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Part of the book series: Rock Mechanics ((ROCK,volume 12))

Summary

Probabilistic and Statistical Methods in Engineering Geology — Part I. Uncertainty about geologic conditions and about geotechnical parameters is probably the most distinctive characteristic of geotechnical engineering and engineering geology. Evidence for this are the role of engineering judgement and design approaches that cannot be found in any other engineering discipline. However, a more quantitative and systematic treatment of uncertainty through the use of statistical and probabilistic methods can greatly aid the engineering geologist and geotechnical engineer. In this Supplementum 12 a first part of a paper on this topic will be presented, describing sources of uncertainty and their consequences. Traditional approaches for analyzing uncertainty and their deficiencies are discussed leading to the conclusion that they can gain from being complemented by probabilistic and statistical methods (Part 11 of the paper describing the details of such methods will be pubhshed in a future issue of Rock Mechanics).

Zusammenfassung

Wahrscheinlichkeitstheoretische und statistische Methoden in der Baugeologie — Teil 1. Unsicherheit über geologische Zustände und geotechnische Parameter ist vermutlich das bezeichnendste Merkmal der Geotechnik und der Baugeologie. Dies zeigt sich in der Rolle, welche die Erfahmng spielt, und in Entwurfsprozessen, die in keiner anderen Ingenieurdisziplin zu finden sind. Was aber oft fehlt, ist eine quantitative und systematische Behandlung der Unsicherheit. Durch Einfühmng probabilistischer und statistischer Methoden kann dieser Mangel behoben werden. Der hier publizierte Artikel ist der erste Teil einer Behandlung dieses Themas. Dabei wird zuerst auf die Quellen der Unsicherheit und deren Folgen eingegangen. Dann werden die traditionellen Verfahren zur Behandlung der Unsicherheit diskutiert, was zum Schluß fuhrt, daß sie durch probabilistische und statistische Methoden komplementiert und verbessert werden körmen. (Teil II dieses Artikels, der in einer zukünftigen Ausgabe von Rock Mechanics veröffentlicht werden wird, wird diese Methoden im Detail behandeln).

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References

  • Alonzo, E. E.: Risk Analysis of Slopes and Its Application to Slopes in the Canadian Sensitive Clays. Geotechnique 26, 453–472 (1976).

    Article  Google Scholar 

  • Ashley, D. B., Tse, E. C, Einstein, H. K: Advantages and Limitations of Adaptable Tunnel Design and Construction Methods. Proceedings, Rapid Excavation and Tunneling Conference, Atlanta, 989–1011, 1979.

    Google Scholar 

  • Ashley, D. B., Veneziano, D., Einstein, H. K, Chan, M. H.: Geologic Prediction and Updating in Tunneling — A Probabilistic Approach. Proceedings, 22nd U.S. Symposium on Rock Mechanics, MIT, 1981.

    Google Scholar 

  • Baecher, G. B.: Site Exploration — A Probabilistic Approach. Ph. D. Thesis, MIT, 1972.

    Google Scholar 

  • Baecher, G. B.: Analyzing Exploration Strategies. In: C. H. Dowding (ed.), Site Characterization and Exploration, ASCE/NSF, 1978.

    Google Scholar 

  • Baecher, G. B.: Progressively Censored Sampling of Rock Joint Traces. Mathematical Geology 12, 33–40(1980).

    Article  Google Scholar 

  • Baecher, G. B.: FOSM Methods in Geotechnical Analysis. In: Baecher, G. B. and Rackwitz, R., Notes on Geotechnical Reliability, from a short course given at the Computational Mechanics Centre, Southampton, 1980.

    Google Scholar 

  • Baecher, G. B., Lanney, N. A.: Sampling for Joint Persistence. 19th U.S. National Symposium on Rock Mechanics, 1978.

    Google Scholar 

  • Barnett, K: Comparative Statistical Inference. New York: John Wiley & Sons 1973.

    Google Scholar 

  • Brinch-Hansen, J., Lundgren, H.: Hauptprobleme der Bodenmechanik. Berlin, Gôttingen, Heidelberg: Springer 1960.

    Google Scholar 

  • Call, R. D., Kim, Y. C: Composite Probability of Instabty for Optimizing Pit Slope Design. 19th U.S. Symposium on Rock Mechanics, 1978.

    Google Scholar 

  • Call, R. D, Nicholas, D. K: Prediction of Step Path Failure Geometry for Slope Stability Analysis. 19th U.S. Symposium on Rock Mechanics, 1978.

    Google Scholar 

  • CANMET.: Pit Slope Manual. Department of Energy, Mines and Mineral Resources, 1977.

