tajareh limestone mine using metaheuristics method of firefly algorithm. Engineering with Computers, 34, 241–251. https://doi.org/10.1007/s00366-017-0535-9.
[39] Huang, J., Asteris, P.G., Pasha, S.M.K., Mohammed, A.S. & Hasanipanah, M. (2020). A new auto-tuning model for predicting the rock fragmentation: a cat swarm optimization algorithm. Engineering with Computers. https://doi.org/10.1007/
s00366-020-01207-4.
[40] Montgomery, D.C. & Peck, E.A. (1992). Introduction to Linear Regression Analysis. Wiley, New York, USA.
[41] Shakeri, J., Shokri, B.J. & Dehghani, H. (2020). Prediction of blast-induced ground vibration using gene expression programming (GEP), artificial neural networks (ANNS), and linear multivariate regression (MLR). Archives of Mining Sciences, 65(2), 317-335. https://doi.org/10.24425/
ams.2020.133195.
[42]. Onyelowe, K. C., Shakeri, J., Amini-Khoshalan, H., Usungedo, T. F., & Alimoradi-Jazi, M. (2022). Computational Modeling of Desiccation Properties (CW, LS, and VS) of Waste-Based Activated Ash-Treated Black Cotton Soil for Sustainable Subgrade Using Artificial Neural Network, Gray-Wolf, and Moth-Flame Optimization Techniques. Advances in Materials Science and Engineering. doi: 10.1155/2022/4602064.
[43] Rosin P., Rammler, E. (1933). The laws governing the fineness of powdered coal, Journal of the Institute of Fuel, 7: 29–36.
[44] Onyelowe, K. C., Shakeri, J., Amini-Khoshalann, H., Salahudeen, A. B., Arinze, E. E., & Ugwu, H. U. (2021). Application of ANFIS hybrids to predict coefficients of curvature and uniformity of treated unsaturated lateritic soil for sustainable earthworks. Cleaner Materials, 1, 100005.
[45] Abyaneh, H.Z. (2014). Evaluation of multivariate linear regression and artificial neural networks in prediction of water quality parameters. Journal of Environmental Health Science and Engineering, 12(1), 40. https://doi.org/10.1186/2052-336X-12-40.
[46] Ferreira, C. (2006). Gene expression programming: mathematical modeling by artificial intelligence. 21, Springer.
[47] Majidifard, H., Jahangiri, B., Buttlar, W.G. & Alavi, A.H. (2019). New machine learning-based prediction models for fracture energy of asphalt mixtures. Measurement, 135, 438-451. https://doi.org/10.1016/j. measurement. 2018.11.081.
[48] Mahdiyar, A., Jahed Armaghani, D., Koopialipoor, M., Hedayat, A., Abdullah, A. & Yahya, K. (2020). Practical Risk Assessment of Ground Vibrations Resulting from Blasting Using Gene Expression Programming and Monte Carlo Simulation Techniques. Applied Sciences, 10, 472.
[49] Bolandi, H., Banzhaf, W., Lajnef, N., Barri, K. & Alavi, A.H. (2019). Bond strength prediction of FRP-bar reinforced concrete: a multi-gene genetic programming approach. In Proceedings of the Genetic and Evolutionary Computation Conference Companion, 364-36.
[50] Baykasoğlu, A., Güllü, H., Çanakçi, H. & Özbakir, L., (2008). Prediction of compressive and tensile strength of limestone via genetic programming. Expert Systems with Applications, 35(1-2), 111-123. https://doi.org/10.1016/j. eswa.2007.06.006.
[51] Faradonbeh RS, Jahed Armaghani D, Monjezi M & Mohamad ET. (2016). Genetic programming and gene expression programming for flyrock assessment due to mine blasting. International Journal of Rock Mechanics and Mining Sciences, 88, 254-264. https://doi.org/10.1016/j.ijrmms.2016.07.028.
[52]. Amini Khoshalan, H., Shakeri, J., Najmoddini, I., Asadizadeh, M. (2021). Forecasting copper price by application of robust artificial intelligence techniques, Resources Policy, 73, 102239.
