Document Type : Original Research Paper


Department of Mining Engineering, Bandung Institute of Technology, Kota Bandung, Indonesia


Drillability is one of the significant issues in rock engineering. The drilling rate index (DRI) is an important tool in analyzing the drillability of rocks. Several efforts have been made by the researchers to correlate and evaluate DRI of rocks. The ensemble learning methods including the decision tree (DT), adaptive boosting (AdaBoost), and random forest (RF) are employed in this research work in order to predict DRI of rocks. A drillability database with four parameters is compiled in this work. A relationship between the input parameters and DRI is established using the simple regression analysis. In order to train the model, different mechanical properties of rocks incorporating the uniaxial compressive strength (UCS), Brazilian tensile strength (BTS), brittleness test (S20), and sievers’ J-miniature drill value (Sj) are taken as the input variables. The original DRI database is randomly divided into the training and test sets with an 80/20 sampling method. Various algorithms are developed, and consequently, several approaches are followed in order to predict DRI of the rock samples. The model performance has revealed that RF predicts DRI with a high accuracy rate. Besides, the Monte Carlo simulations exhibit that this approach is more reliable in predicting the probability distribution of DRI. Therefore, the proposed model can be practiced for the stability risk management and the investigative design of DRI.


[1]. Selmer-Olsen, R. and Lien, R. (1960). Bergartens borbarhet og sprengbarhet. Teknisk Ukeblad, 34, 3-11.
[2]. Hossain, M.E. and Al-Majed, A.A. (2015). Fundamentals of sustainable drilling engineering. John Wiley & Sons.
[3]. Eren, T. and Ozbayoglu, M.E. (2010). Real-time optimization of drilling parameters during drilling operations. In SPE oil and gas India conference and exhibition. Society of Petroleum Engineers.
[4]. Payette, G.S., Spivey, B.J., Wang, L., Bailey, J.R., Sanderson, D., Kong, R. and Eddy, A. (2017). A Real-Time Well-Site based Surveillance and Optimization Platform for Drilling: Technology, Basic Workflows and Field Results. In SPE/IADC Drilling Conference and Exhibition. Society of Petroleum Engineers.
[5]. Osgouei, R.E. (2007). Rate of Penetration Estimation Model for Directional and Horizontal Wells. Master’s Thesis, Middle East Technical University, Ankara, Turkey.
[6]. Hoseinie, S.H., Ataei, M. and Mikaeil, R. (2019). Effects of microfabric on drillability of rocks. Bulletin of Engineering Geology and the Environment. 78 (3): 1443-1449.
[7]. Soleimani, M. (2017). Well performance optimization for gas lift operation in a heterogeneous reservoir by fine zonation and different well type integration. Journal of Natural Gas Science and Engineering. 40: 277-287.
[8]. Ataei, M., KaKaie, R., Ghavidel, M. and Saeidi, O. (2015). Drilling rate prediction of an open-pit mine using the rock mass drillability index. International Journal of Rock Mechanics and Mining Sciences. 73: 130-138.
[9]. Shad, H.I.A., Sereshki, F., Ataei, M. and Karamoozian, M. (2018). Prediction of rotary drilling penetration rate in iron ore oxides using rock engineering system. International Journal of Mining Science and Technology. 28 (3): 407-413.
[10]. Hoseinie, S.H., Ataei, M. and Mikaiel, R. (2012). Comparison of some rock hardness scales applied in drillability studies. Arabian Journal for Science and Engineering. 37 (5): 1451-1458.
[11]. Kahraman, S., Balcı, C., Yazıcı, S. and Bilgin, N. (2000). Prediction of the penetration rate of rotary blast hole drills using a new drillability index. International Journal of Rock Mechanics and Mining Sciences. 37 (5): 729-743.
[12]. Altindag, R. (2002). The evaluation of rock brittleness concept on rotary blast hold drills. Journal of the Southern African Institute of Mining and Metallurgy. 102 (1): 61-66.
[13]. Bilgin, N. and Kahraman, S. (2003, June). Drillability prediction in rotary blast hole drilling. In Proc. 18th Int. Mining Congress and Exhibition of Turkey, Antalya, Turkey (pp. 177-182).
[14]. Kahraman, S., Bilgin, N. and Feridunoglu, C. (2003). Dominant rock properties affecting the penetration rate of percussive drills. International Journal of Rock Mechanics and Mining Sciences. 40 (5): 711-723.
[15]. Grima, M.A. and Babuška, R. (1999). Fuzzy model for the prediction of unconfined compressive strength of rock samples. International Journal of Rock Mechanics and Mining Sciences. 36 (3): 339-349.
[16]. Hoseinie, S.H., Ataei, M. and Osanloo, M. (2009). A new classification system for evaluating rock penetrability. International Journal of Rock Mechanics and Mining Sciences. 46 (8): 1329-1340.