    Google Scholar 

  • Casagrande, A.: The Role of the “Calculated Risk” in Earthwork and Foundation Engineering. Proceedings, ASCE 91, No. SM4, 1–40 (1965).

    Google Scholar 

  • Chan, M. K: A Geological Prediction and Updating Model in Tunneling. M. S. Thesis, MIT, 1981.

    Google Scholar 

  • Cruden, D. M.: Describing the Size of Discontinuities. Int. J. Rock. Mech. and Min. Sc. 14, 133–137(1977).

    Article  Google Scholar 

  • Einstein, H. H., Vick, G. G.: Geologic Model for a Tunnel Cost Model. Proceedings, 2nd Rapid Excavation and Tunneling Conference, San Francisco, 1701–1720, 1974.

    Google Scholar 

  • Einstein, H. H., Markow, M. J., Chew, K: Assessing the Value of Exploration for Underground Gas Storage. Proceedings, Rockstore, 1977.

    Google Scholar 

  • Einstein, H. H., Labreche, D. A., Markow, M. J., Baecher, G. B.: Decision Analysis Applied to Rock Tunnel Exploration. Engineering Geology 12, 143–161 (1978).

    Article  Google Scholar 

  • Einstein, H. K, et al.: Risk Analysis for Rock Slopes in Open Pit Mines. Parts I-V, USBM Technical Report J0275015, 1980.

    Google Scholar 

  • Epstein, B.: Tmncated Life Tests in the Exponential Case. Annals of Mathematical Statistics 25, 555 (1954).

    Article  Google Scholar 

  • Fisher, R. A.: The Tmncated Normal Distribution. British Association of Advanced Science. Math. Tables, I;XXXIII-XXXIV, 1931.

    Google Scholar 

  • Glynn, E. F.: A Probabstic Approach to the Stabihty of Rock Slopes. Ph. D. Dissertation, MIT, 1979.

    Google Scholar 

  • Habib, P.: Le coefficient de sécurité dans les ouvrages au rocher. Presidential adress. Proceedings, 4th Int. Congr. of the ISRM, Montreux, 1979.

    Google Scholar 

  • Hald, A.: Maximum Likelihood Estimators of the Parameters of a Normal Distribution Truncated at a Known Point. Skand. Aktuarietidskr. 32, 119 (1949).

    Google Scholar 

  • Hasofer, A. M., Lind, N C.: Exact and Invariant Second Moment Code Format. ASCE Journal of the Engineering Mechanics Division. 100, 111–121 (1974).

    Google Scholar 

  • Herget, G.: Analysis of Discontinuity Orientation for a Probabilistic Slope Stability Design. 19th U.S. Symposium on Rock Mechanics, 1978.

    Google Scholar 

  • Hoek, E., Bray, J. W.: Rock Slope Engineering. Inst, of Mining and Metallurgy, London, 1973.

    Google Scholar 

  • Hogarth, R. M.: Cognitive Processes and the Assessment of Subjective Probability Distribution. J. of American Statistical Assessment 70, 271–289 (1975).

    Article  Google Scholar 

  • Jennings, J. E.: A Mathematical Theory for the Calculation of the Stability of Open Cast Mines. Proceedings, Symposium on the Theoretical Background to the Planning of Open Pit Mines, Johaimesburg, South Africa, 1970.

    Google Scholar 

  • John, K. W.: Graphical Stabihty Analysis of Slopes in Jointed Rock. J. of Soil Mechanics and Foundations Division, ASCE 94, 1968.

    Google Scholar 

  • Kendall, M. G., Stuart, A.: The Advanced Theory of Statistics. New York: Hafner 1967.

    Google Scholar 

  • Kim, H, Major, G., Ross-Brown, D.: Application of Monte Carlo Techniques to Slope Stability Analyses. Supplement to 19th U.S. Symposium on Rock Mechanics, 1978.

    Google Scholar 

  • Kim, Y. C., et al.: Economic Aspects of Pit Slope Design. Rock Mechanics Symposium, Vancouver, 1976.

    Google Scholar 

  • Kovari, K., Fritz, P.: Ein Bdtrag zum Problem der Standsicherheit von Felsböschungen. Proceedings, 2. Nat. Tagung fiir Felsmechanik, Aachen, 1976.

    Google Scholar 

  • Marek, J. M., Savely, J. P.: Probabilistic Analysis of Plane Shear Failure Mode. Proceedings, 19th U.S. Symposium on Rock Mechanics, 1978.

    Google Scholar 

  • Matsuo, M.: Reliability in Embankment Design. Department of Civil Engineering, MIT, Technical Report R76–33, 1976.

    Google Scholar 

  • McMahon, B.: Design of Rock Slopes Against Sliding on Pre-existing Fractures. Proceedings, 3rd Congress Int. Soc. Rock Mechanics, II-B: 308–313 (1974).