[53]. Onyelowe, K. C., & Shakeri, J. (2021). Intelligent prediction of coefficients of curvature and uniformity of hybrid cement modified unsaturated soil with NQF inclusion. Cleaner Engineering and Technology, 4, 100152.
[54] Ramesh, A., Hajihassani, M. & Rashiddel, A. (2020). Ground movements prediction in shield-driven tunnels using gene expression programming. Open Construction and Building Technology Journal, 14(1), 286-297. https://doi.org/10.2174/ 1874836802014010286.
[55] Mollahasani, A., Alavi, A.H. & Gandomi, A.H. (2011). Empirical modeling of plate load test moduli of soil via gene expression programming. Computers and Geotechnics, 38(2), 281-286. https://doi.org/10.1016/j. compgeo. 2010. 11 .008.
[56] Dindarloo, S.R, Prediction of blast-induced ground vibrations via genetic programming. International Journal of Mining Science and Technology, 2015, 25(6), 1011-1015. https://doi.org/10.1016/j.ijmst.2015.09.020.
[57] Jahed Armaghani, D., Safari, V., Fahimifar, A., Monjezi, M. & Mohammadi., M.A. (2018). Uniaxial compressive strength prediction through a new technique based on gene expression programming. Neural Computing and Applications, 30(11), 3523-3532.  https://doi.org/10.1007/s00521-017-2939-2.
[58] Ferreira, C. (2001). Gene expression programming: a new adaptive algorithm for solving problems. arxiv preprint cs/0102027.
[59] Faradonbeh, R.S., Armaghani, D.J., Monjezi, M. & Mohamad, E.T. (2016). Genetic programming and gene expression programming for flyrock assessment due to mine blasting. International Journal of Rock Mechanics and Mining Sciences, 88, 254-264. https://doi.org/10.1016/j.ijrmms.2016.07.028.
[60] Lilly, P.A. (1986). An empirical method of assessing rock mass blastability. In:   Proceedings of the large open-pit planning conference. Australian IMM, Parkville, Victoria,  89–92
[61] Lilly, P.A. (1992). The use of the Blastability Index in the design of blasts for open-pit mines. Western Australian Conference on Mining Geotechnics, Kalgoorlie, 421–426.
[62] Split Engineering LLC Team, (2015). Manual of split desktop image analysis software, Version 3.1. P.O. Box 41766, Tucson, AZ 85717–1766, http://www.spliteng.com.
[63] Masoumi Nasab, S.M., Jalali, S.E. & Noroozi, M. (2019). Performance comparison of commercial software tools to determine size distribution of fragmented rocks. Journal of Mineral Resources Engineering, 4(3), 61 – 65. https://doi.org/ 10.30479/ JMRE.2019.8892.1136.
[64] Azizi, A. & Moomivand, H. (2021). A New Approach to Represent Impact of Discontinuity Spacing and Rock Mass Description on the Median Fragment Size of Blasted Rocks Using Image Analysis of Rock Mass. Rock Mechanics and  Rock Engineering, 4, 1-26.  https://doi.org/10.1007/s00603-020-02360-4.
[65] Shakeri, J., Asadizadeh, M., & Babanouri, N. (2022). The prediction of dynamic energy behavior of a Brazilian disk containing nonpersistent joints subjected to drop hammer test utilizing heuristic approaches. Neural Computing and Applications, 1-16.
[66] Onyelowe, K. C., Mahesh, C. B., Srikanth, B., Nwa-David, C., Obimba-Wogu, J., & Shakeri, J. (2021). Support vector machine (SVM) prediction of coefficients of curvature and uniformity of hybrid cement modified unsaturated soil with NQF inclusion. Cleaner Engineering and Technology, 5, 100290.
[67] Yang, Y., & Zhang, Q. (1997). A hierarchical analysis for rock engineering using artificial neural networks. Rock Mechanics and Rock Engineering, 30(4), 207-222.