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Incorporation of uncertainty in estimating the rock mass uniaxial strength using a fuzzy inference system

  • Mehmet SariEmail author
Original Paper
  • 98 Downloads

Abstract

Due to its complex nature and inherent uncertainty, it is very hard to directly measure the uniaxial strength of jointed rock masses. In rock mechanics, it is a necessity to employ empirical equations and numerical methods for the estimation of rock mass uniaxial strength. In addition to the existing empirical equations and numerical methods, it is essential to pursuit approaches to incorporate uncertainty in estimating rock mass uniaxial strength. One of the promising techniques pertinent to such situations is the fuzzy inference system (FIS). In the application of FIS, it is expected that the problem or system under investigation should be uncertain and fuzzy, and calculations are drawn mostly from judgment and experience, rather than mathematical expressions. This study proposes a new method of estimating the rock mass uniaxial strength using fuzzy sets theory. For this purpose, three dominant elements essential for the determination of rock mass uniaxial strength; i.e., intact rock uniaxial strength, block size, and joint surface condition, were evaluated as fuzzy variables in the analysis involving the assignment of proper membership functions. A logical and systematic combination of three input variables was employed under a Mamdani rule-based FIS environment, which explicitly takes into account the expert knowledge using built lookup charts. To check the accuracy of the FIS model estimates, an extensive data set was compiled from the published sources. This data set used in the analysis covered a wide range of rock mass types in typical rock engineering projects. It was seen that the uniaxial strength values estimated by the proposed FIS model were mostly in fair agreement (R2 = 0.77) with those estimated by well-known empirical equations.

Keywords

Rock mass uniaxial strength Fuzzy logic Fuzzy inference system Empirical equations 

Notes

Acknowledgements

The author is deeply grateful to Prof. Dr. P.H.S.W. Kulatilake (Associate Editor) and two anonymous reviewers for insightful comments and criticism that improved the original manuscript.

