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Deformation Modulus of Rock Masses: An Assessment of the Existing Empirical Equations

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Abstract

Rock mass deformation modulus is an important parameter for all geotechnical applications. However, the determination of rock mass deformation modulus with in situ tests are highly expensive and time consuming. For this reason, rock engineers and engineering geologists have proposed numerous empirical equations based on various rock mass and intact rock properties to estimate the deformation modulus of rock masses. In the present study, an assessment of the existing empirical equations was undertaken. For the purpose of the study, the data obtained from four investigation galleries opened during a dam construction (Artvin Dam, Turkey) were used. A total of 34 plate loading tests were employed in these galleries. The tested rock mass is poor quality tuff. Rock mass rating (RMR89), rock tunnelling quality index (Q) and geological strength index of each test levels were determined. The empirical deformation modulus values of rock mass were calculated by the 26 most cited empirical equations proposed by various researchers. The cross-checks between the measured rock mass deformation modulus and the empirically calculated rock mass modulus values were performed by simple regression analyses. The empirical equations with higher prediction capacity were also examined with root mean square error, values account for and prediction error evaluations. Among the empirical equations compared in this study, two empirical equation giving best performance and other four empirical equations providing acceptable results were determined.

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References

  • Aksoy OC, Geniş M, Aldaş UC, Özacar V, Özer CS, Yılmaz Ö (2012) A comparative study of the determination of rock mass deformation modulus by using empirical approaches. Eng Geol 131–132:19–28

    Article  Google Scholar 

  • Alemdag S, Gurocak Z, Gokceoglu C (2015) A simple regression based approach to estimate deformation modulus of rock masses. J Afr Earth Sci 110:75–80

    Article  Google Scholar 

  • Alemdag S, Gurocak Z, Cevik A, Cabalar AF, Gokceoğlu C (2016) Modeling deformation modulus of a stratified sedimentary rock mass using neural network, fuzzy inference and genetic programming. Eng Geol 203:70–82

    Article  Google Scholar 

  • Aydan Ö, Ulusay R, Kawamoto T (1997) Assessment of rock mass strength for underground excavations. In: Proceedings of the 36th US rock mechanics symposium, New York, pp 777–786

  • Barton N (2002) Some new Q value correlations to assist in site characterization and tunnel design. Int J Rock Mech Min Sci 39:185–216

    Article  Google Scholar 

  • Barton N, Loset F, Lien R, Lune J (1980) Application of Q-system in design decisions concerning dimensions and appropriate support for underground installations. Subsurface Space, Pergamon, pp 553–561

    Google Scholar 

  • 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 47:1091–1103

    Article  Google Scholar 

  • Bieniawski Z (1973) Engineering classification of rock masses. Trans S Afr Inst Civ Eng 15:335–344

    Google Scholar 

  • Bieniawski ZT (1978) Determining rock mass deformability: experience fromcase histories. Int J Rock Mech Min Sci Geomech Abstr 15:237–247

    Article  Google Scholar 

  • Bieniawski ZT (1989) Engineering rock mass classifications. Wiley, New York

    Google Scholar 

  • Chun B, Lee Y, Seo D, Lim B (2006) Correlation of deformation modulus by PMT with RMR and rock mass condition. Tunn Undergr Space Technol 21(3–4):231–232

    Article  Google Scholar 

  • Farmer IW, Kemeny JM (1992) Deficiencies in rock test data. In: Proceedings of international conference on Eurock 1992. Thomas Telford, London. pp 298–303

  • Feng X, Jimenez R (2015) Estimation of deformation modulus of rock masses based on Bayesian model selection and Bayesian updating approach. Eng Geol 199:19–27

    Article  Google Scholar 

  • Galera JM, Alvarez Z, Bieniawski ZT (2005) Evaluation of the deformation modulus of rock masses: comparison between pressure meter and dilatometer tests with RMR predictions. In: Gambin M, Mestat P, Baguelin F (eds) Proceedings of ISP5-PRESSIO 2005. LCPC publication Paris

  • Ghamgosar M, Fahimifar A, Rasouli V (2010) Estimation of rock mass deformation modulus from laboratory experiments in Karun dam. In: Zhao, Laboise, Dudt, Mathier (eds) Proceedings of the international symposium of the international society for rock mechanics. Taylor & Francis Group, pp 805–808

  • Gokceoglu C, Sonmez H, Kayabasi A (2003) Predicting the deformation moduli of rock masses. Int J Rock Mech Min Sci 40:701–710

    Article  Google Scholar 

  • Grimstad E, Barton N (1993) Updating the Q-System for NMT. In: Proceedings of the international symposium on sprayed concrete-modern use of wet mix sprayed concrete for underground support, Oslo, Norwegian Concrete Association

  • Grimstad E, Kankes K, Bhasin R, Magnussen AW, Kaynia A (2002) Rock Mass Q used in designing Reinforced Ribs of Sprayed Concrete and Energy Absorption. 4 th Int. Symp. on Sprayed Concrete, Davos, Switzerland