[17]. Moradi, H., Bahari, M.H., Sistani, M.B.N. and Bahari, A. (2010). Drilling rate prediction using an innovative soft computing approach. Scientific Research and Essays. 5 (13): 1583-1588.
[18]. Nandi, A.K. and Davim, J.P. (2009). A study of drilling performances with minimum quantity of lubricant using fuzzy logic rules. Mechatronics. 19 (2): 218-232.
[19]. Hashmi, K., Graham, I.D. and Mills, B. (2000). Fuzzy logic-based data selection for the drilling process. Journal of Materials Processing Technology. 108 (1): 55-61.
[20]. Khandelwal, M. and Armaghani, D.J. (2016). Prediction of drillability of rocks with strength properties using a hybrid GA-ANN technique. Geotechnical and Geological Engineering. 34 (2): 605-620.
[21]. Feng, X. (1995). A neural network approach to comprehensive classification of rock stability, blastability and drillability. International Journal of Surface Mining and Reclamation. 9 (2): 57-62.
[22]. Gamal, H., Elkatatny, S. and Abdulraheem, A. (2020, November). Rock Drillability Intelligent Prediction for a Complex Lithology Using Artificial Neural Network. In Abu Dhabi International Petroleum Exhibition & Conference. Society of Petroleum Engineers.
[23]. Fattahi, H. and Bazdar, H. (2017). Applying improved artificial neural network models to evaluate drilling rate index. Tunneling and Underground Space Technology. 70: 114-124.
[24]. Wang, L.N. and Feng, X.T. (1993, January). Comprehensive Classification Iof Rock Stability, Blastability and Drillability based on Neural Networks. In The 34th US Symposium on Rock Mechanics (USRMS). American Rock Mechanics Association.
[25]. Gan, C., Cao, W., Wu, M., Chen, X., Lu, C., Hu, Y. and Wen, G. (2016). Intelligent Nadaboost-ELM modeling method for formation drillability using well logging data. Journal of Advanced Computational Intelligence and Intelligent Informatics. 20 (7): 1103-1111.
[26]. Gan, C., Cao, W., Wu, M., Chen, X., Hu, Y., Wen, G. and Ding, H. (2017). An online modeling method for formation drillability based on OS-Nadaboost-ELM algorithm in deep drilling process. IFAC-PapersOnLine. 50 (1): 12886-12891.
[27]. Tewari, S., Dwivedi, U.D. and Biswas, S. (2021). A Novel Application of Ensemble Methods with Data Resampling Techniques for Drill Bit Selection in the Oil and Gas Industry. Energies. 14 (2): 432.
[28]. Li, S., Zhang, J., Wu, S., Chen, W., Chen, D., Li, X. and Wang, H. (2019, September). Prediction of Rate of Penetration based on Random Forest in Deep Well. In International Conference on Inforatmion technology in Geo-Engineering. (pp. 517-526). Springer, Cham.
[29]. Mikaeil, R., Haghshenas, S.S. and Hoseinie, S.H. (2018). Rock penetrability classification using artificial bee colony (ABC) algorithm and self-organizing map. Geotechnical and Geological Engineering. 36 (2): 1309-1318.
[30]. Basarir, H., Tutluoglu, L. and Karpuz, C. (2014). Penetration rate prediction for diamond bit drilling by adaptive neuro-fuzzy inference system and multiple regressions. Engineering Geology. 173: 1-9.
[31]. Saeidi, O., Torabi, S.R., Ataei, M. and Rostami, J. (2014). A stochastic penetration rate model for rotary drilling in surface mines. International Journal of Rock Mechanics and Mining Sciences. 68: 55-65.
[32]. Sagi, O. and Rokach, L. (2018). Ensemble learning: A survey. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery. 8 (4): e1249.
[33]. Kotsiantis, S.B. (2013). Decision trees: a recent overview. Artificial Intelligence Review, 39(4), 261-283.
[34]. Breiman, L. (2001). Random forests. Machine learning. 45 (1): 5-32.
[35]. Freund, Y. and Schapire, R.E. (1997). A decision-theoretic generalization of on-line learning and an application to boosting. Journal of computer and system sciences. 55 (1): 119-139.
[36]. Lyubartsev, A.P., Martsinovski, A.A., Shevkunov, S.V. and VorontsovVelyaminov, P.N. (1992). New approach to Monte Carlo calculation of the free energy: Method of expanded ensembles. The Journal of chemical physics. 96 (3): 1776-1783.
[37]. Iba, Y. (2001). Extended ensemble Monte Carlo. International Journal of Modern Physics C, 12(05), 623-656.
[38]. Yenice, H. (2019). Determination of Drilling Rate Index Based on Rock Strength Using Regression Analysis. Anais da Academia Brasileira de Ciências, 91 (3).
