Skip to main content

Advertisement

Log in

A New Predictive Model for Uniaxial Compressive Strength of Rock Using Machine Learning Method: Artificial Intelligence-Based Age-Layered Population Structure Genetic Programming (ALPS-GP)

  • Research Article-Earth Sciences
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

Uniaxial compressive strength (UCS) of rocks is the most commonly used parameter in geo-engineering application. However, this parameter is hard for measurement due to a time consuming and requires expensive equipment. Therefore, obtaining this value indirectly using non-destructive testing methods has been a frequently preferred method for a long time. In order to obtain multiple regression models, input parameters need many assumptions. Thus, the estimation of the mechanical properties of rocks using by machine learning methods has been investigated. In this study, UCS values of rocks were estimated by reformulating with artificial intelligence-based age-layered population structure genetic programming (ALPS-GP) which is one of machine learning methods. Artificial neural network (ANN) and ALPS-GP models were performed to predict UCS from porosity, Schmidt hammer hardness and ultrasonic wave velocity test methods. For this purpose, the mentioned three tests (porosity, Schmidt hammer hardness and P-wave velocity) were carried out on ten different stones from Turkey. ANN was performed to evaluate this new technique. Reliability of UCS values determined by models was checked with mean absolute error (MAE), coefficient of determination (R2), root mean square error (RMSE) and variance account for (VAF) values. These values were calculated as 1.64, 0.98, 2.11 and 99.81 for ANN, and 2.11, 0.98, 2.50 and 97.86 for ALPS-GP, respectively. It was observed that both methods used were quite successful in UCS estimation. The most important advantage of the ALPS-GP model is providing an equation for UCS estimation. In the light of the obtained findings, it has been revealed that this equation derived from ALPS-GP can be used in UCS estimation processes of similar rock types (limestone, dolomite and onyx).

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Khandelwal, M.; Ranjith, P.G.: Correlating index properties of rocks with P-wave measurements. J. Appl. Geophys. 71, 1–5 (2010)

    Google Scholar 

  2. Sharma, P.K.; Singh, T.N.: A correlation between P-wave velocity, impact strength index, slake durability index and uniaxial compressive strength. Bull. Eng. Geol. Env. 67, 17–22 (2008)

    Google Scholar 

  3. Deere, D.U.; Miller, R.P.: Engineering classification and index properties of intact rock. Tech rep no. AFWL-TR 65-116. Univ Illinois: 300 (1966)

  4. Singh, R.N.; Hassani, F.P.; Elkington, P.A.S.: The application of strength and deformation index testing to the stability assessment of coal measures excavations. In: Proc 24th US Symp rock Mech, Texas, AEG. Balkema, Rotterdam, 599–609 (1983)

  5. Sheorey, P.R.; Barat, D.; Das, M.N.; Mukherjee, K.P.; Singh, B.: Schmidt hammer rebound data for estimation of large scale in situ coal strength. Int. J. Rock Mech. Min. Sci. 21, 39–42 (1984)

    Google Scholar 

  6. Haramy, K.Y.; De Marco, M.J.: Use of Schmidt hammer for rock and coal testing. In: Proc 26th US Symp rock Mech, 26–28 June, Rapid City, SD. Balkema, Rotterdam, 549–555 (1985)

  7. Ghose, A.K.; Chakraborti, S.: Empirical strength indices of Indian coals: an investigation. Proceedings 27th US Symposium on Rock Mechanics, Rotterdam: Balkema, 59–61 (1986)

  8. O'Rourke, J.E.: Rock index properties for geoengineering, underground development. Minerals Engineering 106–110 (1989)

  9. Gokceoglu, C.: Schmidt sertlik çekici kullanılarak tahmin edilen tek eksenli sıkışma dayanımı verilerinin güvenilirliği üzerine bir değerlendirme. Jeoloji Mühendisliği 48, 78–81 (1996)

    Google Scholar 

  10. Katz, O.; Reches, Z.; Roegiers, J.C.: Evaluation of mechanical rock properties using a Schmidt hammer. Int. J. Rock Mech. Min. Sci. 37, 723–728 (2000)

