Abstract
An important index to evaluate the rock drilling ability in mines, tunnel drilling and underground drilling is the drilling rate index (DRI). Due to the complexity and nonlinearity of mechanical and physical properties of rocks, there are many uncertainties in DRI evaluation. For this reason, teaching–learning-based optimization (TLBO) and gray wolf optimization (GWO) have been used to consider uncertainties and establish a precise nonlinear relationship in the estimation of the DRI. In this study, 32 different rock types included metamorphic, igneous and sedimentary rocks were investigated in the laboratory to investigate the relationships between the DRI and input parameters. The modeling results show that the relationships determined for estimating the DRI by TLBO and GWO algorithms are accurate and close to the real value. It can also be concluded that the use of optimization algorithms to predict the DRI is very efficient.















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References
Abu Arqub O (2017) Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm-Volterra integrodifferential equations. Neural Comput Appl 28:1591–1610
Abu Arqub O, Singh J, Alhodaly M (2021) Adaptation of kernel functions-based approach with Atangana–Baleanu–Caputo distributed order derivative for solutions of fuzzy fractional Volterra and Fredholm integrodifferential equations. Math Methods Appl Sci. https://doi.org/10.1002/mma.7228
Abu Arqub O, Singh J, Maayah B, Alhodaly M (2021) Reproducing kernel approach for numerical solutions of fuzzy fractional initial value problems under the Mittag-Leffler kernel differential operator. Math Methods Appl Sci. https://doi.org/10.1002/mma.7305
Afradi A, Ebrahimabadi A, Hallajian T (2019) Prediction of the penetration rate and number of consumed disc cutters of tunnel boring machines (TBMs) using artificial neural network (ANN) and support vector machine (SVM)—case study: beheshtabad water conveyance tunnel in iran. Asian J Water Environ Pollut 16:49–57
Agrawal N, Kumar A, Bajaj V (2017) A new design method for stable IIR filters with nearly linear-phase response based on fractional derivative and swarm intelligence. IEEE Trans Emerg Top Comput Intell 1:464–477
Agrawal N, Kumar A, Bajaj V, Singh GK (2018) Design of bandpass and bandstop infinite impulse response filters using fractional derivative. IEEE Trans Ind Electron 66:1285–1295
Agrawal N, Kumar A, Bajaj V (2020) Design of infinite impulse response filter using fractional derivative constraints and hybrid particle swarm optimization. Circuits Syst Signal Process 39:6162–6190
Agrawal N, Kumar A, Bajaj V, Singh GK (2021) Design of digital IIR filter: a research survey. Appl Acoust 172:107669
Akin S, Karpuz C (2008) Estimating drilling parameters for diamond bit drilling operations using artificial neural networks. Int J Geomech 8:68–73
Akün M, Karpuz C (2005) Drillability studies of surface-set diamond drilling in Zonguldak region sandstones from Turkey. Int J Rock Mech Min Sci 42:473–479
Altindag R (2004) Evaluation of drill cuttings in prediction of penetration rate by using coarseness index and mean particle size in percussive drilling. Geotech Geol Eng 22:417–425
Altindag R (2010) Assessment of some brittleness indexes in rock-drilling efficiency. Rock Mech Rock Eng 43:361–370
Altindag R (2000) The role of rock brittleness on analysis of percussive drilling performance. In: Proceedings of 5th National Rock Mech, pp. 105–112
Arqub OA, Abo-Hammour Z (2014) Numerical solution of systems of second-order boundary value problems using continuous genetic algorithm. Inf Sci 279:396–415
Ataei M, KaKaie R, Ghavidel M, Saeidi O (2015) Drilling rate prediction of an open pit mine using the rock mass drillability index. Int J Rock Mech Min Sci 73:130–138
Babanouri N, Fattahi H (2018) Constitutive modeling of rock fractures by improved support vector regression. Environ Earth Sci 77:243
Bahrampour S, Rostami J, Naeimipour A, Collins G (2014) Rock characterization using time-series classification algorithms. In: Proceedings of 33rd international conference on ground control in mining, Morgantown WV
Bakhtavar E, Shirvand Y (2019) Designing a fuzzy cognitive map to evaluate drilling and blasting problems of the tunneling projects in Iran. Eng Comput 35:35–45
Bardhan A, Kardani N, GuhaRay A, Burman A, Samui P, Zhang Y (2021) Hybrid ensemble soft computing approach for predicting penetration rate of tunnel boring machine in a rock environment. J Rock Mech Geotech Eng 13:1398–1412
Barton NR (2000) TBM tunnelling in jointed and faulted rock. CRC Press, Boca Raton
Benardos A, Kaliampakos D (2004) Modelling TBM performance with artificial neural networks. Tunn Undergr Space Technol 19:597–605
Camp CV (2007) Design of space trusses using big bang-big crunch optimization. J Struct Eng 133:999–1008
Capik M, Yilmaz AO, Yasar S (2017) Relationships between the drilling rate index and physicomechanical rock properties. Bull Eng Geol Env 76:253–261
Dahl F, Bruland A, Grov E, Nilsen B (2010) Trademarking the NTNU/SINTEF drillability test indices. Tunn Tunn Int 6:44–46
Dahl F, Bruland A, Jakobsen PD, Nilsen B, Grøv E (2012) Classifications of properties influencing the drillability of rocks, based on the NTNU/SINTEF test method. Tunn Undergr Space Technol 28:150–158
Das B, Hucka V (1975) Laboratory investigation of penetration properties of the complete coal series. Int J Rock Mech Min Sci Geomech Abstr 7:213–217
F D (2003) DRI, BWI, CLI standards. NTNU, Trondheim, p. 20
Fattahi H (2016a) Adaptive neuro fuzzy inference system based on fuzzy c–means clustering algorithm, a technique for estimation of TBM penetration rate. Int J Optim Civ Eng 6:159–171
Fattahi H (2016b) Application of improved support vector regression model for prediction of deformation modulus of a rock mass. Eng Comput 32:567–580
Fattahi H (2016c) Indirect estimation of deformation modulus of an in situ rock mass: an ANFIS model based on grid partitioning, fuzzy c-means clustering and subtractive clustering. Geosci J 5:681–690
Fattahi H (2017) Applying soft computing methods to predict the uniaxial compressive strength of rocks from schmidt hammer rebound values. Comput Geosci 21:665–681
Fattahi H (2018) Applying rock engineering systems to evaluate shaft resistance of a pile embedded in rock. Geotech Geol Eng. https://doi.org/10.1007/s10706-018-0536-5
Fattahi H, Babanouri N (2017) Applying optimized support vector regression models for prediction of tunnel boring machine performance. Geotech Geol Eng 35:2205–2217
Fattahi H, Bayat N (2020) RETRACTED ARTICLE: Forecasting of rock drillability using a new computational intelligent method. Geotech Geol Eng 38:5693–5693
Fattahi H, Bazdar H (2017) Applying improved artificial neural network models to evaluate drilling rate index. Tunn Undergr Space Technol 70:114–124
Gholamnejad J, Tayarani N (2010) Application of artificial neural networks to the prediction of tunnel boring machine penetration rate. Min Sci Tech 20:727–733
Girmscheid G, Schexnayder C (2002) Drill and blast tunneling practices. Pract Period Struct Des Constr 7:125–133
Grima MA, Bruines P, Verhoef P (2000) Modeling tunnel boring machine performance by neuro-fuzzy methods. Tunn Undergr Space Technol 15:259–269
Heidari AA, Pahlavani P (2017) An efficient modified grey wolf optimizer with Lévy flight for optimization tasks. Appl Soft Comput 60:115–134
Hetenyi MI (1966) Handbook of experimental stress analysis. Wiley, New York
Hoseinie S, Ataei M, Mikaiel R (2012) Comparison of some rock hardness scales applied in drillability studies. Arab J Sci Eng 37:1451–1458
Hosseini SH, Ataie M, Aghababaie H (2014) A laboratory study of rock properties affecting the penetration rate of pneumatic top hammer drills. J Min Environ 5:25–34
Hucka V, Das B (1974) Brittleness determination of rocks by different methods. Int J Rock Mech Min Sci Geomech Abstr 10:389–392
Janjanam L, Saha SK, Kar R, Mandal D (2021) Global gravitational search algorithm-aided Kalman filter design for Volterra-based nonlinear system identification. Circuits Syst Signal Process 40:2302–2334
Kahraman S, Bilgin N, Feridunoglu C (2003) Dominant rock properties affecting the penetration rate of percussive drills. Int J Rock Mech Min Sci 40:711–723
Kamran M (2021) A probabilistic approach for prediction of drilling rate index using ensemble learning technique. J Min Environ 12:327–337
Karrari SS, Heidari M, Hamidi JK, Khaleghi-Esfahani M, Teshnizi ES (2022) Predicting tunnel-boring machine penetration rate utilizing geomechanical properties. Q J Eng Geol Hydrogeol 55:qjegh2021-2126
Kaveh A, Talatahari S (2009) Size optimization of space trusses using Big Bang-Big Crunch algorithm. Comput Struct 87:1129–1140
Kelessidis V (2011) Rock drillability prediction from in situ determined unconfined compressive strength of rock. J South Afr Inst Min Metall 111:429–436
Khademi Hamidi J, Shahriar K, Rezai B, Bejari H (2010) Application of fuzzy set theory to rock engineering classification systems: an illustration of the rock mass excavability index. Rock Mech Rock Eng 43:335–350
Khandelwal M, Armaghani DJ (2016) Prediction of drillability of rocks with strength properties using a hybrid GA-ANN technique. Geotech Geol Eng 34:605–620
Koopialipoor M, Tootoonchi H, Jahed Armaghani D, Tonnizam Mohamad E, Hedayat A (2019) Application of deep neural networks in predicting the penetration rate of tunnel boring machines. Bull Eng Geology Envir 78:6347–6360
Kumar A, Agrawal N, Sharma I, Lee S, Lee H-N (2018) Hilbert transform design based on fractional derivatives and swarm optimization. IEEE Trans Cybern 50:2311–2320
Li G, Yang M, Meng Y, Liu H, Han L, Zhou F, Zhang H (2016) The assessment of correlation between rock drillability and mechanical properties in the laboratory and in the field under different pressure conditions. J Nat Gas Sci Eng 30:405–413
Lovitt M, Collins A (2013) Improved tunneling performance through smarter drilling and design. In: Tunnelling in rock by drilling and blasting, 1st edn. CRC Press, Boca Raton, USA, pp 7–14
Mahdevari S, Shahriar K, Yagiz S, Shirazi MA (2014) A support vector regression model for predicting tunnel boring machine penetration rates. Int J Rock Mech Min Sci 72:214–229
Mahmoodzadeh A, Nejati HR, Mohammadi M, Ibrahim HH, Rashidi S, Rashid TA (2022) Forecasting tunnel boring machine penetration rate using LSTM deep neural network optimized by grey wolf optimization algorithm. Expert Syst Appl 209:118303
Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61
Mohammadi S, Torabi-Kaveh M, Bayati M (2015) Prediction of TBM penetration rate using intact and mass rock properties (case study: Zagros long tunnel, Iran). Arab J Geosci 8:3893–3904
Morley A (1994) Strength of materials. Longman, London
Mottahedi A, Sereshki F, Ataei M (2018) Development of overbreak prediction models in drill and blast tunneling using soft computing methods. Eng Comput 34:45–58
Obert L, Duvall WI (1967) Rock mechanics and the design of structures in rock, vol 650. Wiley, New York
Olgay Y, Eren S (2011) The effect of mechanical rock properties and brittleness on drillability. Sci Res Essays 6:1077–1088
Poole R, Farmer I (1978) Geotechnical factors affecting tunnelling machine performance in coal measures rock. Tunn Tunn (U K) 10:1–10
Protodyakonov M Mechanical properties and drillability of rocks. In: Proceedings of the 5th Symposium on Rock Mechanics, 1962. University of Minnesota Minneapolis, Minnesota, USA, p 118
Ramsay JG (1967) Folding and fracturing of rocks. Mc Graw Hill Book Company, New York, p 568
Rao RV, Savsani VJ, Vakharia D (2011) Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems. Comput-aided Des 43:303–315
Rodríguez L et al (2017) A fuzzy hierarchical operator in the grey wolf optimizer algorithm. Appl Soft Comput 57:315–328
Ru Z, Zhao H, Zhu C (2019) Probabilistic evaluation of drilling rate index based on a least square support vector machine and Monte Carlo simulation. Bull Eng Geol Env 78:3111–3118
Sabah M, Talebkeikhah M, Wood DA, Khosravanian R, Anemangely M, Younesi A (2019) A machine learning approach to predict drilling rate using petrophysical and mud logging data. Earth Sci Inf 12:319–339
Saeidi O, Torabi SR, Ataei M (2013) Development of a new index to assess the rock mass drillability. Geotech Geol Eng 31:1477–1495
Saha SK, Kar R, Mandal D, Ghoshal SP (2014) Harmony search algorithm for infinite impulse response system identification. Comput Electr Eng 40:1265–1285
Sakız U, Kaya GU, Yaralı O (2021) Prediction of drilling rate index from rock strength and cerchar abrasivity index properties using fuzzy inference system. Arab J Geosci 14:1–16
Salimi A, Esmaeili M (2013) Utilising of linear and non-linear prediction tools for evaluation of penetration rate of tunnel boring machine in hard rock condition. Int J Min Miner Eng 4:249–264
Saremi S, Mirjalili SZ, Mirjalili SM (2015) Evolutionary population dynamics and grey wolf optimizer. Neural Comput Appl 26:1257–1263
Selmer-Olsen R, Lien R (1960) Bergartens Borbarhet Og Sprengbarhet. Teknisk Ukeblad 34:3–11
Servet D, Nazmi S, Ibrahim U, Tamer E, Deniz A, Rasit A (2014) Variation of vertical and horizontal drilling rates depending on some rock properties in the marble quarries. Int J Min Sci Technol 24:269–273
Shahani NM, Kamran M, Zheng X, Liu C (2022) Predictive modeling of drilling rate index using machine learning approaches: LSTM, simple RNN, and RFA. Pet Sci Technol 40:534–555
Singh N, Singh S (2017) A novel hybrid GWO-SCA approach for optimization problems. Eng Sci Technol Int J 20:1586–1601
Sonmez M (2011) Artificial Bee Colony algorithm for optimization of truss structures. Appl Soft Comput 11:2406–2418
Su O (2016) Performance evaluation of button bits in coal measure rocks by using multiple regression analyses. Rock Mech Rock Eng 49:541–553
Tanaino A (2005) Rock classification by drillability. Part i: analysis of the available classifications. J Min Sci 41:541–549
Yagiz S (2009) Assessment of brittleness using rock strength and density with punch penetration test. Tunn Undergr Space Technol 24:66–74
Yagiz S, Karahan H (2011) Prediction of hard rock TBM penetration rate using particle swarm optimization. Int J Rock Mech Min Sci 48:427–433
Yagiz S, Karahan H (2015) Application of various optimization techniques and comparison of their performances for predicting TBM penetration rate in rock mass. Int J Rock Mech Min Sci 80:308–315
Yarali O, Soyer E (2007) Prediction of drilling rate index (DRI) using performance analysis of tunnel boring machines. In: Proceedings of the 2th Symposium on Underground Excavations for Transportation, Istanbul Turkey, pp 15–17
Yarali O, Kahraman S (2011) The drillability assessment of rocks using the different brittleness values. Tunn Undergr Space Technol 26:406–414
Yarali O, Soyer E (2013) Assessment of relationships between drilling rate index and mechanical properties of rocks. Tunn Undergr Space Technol 33:46–53
Yasar S, Capik M, Yilmaz AO (2015) Cuttability assessment using the drilling rate index (DRI). Bull Eng Geol Environ 74:1349–1361
Zare S, Bruland A (2013) Applications of NTNU/SINTEF drillability indices in hard rock tunneling. Rock Mech Rock Eng 46:179–187
Zhang Y, Wei M, Su G, Li Y, Zeng J, Deng X (2020) A novel intelligent method for predicting the penetration rate of the tunnel boring machine in rocks. Math Probl Eng. https://doi.org/10.1155/2020/3268694
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Conceptualization, data curation, writing—review and editing and supervision contributed by HF. Methodology and software contributed by HF and HG. Validation and investigation contributed by HF and FM.
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Fattahi, H., Ghaedi, H. & Malekmahmoodi, F. Prediction of rock drillability using gray wolf optimization and teaching–learning-based optimization techniques. Soft Comput 28, 461–476 (2024). https://doi.org/10.1007/s00500-023-08233-6
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DOI: https://doi.org/10.1007/s00500-023-08233-6