[39]. Yenice, H., Özdoğan, M.V., and Özfırat, M.K. (2018). A sampling study on rock properties affecting drilling rate index (DRI). Journal of African Earth Sciences, 141, 1-8.
[40]. Azizi, A., Shafaei, S.Z., Rooki, R., Hasanzadeh, A. and Paymard, M. (2012). Estimating of gold recovery by using back propagation neural network and multiple linear regression methods in cyanide leaching process.
[41]. Williamson, D.F., Parker, R.A. and Kendrick, J.S. (1989). The box plot: a simple visual method to interpret data. Annals of internal medicine. 110 (11): 916-921.
[42]. Witten, I.H. and Frank, E. (2005). Data Mining — Practical Machine Learning Tools and Techniques, Second Edition. Elsevier, Amsterdam.
[43]. Friedl, M.A. and Brodley, C.E. (1997). Decision tree classification of land cover from remotely sensed data. Remote sensing of environment. 61 (3): 399-409.
[44]. Pal, M. and Mather, P.M. (2003). An assessment of the effectiveness of decision tree methods for land cover classification. Remote sensing of environment. 86 (4): 554-565.
[45]. Zhang, J., Li, D. and Wang, Y. (2020). Toward intelligent construction: prediction of mechanical properties of manufactured-sand concrete using tree-based models. Journal of Cleaner Production. 258: 120665.
[46]. Sun, W. and Gao, Q. (2019). Exploration of energy saving potential in China power industry based on Adaboost back propagation neural network. Journal of Cleaner Production. 217: 257-266.
[47]. Hong, H., Liu, J., Bui, D.T., Pradhan, B., Acharya, T.D., Pham, B.T. and Ahmad, B.B. (2018). Landslide susceptibility mapping using J48 Decision Tree with AdaBoost, Bagging and Rotation Forest ensembles in the Guangchang area (China). Catena. 163: 399-413.
[48]. Maniruzzaman, M., Rahman, M.J., Al-MehediHasan, M., Suri, H.S., Abedin, M.M., El-Baz, A. and Suri, J.S. (2018). Accurate diabetes risk stratification using machine learning: role of missing value and outliers. Journal of medical systems. 42 (5): 1-17.
[49]. Zhang, J., Xu, J., Hu, X., Chen, Q., Tu, L., Huang, J. and Cui, J. (2017). Diagnostic method of diabetes based on support vector machine and tongue images. BioMed research international, 2017.
[50]. Yang, P., Hwa Yang, Y., B Zhou, B. and Y Zomaya, A. (2010). A review of ensemble methods in bioinformatics. Current Bioinformatics. 5 (4): 296-308.
[51]. Breiman, L. (1996). Bagging predictors. Machine learning. 24 (2): 123-140.
[52]. Liang, W., Sari, A., Zhao, G., McKinnon, S.D. and Wu, H. (2020). Short-term rockburst risk prediction using ensemble learning methods. Natural Hazards, 104 (2): 1923-1946
[53]. Wattimena, R.K., Kramadibrata, S., Sidi, I.D., Arif, I. and Azizi, M.A. (2012, January). Probabilistic analysis of single bench using new slope stability curves. In ISRM Regional Symposium-7th Asian Rock Mechanics Symposium. International Society for Rock Mechanics and Rock Engineering.
[54]. Azizi, M.A., Kramadibrata, S., Wattimena, R.K. and Sidi, I.D. (2013). Probabilistic analysis of physical models slope failure. Procedia Earth and Planetary Science, 6: 411-418.
[55]. Solver, F. (2010). Premium solver platform. User Guide, Frontline Systems.
[56]. EPA, U. (1997). Environmental Protection Agency. Guiding principles for Monte Carlo analysis. EPA/630/R-97/001.
[57]. Sari, M. and Ataei, M. (2012). Development of an empirical model for predicting the effects of controllable blasting parameters on fly-rock distance in surface mines. International Journal of Rock Mechanics and Mining Sciences, 52, 163-170.
[58]. Steinfeld, B., Scott, J., Vilander, G., Marx, L., Quirk, M., Lindberg, J. and Koerner, K. (2015). The role of lean process improvement in implementation of evidence-based practices in behavioral health care. The Journal of Behavioral Health Services and Research, 42 (4): 504-518.
[59]. Mahdiyar, A., Hasanipanah, M., Armaghani DJ et al A Monte Carlo technique in safety assessment of slope under seismic condition. Eng Comput. 2017. https :// 6-016-0499-1
[60]. Bianchini, F. and Hewage, K. (2012). Probabilistic social cost-benefit analysis for green roofs: A lifecycle approach. Building and Environment, 58: 152-162.
[61]. Dunn, W.L. And Shultis, J.K. Monte Carlo methods for design and analysis of radiation detectors. Radiat Phys Chem. 2009; 78:852–858. https :// ysche m.2009.04.030.