References

  1. Aydan O, Dalgic S (1998) Prediction of deformation behaviour of 3 lanes Bolu tunnels through squeezing rocks of North Anotolian Fault Zone (NAFZ). In: Proc. of the Reg. Sym. on Sedim. Rock Eng, Taipei, pp 228–233Google Scholar
  2. Aydan, O., Kawamoto, T. 2000. Assessing mechanical properties of rock masses through RMR rock classification system. In: Proc. of the GeoEng 2000 Symp. Sydney, AustraliaGoogle Scholar
  3. Aydan O, Ulusay R, Tokashiki N (2014) A new rock mass quality rating system: rock mass quality rating (RMQR) and its application to the estimation of geomechanical characteristics of rock masses. Rock Mech Rock Eng 47:1255–1276CrossRefGoogle Scholar
  4. Bahaaddini M, Hagan P, Mitra R, Hebblewhite BK (2016) Numerical study of the mechanical behavior of non-persistent jointed rock masses. Int J Geomech. 16(1):04015035CrossRefGoogle Scholar
  5. Barton N (2000) TBM tunnelling in jointed and faulted rock. Balkema, RotterdamGoogle Scholar
  6. Barton N, Lien R, Lunde J (1974) Engineering classification of rock masses for the design of tunnel support. Rock Mech 6(4):189–239CrossRefGoogle Scholar
  7. Basarir H (2006) Engineering geological studies and tunnel support design at Sulakyurt dam site, Turkey. Engng Geol 86:225–237CrossRefGoogle Scholar
  8. Basarir H, Ozsan A, Karakus M (2005) Analysis of support requirements for a shallow diversion tunnel at Guledar dam site, Turkey. Engng Geol. 81:131–145CrossRefGoogle Scholar
  9. Bhasin R, Grimstad E (1996) The use of stress-strength relationships in the assessment of tunnel stability. Tunell Undergr Space Technol 11:93–98CrossRefGoogle Scholar
  10. Bieniawski ZT (1989) Engineering rock mass classifications. John Wiley & Sons, New YorkGoogle Scholar
  11. Cai M (2011) Rock mass characterization and rock property variability considerations for tunnel and cavern design. Rock Mech Rock Engng. 44(4):379–399CrossRefGoogle Scholar
  12. Cai M, Kaiser PK, Uno H, Tasaka Y, Minami M (2004) Estimation of rock mass strength and deformation modulus of jointed hard rock masses using the GSI system. Int J Rock Mech Min Sci 41:3–19CrossRefGoogle Scholar
  13. Cargill JS, Shakoor A (1990) Evaluation of empirical methods for measuring the uniaxial compressive strength. Int J Rock Mech Min Sci 27:495–503CrossRefGoogle Scholar
  14. Chong WL, Haque A, Gamage RP, Shahinuzzaman A (2013) Modelling of intact and jointed mudstone samples under uniaxial and triaxial compression. Arab J Geosci 6(5):1639–1646CrossRefGoogle Scholar
  15. Dinc OS, Sonmez H, Tunusluoglu C, Kasapoglu KE (2011) A new general empirical approach for the prediction of rock mass strengths of soft to hard rock masses. Int J Rock Mech Min Sci 48:650–665CrossRefGoogle Scholar
  16. Edelbro C, Sjoberg J, Nordlund E (2006) A quantitative comparison of strength criteria for hard rock masses. Tunell Undergr Space Technol. 22:57–68CrossRefGoogle Scholar
  17. Elmo D, Stead D (2010) An integrated numerical modelling–discrete fracture network approach applied to the characterisation of rock mass strength of naturally fractured pillars. Rock Mech Rock Engng 43(1):3–19CrossRefGoogle Scholar
  18. Genis M, Basarir H, Ozarslan A, Bilir E, Balaban E (2007) Engineering geological appraisal of the rock masses and preliminary support design, Dorukhan Tunnel, Zonguldak, Turkey. Engng Geol. 92:14–26CrossRefGoogle Scholar
  19. Genis M, Colak B (2015) Stability assessment of the Gokgol karstic cave (Zonguldak, Turkey) by analytical and numerical methods. Rock Mech Rock Eng 48:2383–2403CrossRefGoogle Scholar
  20. Gokceoglu C, Sonmez H, Kayabasi A (2003) Predicting the deformation moduli of rock masses. Int J Rock Mech Min Sci 40:701–710CrossRefGoogle Scholar
  21. Gokceoglu C, Zorlu K (2004) A fuzzy model to predict the uniaxial compressive strength and the modulus of elasticity of a problematic rock. Engng Appl Artf Intll 17:61–72CrossRefGoogle Scholar
  22. Grima, M.A. 2000. Neuro-fuzzy modeling in engineering geology. A.A. Balkema:RotterdamGoogle Scholar
  23. Grima MA, Babuska R (1999) Fuzzy model for the prediction of unconfined compressive strength of rock samples. Int J Rock Mech Min Sci 36:339–349CrossRefGoogle Scholar
  24. Gurocak Z (2011) Analyses of stability and support design for a diversion tunnel at the Kapikaya dam site, Turkey. Bull Engng Geol Environ 70:41–52CrossRefGoogle Scholar