  • Gürsoy N, Uysal B (1988) Orta Çoruh Havzası Artvin Baraj Yeri Hidrolik Kriko Yükleme Deney Sonuçları. General Directorate of Electrical Power Researchers Survey and Development Administration Report (in Turkish)

  • Hoek E, Brown ET (1997) Practical estimates of rock mass strength. Int J Rock Mech Min Sci 34(8):1165–1186

    Article  Google Scholar 

  • Hoek E, Diederichs M (2006) Empirical estimation of rock mass modulus. Int J Rock Mech Min Sci 43:203–215

    Article  Google Scholar 

  • Işık NS, Ulusay R, Doyuran V (2008) Deformation modulus of heavily jointed-sheared and blocky greywackes by pressuremeter tests: numerical, experimental and empirical assessments. Eng Geol 101:269–282

    Article  Google Scholar 

  • ISRM (International Society for Rock Mechanics) (1981) Part 1. Site characterization, the quantitative description of discontinuities in rock masses. In: Brown ET (ed) ISRM suggested method: rock characterization, testing and monitoring. Pergamon Press, London

  • Kayabasi A, Gokceoglu C, Ercanoglu M (2003) Estimating the deformation modulus of rock masses: a comparative study. Int J Rock Mech Min Sci 40:55–63

    Article  Google Scholar 

  • Mitri HS, Edrissi R, Henning J (1994) Finite element modeling of cable bolted stopes in hard rock ground mines. Presented at the SME annual meeting, New Mexico, Albuquerque pp 94–116

  • Mohammadi H, Rahmannejad R (2010) The estimation of deformation modulus using regression and artificial neural network analyis. Arab J Sci Eng 15:205–217

    Google Scholar 

  • Nicholson GA, Bieniawski ZT (1990) A nonlinear deformation modulus based on rock mass classification. Int J Min Geol Eng 8:181–202

    Article  Google Scholar 

  • Palmström A, Singh R (2001) The deformation modulus of rock masses—comparisons between in situ tests and indirect estimates. Tunn Undergr Space Technol 16(3):115–131

    Article  Google Scholar 

  • Ramamurthy T (2004) A geo-engineering classification for rocks and rock masses. Int J Rock Mech Min Sci 41:89–101

    Article  Google Scholar 

  • Read SAL, Richards LR, Perrin ND (1999) Applicability of the Hoek–Brown failure criterion to New Zealand greywacke rocks. In: Vouille G, Berest P (eds) Proceedings of the nineth international congress on rock mechanics, Paris, August 2, pp 655–660

  • Serafim JL, Pereira JP (1983) Considerations on the geomechanical classification of Bieniawski. In: Proceedings of the symposium on engineering geology and underground openings, Lisboa, Portugal, pp 1133–1144

  • Shen J, Karakus M, Xu C (2012) A comparative study for empirical equation in estimating deformation modulus of rock masses. Tunn Undergr Space Technol 32:245–250

    Article  Google Scholar 

  • 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 36:743–760

    Article  Google Scholar 

  • Sönmez H, Ulusay R (2002) A discussion on the Hoek-Brown failure criterion and suggested modification to the criterion verified by slope stability case studies. Yerbilimleri (Earthsciences) 26:77–99

    Google Scholar 

  • Sonmez H, Gokceoglu C, Ulusay R (2004) Indirect determination of the modulus of deformation of rock masses based on the GSI system. Int J Rock Mech Min Sci 1:849–857

    Article  Google Scholar 

  • Sonmez H, Nefeslioglu HA, Gokceoglu C, Kayabasi A (2006) Estimating of rock modulus: for intact rocks with an artificial neural network and for rock masses with a new empirical equation. Int J Rock Mech Min Sci 43:224–235

    Article  Google Scholar 

  • Tahir M, Mohammad N (2014) Prediction performance and generalization of the empirical estimationof rockmass deformation modulus based on rockmass classification systems. Int J Sci Eng Technol 3(12):1488–1498

    Google Scholar 

  • Zhang L (2017) Evaluation of rock mass deformability using empirical methods—a review. Undergr Space. https://doi.org/10.1016/j.undsp.2017.03.003

    Article  Google Scholar 

  • Zhang L, Einstein HH (2004) Using RQD to estimate the deformation modulus of rock masses. Int J Rock Mech Min Sci 41:337–341

    Article  Google Scholar 

Download references

Acknowledgements

The authors thank Geological Engineers N. Gürsoy and B. Uysal for permission to use the data and the General Directorate of Electrical Power Research Survey and Development Administration for performing the tests.

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Correspondence to C. Gokceoglu.

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Kayabasi, A., Gokceoglu, C. Deformation Modulus of Rock Masses: An Assessment of the Existing Empirical Equations. Geotech Geol Eng 36, 2683–2699 (2018). https://doi.org/10.1007/s10706-018-0491-1

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  • DOI: https://doi.org/10.1007/s10706-018-0491-1

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