    Google Scholar 

  • Merritt, A. K, Baecher, G. B.: Site Characterization in Rock Engineering. State of the Art Paper in Proceedings, 22nd U.S. Symposium on Rock Mechanics, Cambridge, 1981.

    Google Scholar 

  • Moavenzadeh, F., Markov, M. J.: Tunnel Cost Model. Series of 10 reports (1974–1978).

    Google Scholar 

  • Morla-Catalan, J., Cornell, C A.: Earth Slope Rability by a Level Crossing Method. J. Geot. Div., ASCE 102, 591–604 (1976).

    Google Scholar 

  • Müller, L: Der Felsbau. Bd. 2. Stuttgart: Enke 1978.

    Google Scholar 

  • O’Reilly, K. J.: The Effect of Joint Plane Persistence on Slope Reliability. M.S. Thesis, MIT, 1980.

    Google Scholar 

  • Pacher, F: Deformationsmessungen im Versuchsstollen als Mittel zur Erforschung des Ge- birgsverhaltens und zur Bemessung des Ausbaus.

    Google Scholar 

  • Peck, R. B.: Advantages and Limitations of the Observational Method in Applied Soil Mechanics, 9th Rankine Lecture, Geotechnique 79, 171–187 (1969).

    Google Scholar 

  • Priest, S. D., Hudson, J.: Discontinuity Spacings in Rock. Int. J. Rock Mech. Min. Sci. 13, 135–148(1976).

    Google Scholar 

  • Priest, S. D., Hudson, J.: Estimation of Discontinuity Spacing and Trace Lengths Using Scan Line Surveys. Int. J. Rock Mech. Min. Sci. 18, 183–198 (1981).

    Article  Google Scholar 

  • Rabcewicz, L: The Stability of Tunnels Under Rock Load. Water Power 225–229, 266–273 297–302 (1969).

    Google Scholar 

  • Rackwitz, R., Peintinger, B.: Numerical Uncertainty Analysis of Slopes. Berichte zur Zuverlässigkeitstheorie der Bauwerke, Laboratorium für den konstmktiven Ingenieurbau, Technische Universität München 1980.

    Google Scholar 

  • Ramsey, F. P.: Tmth and Probabihty. Reprinted in Kyberg and Smokier (eds.), Studies in Subjective Probability. John Wiley & Sons 1926.

    Google Scholar 

  • Snow, D.: Discussion — Theme III. Int. Congress Rock Mechanics, Lisbon 1966.

    Google Scholar 

  • Stael von Holstein, C. S.: A Tutorial m Decision Analysis. In Howard, R. A., et al. (eds.), Reading in Decision Analysis, SRI 1974.

    Google Scholar 

  • Terzaghi, K.: Engineering Geology on the Job and in the Classroom. J. Boston Soc. of Civ. Engs., 48, 97–109 (1961). Discussions in 49,44–95 (1962). (Reprinted as Harvard Soü Mechanics Series No. 62, also in Contributions to Soil Mechanics 1954–1962, Boston Soc. of Civil Engineers, 1965.)

    Google Scholar 

  • Terzaghi, R.: Sources of Error in Joint Surveys. Geotechnique 15, 287–304 (1964).

    Google Scholar 

  • Vanmarcke, E.: On the Reliability of Earth Slopes. J. Geot. Div., ASCE 103, 1247–1265 (1977).

    Google Scholar 

  • Vanmarcke, E.: Probabilistic Stability Analysis of Earth Slopes. Engineering Geology (1981).

    Google Scholar 

  • Veneziano, D., et al.: Three Dimensional Models of Slope Reliability. Dept. of Civil Engineering, MIT, Technical Report R77–17, 1977.

    Google Scholar 

  • Visca, P. J., Marek, J. M.: Monte Carlo Simulation of Rotational Shear Analysis. Proceedings, 19th U.S. Symposium on Rock Mechanics.

    Google Scholar 

  • Wu, T H, Thayer, W. B., Lin, S. S: Stability of Embankment on Clay, ASCE 101 (GT9), 913–948 (1975).

    Google Scholar 

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Einstein, H.H., Baecher, G.B. (1982). Probabilistic and Statistical Methods in Engineering Geology I. Problem Statement and Introduction to Solution. In: Müller, L. (eds) Ingenieurgeologie und Geomechanik als Grundlagen des Felsbaues / Engineering Geology and Geomechanics as Fundamentals of Rock Engineering. Rock Mechanics, vol 12. Springer, Vienna. https://doi.org/10.1007/978-3-7091-8665-7_4

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  • DOI: https://doi.org/10.1007/978-3-7091-8665-7_4

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-81697-4

  • Online ISBN: 978-3-7091-8665-7

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