    Google Scholar 

  11. Kahraman, S.: Evaluation of simple methods for assessing the uniaxial compressive strength of rock. Int. J. Rock Mech. Min. Sci. 38, 981–994 (2001)

    Google Scholar 

  12. Yilmaz, I.; Sendir, H.: Correlation of Schmidt hardness with unconfined compressive strength and Young’s modulus in gypsum from Sivas (Turkey). Eng. Geol. 66, 211–219 (2002)

    Google Scholar 

  13. Basarir, H.; Kumral, M.; Ozsan, A.: Predicting uniaxial compressive strength of rocks from simple test methods. Rockmec′2004-VIIth Regional Rock Mechanics Symposium. Sivas, Turkey (2004)

  14. Kılıc, A.; Teymen, A.: Determination of mechanical properties of rocks using simple methods. Bull. Eng. Geol. Env. 67, 237–244 (2008)

    Google Scholar 

  15. Torabi, S.R.; Ataei, M.; Javanshir, M.: Application of Schmidt rebound number for estimating rock strength under specific geological conditions. J. Mining Environ. 1(2), 1–8 (2010)

    Google Scholar 

  16. Nazir, R.; Momeni, E.; Armaghani, D.J.; Mohd Amin, M.F.M.: Prediction of unconfined compressive strength of limestone rock samples using L-type Schmidt hammer. Electron. J. Geotech. Eng. 18(1), 1767–1775 (2013)

    Google Scholar 

  17. Inoue, M.; Ohomi, M.: Relation between uniaxial compres-sive strength and elastic wave velocity of soft rock.Proc., Int. Symp.on Weak Rock, Tokyo, Japan, Balkema, Rotterdam, 9–13 (1981)

  18. Starzec, P.: Dynamic elastic properties of crystalline rocks fromsouth-west Sweden. Int. J. Rock Mech. Min. Sci. 362, 265–272 (1999)

    Google Scholar 

  19. Moradian, Z.A.; Behnia, M.: Predicting the uniaxial compressive strength and static Young’s modulus of ıntact sedimentary rocks using the ultrasonic test. Int. J. Geomech. 9(1), 14–19 (2009)

    Google Scholar 

  20. Kahraman, S.: A correlation between P-wave velocity, number of joints and Schmidt hammer rebound number. Int. J. Rock Mech. Min. Sci. 38, 729–733 (2001)

    Google Scholar 

  21. Yasar, E.; Erdogan, Y.: Correlating sound velocity with the density, compressive strength and Young’s modulus of carbonate rocks. Int. J. Rock Mech. Min. Sci. 415, 871–875 (2004)

    Google Scholar 

  22. Chary, K.B.; Sarma, L.P.; Lakshmi, K.J.P.; et al.: Evaluation of engineering properties of rock using ultrasonic pulse velocity and uniaxial compressive strength, Proc. National Seminar on Non-Destructive Evaluation 7–9 Dec. 379–385 (2006)

  23. Khandelwal, M.: Correlating P-wave velocity with the physico-mechanical properties of different rocks. Pure Appl. Geophys. 170(4), 507–514 (2013)

    Google Scholar 

  24. Nourani, M.H.; Moghadder, T.M.; Safari, M.: Classification and assessment of rock mass parameters in Choghart iron mine using P-wave velocity. J. Rock Mech. Geotech. Eng. 9(2), 318–328 (2017)

    Google Scholar 

  25. Mishra, D.A.; Basu, A.: Estimation of uniaxial compressive strength of rock materials by index tests using regression analysis and fuzzy inference system. Eng. Geol. 160, 54–68 (2013)

    Google Scholar 

  26. Yesiloglu-Gultekin, N.; Sezer, E.A.; Gokceoglu, C.; Bayhan, H.: An application of adaptive neuro fuzzy inference system for estimating the uniaxial compressive strength of certain granitic rocks from their mineral contents. Expert Syst. Appl. 40(3), 921–928 (2013)

    Google Scholar 

  27. Dehghan, S.; Sattari, G.; Chelgani, S.C.; Aliabadi, M.: Prediction of uniaxial compressive strength and modulus of elasticity for Travertine samples using regression and artificial neural networks. Int. J. Min. Sci. Technol. 20, 41–46 (2010)

