Prediction of backbreak in open-pit blasting using fuzzy set theory M. Monjezi * , M. Rezaei, A. Yazdian Faculty of Engineering, Tarbiat Modares University, Tehran, Iran article info Keywords: Backbreak Regression model Fuzzy model Gol-E-Gohar iron mine abstract Although blasting is the most principal method of fragmentation in hard rock mining, the significance of the costs of blast induced rockmass damage in terms of mining efficiency and safety is becoming increas- ingly recognized. Backbreak is one of the adverse phenomena in blasting operations that causes the insta- bility of mine walls, falling down of equipments, improper fragmentation, reduced efficiency of drilling, etc., and consequently increases the total cost of a mining operation. In this paper, predictive models based on fuzzy set theory and multivariable regression have been developed for predicting backbreak in Gol-E-Gohar iron mine of Iran. To evaluate performance of the employed models, the coefficient of cor- relation (R 2 ) and the root mean square error (RMSE) indices were calculated. It was concluded that per- formance of the fuzzy model is considerably better than regression model. For the fuzzy and regression models, R 2 and RMSE were equal to 95.43% and 0.44 and 34.08% and 1.63, respectively. The fuzzy model sensitivity analysis shows that the most effective parameters on backbreak phenomenon are stemming length, hole depth, burden and hole spacing. Application of this model in the Gol-E-Gohar iron mine con- siderably minimized backbreak and improved blasting efficiency. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction Backbreak due to blasting operation has a significant impact on slope stability. This undesirable phenomenon can be defined as limit of damaged rocks beyond the last row of production holes (Ji- meno, Jimeno, & Carcedo, 1995). Bauer (1982) noted that, if back- break is not controlled, a decrease in the overall pit-slope angle would definitely be necessary which in turn cause increasing of stripping ratio. Greater amounts of loose face rock would be pro- duced and planned safety berms would be less effective. Because of destructive consequences of backbreak there would be a considerable increase in the total production costs (Scoble, Lizotte, Paventi, & Mohanty, 1997). In order to identify parameters that may influence the intensity of backbreak, many studies have been performed by various researchers (Jenkins, 1981; Konya & Walter, 1991; Monjezi & Deh- ghani, 2008). Konya (2003) believes that backbreak increases when burden and/or stemming increases. Gate, Ortiz, and Florez (2005) thinks that the main reason of backbreak is insufficient delay tim- ing and/or increasing number of blasting rows. To avoid backbreak, different parameters such as physico- mechanical properties of rockmass, explosives properties and geo- metrical features of the blasting pattern should be considered. In the past, empirical models were developed for the blast design aiming to arrive at necessary requirements such as proper fragmentation, decreasing backbreak, suitable muck pile profile, reducing boulders, etc. However, in such models there is no a straightforward way of predicting backbreak. Also, in the empirical models only some of the effective parameters of blasting operation are accounted for. Considering the above shortcomings of available empirical methods, new solution of fuzzy set theory, a branch of artificial intelligence, may suitably cover all the requirements of predicting backbreak. Fuzzy model can cope with the complexity of complicated and ill-defined systems in a flexible and reliable way (Iphar & Goktan, 2006). In the last two decades, an increase of implementation of this technique has been observed in the field of mining sciences. Chuang (1995) proposed a fuzzy model bridging the discrepancy between the values of in situ shear strengths of soils and labora- tory test results. Similarly, Habibagahi and Katebi (1996) employed this method to develop a rockmass classification maintaining Bie- niawski classification principles. A same attempt was made by Nguyen and Ashworth (1985) keeping the structure of CSIR classi- fication. Mishnaevsky and Schmauder (1996) showed that fuzzy set theory could efficiently be applied to examine the damage evo- lution in heterogeneous rocks. Cebesoy (1997) and Bascetin (1999) used fuzzy technique for the selection of surface mine equipments. Jiang, Park, Deb, and Sanford (1997) applied this approach to char- acterize roof conditions in longwall mining. A fuzzy reasoning sys- tem was developed by Huang and Siller (1997) for geotechnical site characterization of the subsurface conditions. Grima and Babuska (1999) showed superiority of fuzzy concept over multivariable regression analysis in predicting Uniaxial Compressive Strength 0957-4174/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2009.08.014 * Corresponding author. Tel.: +98 2182884312. E-mail address: monjezi@modares.ac.ir (M. Monjezi). Expert Systems with Applications 37 (2010) 2637–2643 Contents lists available at ScienceDirect Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa