Skip to main content
Log in

Prediction of rock drillability using gray wolf optimization and teaching–learning-based optimization techniques

  • Application of soft computing
  • Published:
Soft Computing Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Data availability

Enquiries about data availability should be directed to the authors.

References

  • Abu Arqub O (2017) Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm-Volterra integrodifferential equations. Neural Comput Appl 28:1591–1610

    Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Agrawal N, Kumar A, Bajaj V, Singh GK (2021) Design of digital IIR filter: a research survey. Appl Acoust 172:107669

    Google Scholar 

  • Akin S, Karpuz C (2008) Estimating drilling parameters for diamond bit drilling operations using artificial neural networks. Int J Geomech 8:68–73

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Altindag R (2010) Assessment of some brittleness indexes in rock-drilling efficiency. Rock Mech Rock Eng 43:361–370

    Google Scholar 

  • 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

    MathSciNet  Google Scholar 

  • 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

    Google Scholar 

  • Babanouri N, Fattahi H (2018) Constitutive modeling of rock fractures by improved support vector regression. Environ Earth Sci 77:243

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Barton NR (2000) TBM tunnelling in jointed and faulted rock. CRC Press, Boca Raton

    Google Scholar 

  • Benardos A, Kaliampakos D (2004) Modelling TBM performance with artificial neural networks. Tunn Undergr Space Technol 19:597–605

    Google Scholar 

  • Camp CV (2007) Design of space trusses using big bang-big crunch optimization. J Struct Eng 133:999–1008

    Google Scholar 

  • Capik M, Yilmaz AO, Yasar S (2017) Relationships between the drilling rate index and physicomechanical rock properties. Bull Eng Geol Env 76:253–261

    Google Scholar 

  • Dahl F, Bruland A, Grov E, Nilsen B (2010) Trademarking the NTNU/SINTEF drillability test indices. Tunn Tunn Int 6:44–46

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Fattahi H (2016b) Application of improved support vector regression model for prediction of deformation modulus of a rock mass. Eng Comput 32:567–580

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    MathSciNet  Google Scholar 

  • 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

    Article  Google Scholar 

  • Fattahi H, Babanouri N (2017) Applying optimized support vector regression models for prediction of tunnel boring machine performance. Geotech Geol Eng 35:2205–2217

    Google Scholar 

  • Fattahi H, Bayat N (2020) RETRACTED ARTICLE: Forecasting of rock drillability using a new computational intelligent method. Geotech Geol Eng 38:5693–5693

    Google Scholar 

  • Fattahi H, Bazdar H (2017) Applying improved artificial neural network models to evaluate drilling rate index. Tunn Undergr Space Technol 70:114–124

    Google Scholar 

  • 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

    Google Scholar 

  • Girmscheid G, Schexnayder C (2002) Drill and blast tunneling practices. Pract Period Struct Des Constr 7:125–133

    Google Scholar 

  • Grima MA, Bruines P, Verhoef P (2000) Modeling tunnel boring machine performance by neuro-fuzzy methods. Tunn Undergr Space Technol 15:259–269

    Google Scholar 

  • Heidari AA, Pahlavani P (2017) An efficient modified grey wolf optimizer with Lévy flight for optimization tasks. Appl Soft Comput 60:115–134

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Hucka V, Das B (1974) Brittleness determination of rocks by different methods. Int J Rock Mech Min Sci Geomech Abstr 10:389–392

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Kamran M (2021) A probabilistic approach for prediction of drilling rate index using ensemble learning technique. J Min Environ 12:327–337

    Google Scholar 

  • 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

    Google Scholar 

  • Kaveh A, Talatahari S (2009) Size optimization of space trusses using Big Bang-Big Crunch algorithm. Comput Struct 87:1129–1140

    Google Scholar 

  • Kelessidis V (2011) Rock drillability prediction from in situ determined unconfined compressive strength of rock. J South Afr Inst Min Metall 111:429–436

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61

    Google Scholar 

  • 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

    Google Scholar 

  • Morley A (1994) Strength of materials. Longman, London

    Google Scholar 

  • 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

    Google Scholar 

  • Obert L, Duvall WI (1967) Rock mechanics and the design of structures in rock, vol 650. Wiley, New York

    Google Scholar 

  • Olgay Y, Eren S (2011) The effect of mechanical rock properties and brittleness on drillability. Sci Res Essays 6:1077–1088

    Google Scholar 

  • Poole R, Farmer I (1978) Geotechnical factors affecting tunnelling machine performance in coal measures rock. Tunn Tunn (U K) 10:1–10

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Rodríguez L et al (2017) A fuzzy hierarchical operator in the grey wolf optimizer algorithm. Appl Soft Comput 57:315–328

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Saeidi O, Torabi SR, Ataei M (2013) Development of a new index to assess the rock mass drillability. Geotech Geol Eng 31:1477–1495

    Google Scholar 

  • Saha SK, Kar R, Mandal D, Ghoshal SP (2014) Harmony search algorithm for infinite impulse response system identification. Comput Electr Eng 40:1265–1285

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Saremi S, Mirjalili SZ, Mirjalili SM (2015) Evolutionary population dynamics and grey wolf optimizer. Neural Comput Appl 26:1257–1263

    Google Scholar 

  • Selmer-Olsen R, Lien R (1960) Bergartens Borbarhet Og Sprengbarhet. Teknisk Ukeblad 34:3–11

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Singh N, Singh S (2017) A novel hybrid GWO-SCA approach for optimization problems. Eng Sci Technol Int J 20:1586–1601

    Google Scholar 

  • Sonmez M (2011) Artificial Bee Colony algorithm for optimization of truss structures. Appl Soft Comput 11:2406–2418

    Google Scholar 

  • Su O (2016) Performance evaluation of button bits in coal measure rocks by using multiple regression analyses. Rock Mech Rock Eng 49:541–553

    Google Scholar 

  • Tanaino A (2005) Rock classification by drillability. Part i: analysis of the available classifications. J Min Sci 41:541–549

    Google Scholar 

  • Yagiz S (2009) Assessment of brittleness using rock strength and density with punch penetration test. Tunn Undergr Space Technol 24:66–74

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Yarali O, Soyer E (2013) Assessment of relationships between drilling rate index and mechanical properties of rocks. Tunn Undergr Space Technol 33:46–53

    Google Scholar 

  • Yasar S, Capik M, Yilmaz AO (2015) Cuttability assessment using the drilling rate index (DRI). Bull Eng Geol Environ 74:1349–1361

    Google Scholar 

  • Zare S, Bruland A (2013) Applications of NTNU/SINTEF drillability indices in hard rock tunneling. Rock Mech Rock Eng 46:179–187

    Google Scholar 

  • 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

    Article  Google Scholar 

Download references

Funding

The authors have not disclosed any funding.

Author information

Authors and Affiliations

Authors

Contributions

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.

Corresponding author

Correspondence to Hadi Fattahi.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Ethical approval

This paper does not contain any studies with human participants or animals performed by any of the authors.

Informed consent

Informed consent was obtained from all individual participants included in the study.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-023-08233-6

Keywords

pFad - Phonifier reborn

Pfad - The Proxy pFad of © 2024 Garber Painting. All rights reserved.

Note: This service is not intended for secure transactions such as banking, social media, email, or purchasing. Use at your own risk. We assume no liability whatsoever for broken pages.


Alternative Proxies:

Alternative Proxy

pFad Proxy

pFad v3 Proxy

pFad v4 Proxy