    Google Scholar 

  28. Majdi, A.; Rezaei, M.: Prediction of unconfined compressive strength of rock surrounding a roadway using artificial neural network. Neural Comput. Appl. 23, 381–389 (2013)

    Google Scholar 

  29. Ceryan, N.; Okkan, U.; Samui, P.; Ceryan, S.: Modeling of tensile strength of rocks materials based on support vector machines approaches. Int. J. Numer. Anal. Meth. Geomech. 37(16), 2655–2670 (2012)

    Google Scholar 

  30. Ceryan, N.: Application of support vector machines and relevance vector machines in predicting uniaxial compressive strength of volcanic rocks. J. Afr. Earth Sc. 100, 634–644 (2014)

    Google Scholar 

  31. Liu, Z.; Shao, J.; Xu, W., et al.: Indirect estimation of unconfined compressive strength of carbonate rocks using extreme learning machine. Acta Geotech. 10, 651–663 (2015)

    Google Scholar 

  32. Singh, R.; Vishal, V.; Singh, T.N.; Ranjith, P.G.: A comparative study of generalized regression neural network approach and adaptive neuro-fuzzy inference systems for prediction of unconfined compressive strength of rocks. Neural Comput. Appl. 23, 499–506 (2013)

    Google Scholar 

  33. Mishra, D.; Srigyan, M.; Basu, A.; Rokade, P.: Soft computing methods for estimating the uniaxial compressive strength of intact rock from index tests. Int. J. Rock Mech. Min. Sci. 100, 418–424 (2015)

    Google Scholar 

  34. Mohamad, E.T.; Armaghani, D.J.; Momeni, E., et al.: Prediction of the unconfined compressive strength of soft rocks: a PSO-based ANN approach. Bull. Eng. Geol. Env. 74, 745–757 (2015)

    Google Scholar 

  35. Momeni, E.; Armaghani, D.J.; Hajihassani, M.; Amin, M.F.M.: Prediction of uniaxial compressive strength of rock samples using hybrid particle swarm optimization-based artificial neural networks. Measurement 60, 50–63 (2015)

    Google Scholar 

  36. Mahdiyar, A.; Armaghani, D.J.; Marto, A., et al.: Rock tensile strength prediction using empirical and soft computing approaches. Bull. Eng. Geol. Env. 78, 4519–4531 (2019)

    Google Scholar 

  37. Asheghi, R.; Shahri, A.A.; Zak, M.K.: Prediction of uniaxial compressive strength of different quarried rocks using metaheuristic algorithm. Arab. J. Sci. Eng. 44, 8645–8659 (2019)

    Google Scholar 

  38. Ceryan, N.; Okkan, U.; Kesimal.: A. Application of Generalized Regression Neural Networks in Predicting the Unconfined Compressive Strength of Carbonate Rocks. Rock Mechanics and Rock Engineering 45, 1055–1072 (2012)

  39. Celik, S.B.: Prediction of uniaxial compressive strength of carbonate rocks from nondestructive tests using multivariate regression and LS-SVM methods. Arab. J. Geosci. 12(6), 193 (2019)

    Google Scholar 

  40. Acar, M.C.; Kaya, B.: Models to estimate the elastic modulus of weak rocks based on least square support vector machine. Arab. J. Geosci. 13(14), 590 (2020)

    Google Scholar 

  41. Shahri, A.A.; Asheghi, R.; Khorsand, M.Z.: A hybridized intelligence model to improve the predictability level of strength index parameters of rocks. Neural Comput. Appl. 33, 3841–3854 (2021). https://doi.org/10.1007/s00521-020-05223-9

    Article  Google Scholar 

  42. Shahri, A.A.; Moud, F.M.; Lialestani, S.M.: A hybrid computing model to predict rock strength index properties using support vector regression. Eng. Comput. (2020). https://doi.org/10.1007/s00366-020-01078-9

    Article  Google Scholar 

  43. Koza, J.R.: Genetic Programming: On the Programming of Computers By Means of Natural Selection, 6th edn. MIT Press, London (1992)

