Skip to main content
Log in

Function development for appraising brittleness of intact rocks using genetic programming and non-linear multiple regression models

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

Brittleness of rock is one of the most critical features for design of underground excavation project. Therefore, proper assessing of rock brittleness can be very useful for designers and evaluators of geotechnical applications. In this study, feasibility of genetic programming (GP) model and non-linear multiple regression (NLMR) in predicting brittleness of intact rocks is examined. For this purpose, a dataset developed by conducting various rock tests including uniaxial compressive strength, Brazilian tensile strength, unit weight and brittleness via punch penetration on rock samples gathered from 48 tunnels projects around the world is utilized herein. Considering multiple inputs, several GP models were constructed to estimate brittleness index of the rock and finally, the best GP model was selected. Note that, GP can make an equation for predicting output of the system using model inputs. To show applicability of the developed GP model, non-linear multiple regression (NLMR) was also applied and developed. Considering some model performance indices, performance prediction of the GP and NLMR models were evaluated and it was found that the GP model is superior to NLMR one. Based on coefficient of determination (R 2) of testing datasets, by proposing GP model, it can be improved from 0.882 (obtained by NLMR model) to 0.904. It is worth mentioning that the proposed predictive models in this study should be planned and used for the similar types of rock and the established inputs ranges.

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

Similar content being viewed by others

References

  1. Yagiz S (2009) Assessment of brittleness using rock strength and density with punch penetration test. Tunn Undergr Space Technol 24(1):66–74

    Article  MathSciNet  Google Scholar 

  2. Hetenyi M (1966) Handbook of experimental stress analysis. Wiley, New York, p 115

    Google Scholar 

  3. Ramsay JG (1967) Folding and fracturing of rocks. McGraw-Hill, London

    Google Scholar 

  4. Hucka V, Das B (1974) Brittleness determination of rocks by different methods. Int J Rock Mech Min Sci Geomech Abstr 11:389–392

    Article  Google Scholar 

  5. Gong QM, Zhao J (2007) Influence of rock brittleness on TBM penetration rate in Singapore granite. Tunnel Undergr Sp Technol 22(3):317–324

    Article  Google Scholar 

  6. Kahraman S (2002) Correlation of TBM and drilling machine performances with rock brittleness. Eng Geol 65(4):269–283

    Article  Google Scholar 

  7. Altindag R (2002) The evaluation of rock brittleness concept on rotary blast hole drills. J S Afr Inst Min Metall 102(1):61–66

    Google Scholar 

  8. Protodyakonov MM (1963) Mechanical properties and drillability of rocks. In: Proceedings of the fifth symposium rock mechanics. University of Minnesota, USA

  9. Blindheim OT, Bruland A (1998) Boreability testing, Norwegian TBM tunneling 30 years of experience with TBMs in Norwegian tunneling, Norwegian Soil and Rock Engineering Association. Publication No. 11, pp 29–34. Trondheim, Norway

  10. Yagiz S (2002) Development of rock fracture and brittleness indices to quantify the effects of rock mass features and toughness in the CSM Model basic penetration for hard rock tunneling machines. Ph.D. thesis, p 289. Colorado School of Mines

  11. Copur H, Bilgin N, Tuncdemir H, Balci C (2003) A set of indices based on indentation test for assessment of rock cutting performance and rock properties. J S Afr Inst Min Metal 103(9):589–600

    Google Scholar 

  12. Yagiz S, Gokceoglu C (2010) Application of fuzzy inference system and nonlinear regression models for predicting rock brittleness. Expert Syst Appl 37(3):2265–2272

    Article  Google Scholar 

  13. Altindag R, Guney A (2010) Predicting the relationships between brittleness and mechanical properties (UCS, TS and SH) of rocks. Sci Res Essays 5(16):2107–2118

    Google Scholar 

  14. Khandelwal M, Monjezi M (2013) Prediction of flyrock in open pit blasting operation using machine learning method. Int J Min Sci Technol 23(3):313–316

    Article  Google Scholar 

  15. Khandelwal M (2011) Blast-induced ground vibration prediction using support vector machine. Eng Comput 27(3):193–200

    Article  Google Scholar 

  16. Liang M, Mohamad ET, Faradonbeh RS, Armaghani DJ, Ghoraba S (2016) Rock strength assessment based on regression tree technique. Eng Comput 32(2):343–354

    Article  Google Scholar 

  17. Meulenkamp F, Alvarez Grima M (1999) Application of neural networks for the prediction of the unconfined compressive strength (UCS) from Equotip hardness. Int J Rock Mech Min Sci 36(1):29–39

    Article  Google Scholar 

  18. Tonnizam Mohamad E, Armaghani DJ, Hasanipanah M, Murlidhar BR, Alel MNA (2016) Estimation of air-overpressure produced by blasting operation through a neuro-genetic technique. Environ Earth Sci 75(2):174

    Article  Google Scholar 

  19. Khandelwal M, Kankar PK, Harsha SP (2010) Evaluation and prediction of blast induced ground vibration using support vector machine. Min Sci Technol 20(1):64–70

    Google Scholar 

  20. Hajihassani M, Armaghani DJ, Monjezi M, Mohamad ET, Marto A (2015) Blast-induced air and ground vibration prediction: a particle swarm optimization-based artificial neural network approach. Environ Earth Sci 74(4):2799–2817

    Article  Google Scholar 

  21. Armaghani DJ, Raja Shoib RSNS, Faizi K, Rashid ASA (2015) Developing a hybrid PSO-ANN model for estimating the ultimate bearing capacity of rock-socketed piles. Neural Comput Appl. doi:10.1007/s00521-015-2072-z

