Abstract
Geological Strength Index (GSI) is an important parameter for estimating rock mass properties. GSI can be estimated from quantitative GSI chart, as an alternative to the direct observational method which requires vast geological experience of rock. GSI chart was developed from past observations and engineering experience, with either empiricism or some theoretical simplifications. The GSI chart thereby contains model uncertainty which arises from its development. The presence of such model uncertainty affects the GSI estimated from GSI chart at a specific site; it is, therefore, imperative to quantify and incorporate the model uncertainty during GSI estimation from the GSI chart. A major challenge for quantifying the GSI chart model uncertainty is a lack of the original datasets that have been used to develop the GSI chart, since the GSI chart was developed from past experience without referring to specific datasets. This paper intends to tackle this problem by developing a Bayesian approach for quantifying the model uncertainty in GSI chart when using it to estimate GSI at a specific site. The model uncertainty in the GSI chart and the inherent spatial variability in GSI are modeled explicitly in the Bayesian approach. The Bayesian approach generates equivalent samples of GSI from the integrated knowledge of GSI chart, prior knowledge and observation data available from site investigation. Equations are derived for the Bayesian approach, and the proposed approach is illustrated using data from a drill and blast tunnel project. The proposed approach effectively tackles the problem of how to quantify the model uncertainty that arises from using GSI chart for characterization of site-specific GSI in a transparent manner.
Similar content being viewed by others
References
Ang AH-S, Tang WH (2007) Probability concepts in engineering: emphasis on applications to civil and environmental engineering. Wiley, New York
Baecher GB, Christian JT (2003) Reliability and statistics in geotechnical engineering. Wiley, Hoboken, p 605
Bieniawski ZT (1989) Engineering rock mass classification. Wiley Interscience, New York
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 Mining Sci 41(1):3–19
Cao Z, Wang Y, Li D (2016) Quantification of prior knowledge in geotechnical site characterization. Eng Geol 203:107–116
Carter TG (2010) Applicability of classifications for tunneling valuable for improving insight, but problematic for contractual support definition or final design. In: Proceedings world tunnelling conference (WTC 2010), 36th ITA Congress. Vancouver, Paper 00401, Session 6c, p 8
Carter TG and Marinos V (2014) Use of GSI for rock engineering design. In: Proceedings 1st international conference on applied empirical design methods in mining, Lima-Peru, 9–11th June, 19
Cetin KO, Kiureghian AD, Seed RB (2002) Probabilistic models for the initiation of seismic soil liquefaction. Struct Saf 24:67–82
Deere DU (1963) Technical description of rock cores for engineering purposes. Felsmechanik und Ingenieurgeologie (Rock Mechanics and Engineering Geology) 1(1):16–22
Ditlevsen O (1981) Uncertainty modeling with applications to multidimensional civil engineering systems. McGraw-Hill, New York
Hoek E, Marinos P (2000) Predicting tunnel squeezing problems in weak heterogeneous rock masses. Tunnels and Tunnelling International. Part 1—November 2000, Part 2—December, 2000
Hoek E, Kaiser PK, Bawden WF (1995) Support of underground excavations in hard rock. A.A. Balkema, Rotterdam, p 215
Hoek E, Carter TG, Diederichs MS (2013) Quantification of the Geological Strength Index Chart. Paper prepared for presentation at the 47th US Rock Mechanics/Geomechanics Symposium held in San Francisco
Marinos P, Hoek E (2000) GSI—a geologically friendly tool for rock mass strength estimation. In: Proceedings GeoEng2000 conference, Melbourne, Australia
Marinos P, Marinos V, Hoek E (2007) Geological Strength Index (GSI). A characterization tool for assessing engineering properties for rock masses. In: Romana, Perucho, Olalla (eds) Underground works under special conditions. Taylor and Francis, Lisbon, pp 13–21
Mitchell JK, Soga K (2005) Fundamentals of soil behavior. Wiley, Hoboken
Morelli GL (2015) Variability of the GSI index estimated from different quantitative methods. Geotech Geol Eng 33:983–995
Moss RES, Seed RB, Kayen RE, Steward JP, Der Kiureghian A (2006) CPT-based probabilistic and deterministic assessment of in situ seismic soil liquefaction potential. J Geotech Geoenvironmental Eng 132(8):1032–1051
Phoon KK, Kulhawy FH (1999) Evaluation of geotechnical property variability. Can Geotech J 36(4):625–639
Ronold KO, Bjerager P (1992) Model uncertainty representation in geotechnical reliability analyses. J Geotech Eng 118(3):363–376
Russo G (2007) Improving the reliability of GSI estimation: the integrated GSI-RMi system. In: Proceedings I.S.R.M. workshop ‘‘Underground Works under Special Conditions’’, Madrid, pp 123–130
Sivia DS, Skilling J (2006) Data analysis: a Bayesian tutorial. Oxford University Press, New York
Sonmez H, Ulusay R (1999) Modifications to the geological strength index (GSI) and their applicability to the stability of slopes. Int J Rock Mech Mining Sci 36:743–760
Walpole RE, Myers RH, Myers SL (1998) Probability and statistics for engineers and scientists. Prentice Hall, Upper Saddle River
Wang Y, Aladejare AE (2015) Selection of site-specific regression model for characterization of uniaxial compressive strength of rock. Int J Rock Mech Min Sci 75:73–81
Wang Y, Cao Z (2013) Probabilistic characterization of Young’s modulus of soil using equivalent samples. Eng Geol 159:106–118
Wang Y, Au SK, Cao Z (2010) Bayesian approach for probabilistic characterization of sand friction angles. Eng Geol 114(3–4):354–363
Wang Y, Huang K, Cao ZJ (2013) Probabilistic identification of underground soil stratification using cone penetration tests. Can Geotech J 50(7):766–776
Wang Y, Cao ZJ, Li DQ (2016) Bayesian perspective on geotechnical variability and site characterization. Eng Geol 203:117–125
Acknowledgements
The authors would like to thank the two anonymous reviewers for their constructive and valuable comments, which helped to improve the quality of the paper. The work described in this paper was supported by grants from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. 9042172 (CityU 11200115) and Project No. 8730035 (CityU8/CRF/13G)) and a Strategic Research Grant from City University of Hong Kong (Project No. 7004178). The financial supports are gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, Y., Aladejare, A.E. Evaluating Variability and Uncertainty of Geological Strength Index at a Specific Site. Rock Mech Rock Eng 49, 3559–3573 (2016). https://doi.org/10.1007/s00603-016-0957-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00603-016-0957-5