  25. Gurocak Z, Alemdag S, Zaman MM (2008) Rock slope stability and excavatability assessment of rocks at the Kapikaya dam site, Turkey. Engng Geol. 96:17–27CrossRefGoogle Scholar
  26. Gurocak Z, Solanki P, Zaman MM (2007) Empirical and numerical analyses of support requirements for a diversion tunnel at the Boztepe dam site, eastern Turkey. Engng Geol. 91:194–208CrossRefGoogle Scholar
  27. He P, Kulatilake PHSW, Liu D, He M (2017) Development of a new 3-D coal mass strength criterion. Int J Geomech 17(3):04016067CrossRefGoogle Scholar
  28. He P, Kulatilake PHSW, Yang X, Liu D, He M (2018) Elaborative comparison of nine intact rock strength criteria using polyaxial intact coal strength data obtained through PFC3D simulations. Acta Geotechnica Int J 13(2):419–445Google Scholar
  29. Heidari M, Mohseni H, Jalali SH (2018) Prediction of uniaxial compressive strength of some sedimentary rocks by fuzzy and regression models. Geotech Geol Engng. 36(1):401–412CrossRefGoogle Scholar
  30. Hellendoorn H, Thomas C (1993) Defuzzification in fuzzy controllers. J Intell Fuzzy Syst 1:109–123Google Scholar
  31. Hoek E, Brown ET (1997) Practical estimates of rock mass strength. Int J Rock Mech Min Sci 34:1165–1186CrossRefGoogle Scholar
  32. Hoek, E., Carranza-Torres, C.T., Corkum, B. 2002. Hoek-Brown failure criterion-2002 edition. In: Proc. 5th American rock Mech. Symp., Toronto; p. 267–273Google Scholar
  33. Hoek E., Carter T.G., Diederichs M.S. 2013. Quantification of the geological strength index chart. In: 47th US rock mechanics/geomechanics symposium held in San Francisco, June 23–26Google Scholar
  34. ISRM, 1981. Suggested methods for determining the uniaxial compressive strength and deformability of rock materials. In: Brown ET, editor. Rock characterization, testing and monitoring-ISRM suggested methods. Pergamon Press: OxfordGoogle Scholar
  35. Itasca Consulting Group Inc. (Itasca) 2004. 3DEC (3-Dimensional distinct element code), version 3.0, Itasca, MinneapolisGoogle Scholar
  36. Itasca Consulting Group Inc. (Itasca) 2008. PFC3D (particle flow code in 3 dimensions), version 4.0, Itasca, MinneapolisGoogle Scholar
  37. Justo JL, Justo E, Durand P, Azanon JM (2006) The foundation of a 40-storey tower in jointed basalt. Int J Rock Mech Min Sci 43:267–281CrossRefGoogle Scholar
  38. Kalamaras, G.S., Bieniawski, Z.T. 1993. A rock mass strength concept for coal seams. Proc. 12th Conf. Ground Control in Mining, Morgantown, pp. 274–83Google Scholar
  39. Kalamaras GS, Bieniawski ZT (1995) A rock mass strength concept for coal seams incorporating the effect of time. Proc 8th Int ISRM Congr Tokyo 1:295–302Google Scholar
  40. Karakus M, Tutmez B (2006) Fuzzy and multiple regressions modelling for evaluation of intact rock strength based on point load, Schmidt hammer and sonic velocity. Rock Mech Rock Eng 39:45–57CrossRefGoogle Scholar
  41. Kaya A, Bulut F, Alemdag S, Sayin A (2011) Analysis of support requirements for a tunnel portal in weak rock: a case study from Turkey. Sci Res Essays 6:6566–6583Google Scholar
  42. Kulatilake PHSW (1985) Estimating elastic constants and strength of discontinuous rock. J Geotech Eng 111(7):847–864CrossRefGoogle Scholar
  43. Kulatilake PHSW (2016) Physical, empirical and numerical modeling of jointed rock mass strength. In: Feng XT (ed) Rock mechanics and engineering, vol 2. CRC Press, London, pp 367–394Google Scholar
  44. Kulatilake PHSW, He W, Um J, Wang H (1997) A physical model study of jointed rock mass strength under uniaxial compressive loading. Int J Rock Mech & Min Sci. 34(165, 3–4)Google Scholar
  45. Kulatilake PHSW, Park J, Malama B (2006) A new rock mass strength criterion for biaxial loading conditions. Geotech Geol Engng. 24(4):871–888CrossRefGoogle Scholar
  46. Kulatilake PHSW, Park J, Um J (2004) Estimation of rock mass strength and deformability in 3-D for a 30m cube at a depth of 485m at Äspö Hard Rock Laboratory. Sweden Int J Geotech Geol Engng 22(3):313-30Google Scholar
  47. Kulatilake, P.H.S.W., Wang, S., Stephansson, O. 1993. Effect of finite size joints on deformability of jointed rock at the three-dimensional level. Int J Rock Mech & Min Sci 30(5):479–501Google Scholar