    Google Scholar 

  22. Armaghani DJ, Mohamad ET, Hajihassani M, Yagiz S, Motaghedi H (2016) Application of several non-linear prediction tools for estimating uniaxial compressive strength of granitic rocks and comparison of their performances. Eng Comput 32(2):189–206

    Article  Google Scholar 

  23. Yagiz S, Sezer EA, Gokceoglu C (2012) Artificial neural networks and nonlinear regression techniques to assess the influence of slake durability cycles on the prediction of uniaxial compressive strength and modulus of elasticity for carbonate rocks. Int J Numer Anal Methods 36:1636–1650

    Article  Google Scholar 

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

    Article  Google Scholar 

  25. Li WX, Dai LF, Houa XB, Lei W (2007) Fuzzy genetic programming method for analysis of ground movements due to underground mining. Int J Rock Mech Min Sci 44:954–961

    Article  Google Scholar 

  26. Baykasoglu A, Gullu H, Canakci H, Ozbakır L (2008) Prediction of compressive and tensile strength of limestone via genetic programming. Expert Syst Appl 35:111–123

    Article  Google Scholar 

  27. Beiki M, Bashari A, Majdi A (2010) Genetic programming approach for estimating the deformation modulus of rock mass using sensitivity analysis by neural network. Int J Rock Mech Min Sci 47(7):1091–1103

    Article  Google Scholar 

  28. Asadi M, Eftekhari M, Bagheripour MH (2011) Evaluating the strength of intact rocks through genetic programming. Appl Soft Comput 11(2):1932–1937

    Article  Google Scholar 

  29. Shirani Faradonbeh R, Monjezi M, Armaghani DJ (2016) Genetic programing and non-linear multiple regression techniques to predict backbreak in blasting operation. Eng Comput 32(1):123–133

    Article  Google Scholar 

  30. ISRM (1979) Suggested methods for determining the uniaxial compressive strength and deformability of rock materials. Int J Rock Mech Min Sci Geomech Abstr 16:135–140

    Google Scholar 

  31. Jaeger JC (1967) Failure of rocks under tensile strength. Int J Rock Mech Min Sci 4:219–227

    Article  Google Scholar 

  32. ISRM (1978) Suggested methods for determining tensile strength of rock materials. Int J Rock Mech Min Sci Geomech Abstr 15:101–103

    Google Scholar 

  33. Handewith HJ (1970) Predicting the economic success of continuous tunneling and hard rock. 71st Annual general meeting of the CIM, vol 63, pp 595–599

  34. Dollinger GL, Handewith HJ (1998) Breeds CD. Use of the punch test for estimating TBM performance. Tunnel Undergr Sp Technol 13(4):403–408

    Article  Google Scholar 

  35. Pandey DS, Pan I, Das S, Leahy JJ, Kwapinski W (2015) Multi-gene genetic programming based predictive models for municipal solid waste gasification in a fluidized bed gasifier. Bioresour Technol 179:524–533

    Article  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  37. Cramer NL (1985) A representation for the adaptive generation of simple sequential programs. In: Grefenstette J (ed) Proceedings of the first international conference on genetic algorithms and their applications, Erlbaum

  38. Koza JR (1992) Genetic programming: on the programming of computers by means of natural selection. MIT Press, Cambridge

    MATH  Google Scholar 

  39. Karakus M (2011) Function identification for the intrinsic strength and elastic properties of granitic rocks via genetic programming (GP). Comput Geosci 37(9):1318–1323

    Article  Google Scholar 

  40. Walker M (2001) Introduction to genetic programming. University of Montana, Tech. Np

    Google Scholar 

  41. Nazari A, Rajeev P, Sanjayan JG (2015) Modelling of upheaval buckling of offshore pipeline buried in clay soil using genetic programming. Eng Struct 101:306–317

    Article  Google Scholar 

  42. Swingler K (1996) Applying neural networks: a practical guide. Academic Press, New York

    Google Scholar 

  43. Armaghani DJ, Mohamad ET, Momeni E, Monjezi M, Narayanasamy MS (2016) Prediction of the strength and elasticity modulus of granite through an expert artificial neural network. Arab J Geosci 9(1):1–16

    Article  Google Scholar 

  44. Bahrami A, Monjezi M, Goshtasbi K, Ghazvinian A (2011) Prediction of rock fragmentation due to blasting using artificial neural network. Eng Comput 27(2):177–181

    Article  Google Scholar 

  45. Armaghani DJ, Hajihassani M, Sohaei H, Mohamad ET, Marto A, Motaghedi H, Moghaddam MR (2015) Neuro-fuzzy technique to predict air-overpressure induced by blasting. Arab J Geosci 8(12):10937–10950

    Article  Google Scholar 

  46. Yagiz S, Gokceoglu C, Sezer E, Iplikci S (2009) Application of two non-linear prediction tools to the estimation of tunnel boring machine performance. Eng Appl Artif Intel 22(4):808–814

    Article  Google Scholar 

  47. Inc SPSS (2007) SPSS for windows (version 160). SPSS Inc, Chicago

    Google Scholar 

  48. Yang Y, Zang O (1997) A hierarchical analysis for rock engineering using artificial neural networks. Rock Mech Rock Eng 30:207–222

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Manoj Khandelwal.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khandelwal, M., Shirani Faradonbeh, R., Monjezi, M. et al. Function development for appraising brittleness of intact rocks using genetic programming and non-linear multiple regression models. Engineering with Computers 33, 13–21 (2017). https://doi.org/10.1007/s00366-016-0452-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-016-0452-3

Keywords

Navigation