    MATH  Google Scholar 

  44. Holland, J.H.: Application of natural and artificial systems. University of Michigan Press, Ann Arbor (1975)

    Google Scholar 

  45. Wang, C.; Ma, G.W.; Zhao, J.; Soh, C.K.: Identification of dynamic rock properties using a genetic algorithm. Int. J. Rock Mech. Min. Sci. 41(1), 490–495 (2004)

    Google Scholar 

  46. Majdi, A.; Beiki, M.: Evolving neural network using a genetic algorithm for predicting the deformation modulus of rock masses. Int. J. Rock Mech. Min. Sci. 47, 246–253 (2010)

    Google Scholar 

  47. Ferreira, C.: Gene expression programming: a new adaptive algorithm for solving problems. Complex Syst. 13(2), 87–129 (2001)

    MathSciNet  MATH  Google Scholar 

  48. Baykasoğlu, A.; Güllü, H.; Çanakçı, H.; Özbakır, L.: Prediction of compressive and tensile strength of limestone via genetic programming. Expert Syst. Appl. 35, 111–123 (2008)

    Google Scholar 

  49. Shuhua, Z.; Qian, G.; Jianguo, S.: Genetic programming approach for predicting surface subsidence induced by mining. J. China Univ. Geosci. 17(4), 361–366 (2006)

    Google Scholar 

  50. Li, W.X.; Dai, L.F.; Houa, X.B.; Lei, W.: Fuzzy genetic programming method for analysis of ground movements due to underground mining. Int. J. Rock Mech. Min. Sci. 44, 954–961 (2007)

    Google Scholar 

  51. Çanakcı, H.; Baykasoğlu, A.; Güllü, H.: Prediction of compressive and tensile strength of Gaziantep basalts via neural networks and gene expression programming. Neural Comput. Appl. 18, 1031–1041 (2009)

    Google Scholar 

  52. Ozbek, A.; Unsal, M.; Dikec, A.: Estimating uniaxial compressive strength of rocks using genetic expression programming. J. Rock Mech. Geotech. Eng. 5, 325–329 (2013)

    Google Scholar 

  53. Dindarloo, S.R.; Siami-Irdemoosa, E.: Estimating the unconfined compressive strength of carbonate rocks using gene expression programming. Eur. J. Sci. Res. 135(3), 309–316 (2015)

    Google Scholar 

  54. Behnia, D.; Behnia, M.; Shahriar, K.; Goshtasbi, K.: A New predictive model for rock strength parameters utilizing GEP method. Procedia Engineering 191, 591–599 (2017)

    Google Scholar 

  55. TSE 699: Tabii yapı taşları-muayene ve deney metodları, TSE Publication, Ankara (2009) [in Turkish].

  56. ISRM: Suggested methods for determination of the Schmidt rebound hardness. J. Rock Mech. Mining Sci. & Geomech. Abstracts 15(3), 101–102 (1978)

    Google Scholar 

  57. ISRM: Suggested method for determining sound velocity. Int. J. Rock Mech. Mining Sci. & Geomech. Abstracts 15(2), 53–58 (1978)

    Google Scholar 

  58. ISRM: Suggested methods for determining the uniaxial compressive strength and deformability of rock materials. Int. J. Rock Mech. Mining Sci. & Geomech. Abstracts 16(2), 138–14 (1979)

    Google Scholar 

  59. Karakus, M.; Kumral, M.; Kilic, O.: Predicting elastic properties of intact rocks from index tests using multiple regression modeling. Int. J. Rock Mech. Min. Sci. 42, 323–330 (2005)

    Google Scholar 

  60. Sabatakakis, N.; Koukis, G.; Tsiambaos, G.; Papanakli, S.: Index properties and strength variation controlled by microstructure for sedimentary rocks. Eng. Geol. 97, 80–90 (2008)

    Google Scholar 

  61. Soroush, H.; Qutob, H.: Evaluation of Rock Properties Using Ultrasonic Pulse Technique and Correlating Static to Dynamic Elastic Constants,” The 2nd South Asain Geoscience Conference and Exhibition, GEO India, New Delhi (2011)

