ORIGINAL PAPER Prediction and optimization of back-break and rock fragmentation using an artiﬁcial neural network and a bee colony algorithm Ebrahim Ebrahimi • Masoud Monjezi • Mohammad Reza Khalesi • Danial Jahed Armaghani Received: 12 July 2014 / Accepted: 18 January 2015 Ó Springer-Verlag Berlin Heidelberg 2015 Abstract In blasting works, the aim is to provide proper rock fragmentation and to avoid undesirable environmental impacts such as back-break. Therefore, predicting frag- mentation and back-break is a signiﬁcant step in achieving a technically and economically successful outcome. In this paper, considering the robustness of artiﬁcial intelligence methods utilized in engineering problems, an artiﬁcial neural network (ANN) was applied to predict rock frag- mentation and back-break; an artiﬁcial bee colony (ABC) algorithm was also utilized to optimize the blasting pattern parameters. In this regard, blasting parameters, including burden, spacing, stemming length, hole length and powder factor, as well as back-break and fragmentation were col- lected at the Anguran mine in Iran. Root mean square error (RMSE) values equal to 2.76 and 0.53 for rock fragmenta- tion and back-break, respectively, reveal the high reliability of the ANN model. In addition, ABC algorithm results suggest values of 29 cm and 3.25 m for fragmentation and back-break, respectively. For comparison purposes, an empirical model (Kuz-Ram) was performed to predict the mean fragment size in the Anguran mine. A mean fragment size of 33.5 cm shows the ABC algorithm can optimize rock fragmentation with a high degree of accuracy. Keywords Blasting  Rock fragmentation  Back-break  Artiﬁcial neural network  Artiﬁcial bee colony Introduction Blasting is a common rock fragmentation technique utilized in mining operations, as well as some civil engineering applications such as tunneling and road construction. In blasting operations, only 20–30 % of the produced energy is utilized to fragment and displace the rock mass (Jahed Armaghani et al. 2013; Khandelwal and Monjezi 2013). The rest of this energy is wasted to produce undesirable environmental impacts such as ground vibration, air-overpressure, ﬂyrock and back-break (Monjezi et al. 2012; Go ¨rgu ¨lu ¨ et al. 2013; Hajihassani et al. 2014a, b; Raina et al. 2014). Among these envi- ronmental impacts, back-break is the unwanted conse- quence of an unsuitable blast design (Khandelwal and Monjezi 2013). This phenomenon is deﬁned as frag- mentation of rocks beyond the limits of the rear row of holes in a blast pattern (Jimeno et al. 1995). Back-break may cause rock mine wall instability, fallings, improper fragmentation, and an increased total blasting cost (Es- maeili et al. 2012; Mohammadnejad et al. 2013). In addition, the main objective of blasting is to control the amount and quality of the rock fragmentation. The size distribution of fragmented rock plays an important role in the overall mining and processing plant economics (Michaux and Djordjevic 2005; Monjezi et al. 2009). Blast design is a signiﬁcant factor in the process of securing desired fragmentation. However, it should be mentioned E. Ebrahimi  M. Monjezi (&)  M. R. Khalesi Department of Mining, Faculty of Engineering, Tarbiat Modares University, 14115-143 Tehran, Iran e-mail: monjezi@modares.ac.ir E. Ebrahimi e-mail: e.ebrahimi18@yahoo.com M. R. Khalesi e-mail: mrkhalesi@modares.c.ir D. J. Armaghani Department of Geotechnics and Transportation, Faculty of Civil Engineering, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor, Malaysia e-mail: danialarmaghani@yahoo.com 123 Bull Eng Geol Environ DOI 10.1007/s10064-015-0720-2