  48. Mas Ivars D, Pierce ME, Darcel C, Reyes-Montes J, Potyondy DO, Young RP, Cundall PA (2011) The synthetic rock mass approach for jointed rock mass modelling. Int J Rock Mech Min Sci 48(2):219–244CrossRefGoogle Scholar
  49. Mehranpour MH, Kulatilake PHSW (2016) Comparison of six major intact rock criteria using a particle flow approach under true triaxial stress conditions. Int J Geomech Geophys Geo-Energy Geo-Resources 2:203–229CrossRefGoogle Scholar
  50. Mehranpour MH, Kulatilake PHSW, Xingen M, He M (2018) Development of new three-dimensional rock mass strength criteria. Rock Mech Rock Eng 51(11):3537–3561CrossRefGoogle Scholar
  51. Mishra DA, Basu A (2013) Estimation of uniaxial compressive strength of rock materials by index tests using regression analysis and fuzzy inference system. Enging Geol 160:54–68CrossRefGoogle Scholar
  52. Mishra DA, Srigyan M, Basu A, Rokade PJ (2015) Soft computing methods for estimating the uniaxial compressive strength of intact rock from index tests. Int J Rock Mech Min Sci 80:418–424CrossRefGoogle Scholar
  53. Morelli GL (2015) Variability of the GSI index estimated from different quantitative methods. Geotech Geol Engng 33:983–995CrossRefGoogle Scholar
  54. Palmström, A. 1995. RMi-a rock mass characterization system for rock engineering purposes. Ph.D. thesis, Univ. of OsloGoogle Scholar
  55. Ramamurthy, T. 1986. Stability of rock mass. 8th annual lecture. Indian Geotech J, 1–74Google Scholar
  56. Ross TJ (2010) Fuzzy logic with engineering applications. McGraw-Hill, New YorkCrossRefGoogle Scholar
  57. Russo G (2009) A new rational method for calculating the GSI. Tunell Undergr Space Technol. 24(1):103–111CrossRefGoogle Scholar
  58. Sari M (2009) The stochastic assessment of strength and deformability characteristics for a pyroclastic rock mass. Int J Rock Mech & Min Sci. 46:613–626CrossRefGoogle Scholar
  59. Sari M, Karpuz C (2006) Rock variability and establishing confining pressure levels for triaxial tests on rocks. Int J Rock Mech & Min Sci. 43:328–335CrossRefGoogle Scholar
  60. Sari M, Karpuz C, Ayday C (2010) Estimating rock mass properties using Monte Carlo simulation: Ankara andesites. Comput Geosci 36:959–969CrossRefGoogle Scholar
  61. Sheorey PR (1997) Empirical rock failure criteria. Balkema, RotterdamGoogle Scholar
  62. Singh R, Vishal V, Singh TN, Ranjith PG (2013) 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 23:499–506CrossRefGoogle Scholar
  63. Sonmez H, Ulusay R (1999) Modifications to the geological strength index (GSI) and their applicability to stability of slopes. Int J Rock Mech & Min Sci. 36:743–760CrossRefGoogle Scholar
  64. Stewart, S. 2007. Rock mass strength and deformability of un-weathered closely jointed New Zealand greywacke. Ph.D. thesis, The University of CantenburyGoogle Scholar
  65. Tzamos S, Sofianos AI (2007) A correlation of four rock mass classification systems through their fabric indices. Int J Rock Mech & Min Sci. 44:477–495CrossRefGoogle Scholar
  66. Verma AK, Singh TN (2010) Modeling of a jointed rock mass under triaxial conditions. Arab J Geosci 3(1):91–103CrossRefGoogle Scholar
  67. Verwaal W, Mulder A (1993) Estimating rock strength with the Equotip hardness tester. Int J Rock Mech Min Sci & Geomech Abst 30:659–662CrossRefGoogle Scholar
  68. Wu Q, Kulatilake PHSW (2012) REV and its properties on fracture system and mechanical properties, and an orthotropic constitutive model for a jointed rock mass in a dam site in China. Comput Geotech 43:124–142CrossRefGoogle Scholar
  69. Yesiloglu-Gultekin N, Gokceoglu C, Sezer EA (2013) Prediction of uniaxial compressive strength of granitic rocks by various non-linear tools and comparison of their performances. Int J Rock Mech & Min Sci 62:113–122CrossRefGoogle Scholar
  70. Yudhbir, R.K., Lemanza, W., Prinzl, F. 1983. An empirical failure criterion for rock masses. In: Proc. the 5th Int. Congress on Rock Mech, Melbourne, vol. 1, p. B1–B8Google Scholar
  71. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353CrossRefGoogle Scholar
  72. Zorlu K, Gokceoglu C, Sonmez H (2004) Prediction of the uniaxial compressive strength of a greywacke by fuzzy inference system. Eng Geol Infra Plan Europe:203–210Google Scholar

Copyright information

© Saudi Society for Geosciences 2019

Authors and Affiliations

  1. 1.Department of Mining EngineeringAksaray UniversityAksarayTurkey

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