  62. Kern, H.: P and S wave anisotropy and shear-wave splitting at pressure and temperature in possible mantle rocks and their relation to the rock fabric. Phys. Earth Planet. Inter. 78(3–4), 245–256 (1993)

    Google Scholar 

  63. Karpuz, C.; Pa-Samehmetoglu, A.G.: Field characterization of weathered Ankara andesites. Eng. Geol. 46(1), 1–17 (1997)

    Google Scholar 

  64. Fener, M.: The effect of rock sample dimension on the P-wave velocity. J. Nondestr. Eval. 30(2), 99–105 (2011)

    Google Scholar 

  65. Ercikdi, B.; Karaman, K.; Cihangir, F.; Yılmaz, T.; Aliyazıcıoglu, S.; Kesimal, A.: Core size effect on the dry and saturated ultrasonic pulse velocity of limestone samples. Ultrasonics 72, 143–149 (2016)

    Google Scholar 

  66. Sonmez, H.; Tuncay, E.; Gokceoglu, C.: Models to predict the uniaxial compressive strength and the modulus of elasticity for Ankara agglomerate. Int. J. Rock Mech. Min. Sci. 41(5), 717–729 (2004)

    Google Scholar 

  67. Monjezi, M.; Khoshalan, H.A.; Razifard, M.: A neuro-genetic network for predicting uniaxial compressive strength of rocks. Geotech. Geol. Eng. 30(4), 1053–1062 (2012)

    Google Scholar 

  68. Shahri, A.A.; Larsson, S.; Johansson, F.: CPT-SPT correlations using artificial neural network approach- A case study in Sweden. Electron. J. Geotech. Eng. 20(28), 13439–13460 (2015)

    Google Scholar 

  69. Shahri, A.A.: Assessment and prediction of liquefaction potential using different artificial neural network models: a case study. Geotech. Geol. Eng. 34(3), 807–815 (2016)

    Google Scholar 

  70. Shahri, A.A.; Asheghi, R.: Optimized developed artificial neural network-based models to predict the blast-induced ground vibration. Innov. Infrastruct. Solut. (2018). https://doi.org/10.1007/s41062-018-0137-4

    Article  Google Scholar 

  71. Esmaeilabadi, R.; Shahri, A.A.: Prediction of site response spectrum under earthquake vibration using an optimized developed artificial neural network model. Adv. Sci. Technol. Res. J. 10(30), 76–83 (2016)

    Google Scholar 

  72. Hornby, G.S.: ALPS: The Age Layered Population Structure for Reducing the Problem of Premature Convergence. Proceedings of the 8th annual conference on Genetic and evolutionary computation (GECCO '06). July 2006 pp:815–822 (2006) https://doi.org/10.1145/1143997.1144142

  73. Hornby, G.S.: Steady-state ALPS for real-valued problems. Proceedings of the 11th annual conference on Genetic and evolutionary computation (GECCO '09). July 2009 pp: 795–802 (2009) https://doi.org/10.1145/1569901.1570011

  74. Hornby, G.S.: A Steady-State Version of the Age-Layered Population Structure EA. In: Riolo R., O'Reilly UM., McConaghy T. (eds) Genetic Programming Theory and Practice VII. Genetic and Evolutionary Computation. Springer, Boston, MA. (2010) https://doi.org/10.1007/978-1-4419-1626-6_6

  75. Lim, T.Y.: Structured population genetic algorithms: a literature survey. Artif. Intell. Rev. 41, 385–399 (2014)

    Google Scholar 

  76. Patnaik, A.K.; Agarwal, L.A.; Panda, M.; Bhuyan, P.K.: Entry capacity modelling of signalized roundabouts under heterogeneous traffic conditions. Transp. Lett. 12(2), 100–112 (2020)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Engin Özdemir.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Özdemir, E. A New Predictive Model for Uniaxial Compressive Strength of Rock Using Machine Learning Method: Artificial Intelligence-Based Age-Layered Population Structure Genetic Programming (ALPS-GP). Arab J Sci Eng 47, 629–639 (2022). https://doi.org/10.1007/s13369-021-05761-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-021-05761-x

Keywords

Navigation