Robust Geotechnical Design of Earth Slopes Using Fuzzy Sets
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 141, Issue 1
Abstract
This paper presents a fuzzy set–based robust geotechnical design (RGD) approach for the design of earth slopes in which uncertain soil parameters are represented as fuzzy sets. For a slope with fuzzy sets as inputs, the stability (factor of safety) of the slope is also a fuzzy set. The failure probability of the slope can readily be determined based on the obtained fuzzy factor of safety; further, the design robustness in terms of the signal-to-noise ratio (SNR) can also be evaluated. The purpose of the RGD is to derive a design that is robust against the uncertainty in the input parameters, with an explicit consideration on safety and cost. Therefore, a multiobjective optimization is performed and a three-dimensional or two-dimensional Pareto front showing a trade-off between objectives can be obtained, which allows for an informed design decision. The effectiveness of the proposed fuzzy set–based RGD approach is demonstrated through an illustrative example.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This material is based on work supported in part by the National Science Foundation (Grant No. CMMI-1200117; project titled “Transforming Robust Design Concept into a Novel Geotechnical Design Tool”; Richard Fragaszy was the Program Director at the National Science Foundation and Hsein Juang of Clemson University was the Principal Investigator). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. The first author acknowledges the financial support provided by the Open Fund of Chongqing Key Laboratory of Geomechanics & Geoenvironment Protection (Logistical Engineering University) (Grant No. CKLGGP2013-04); he also wishes to acknowledge the financial support provided by the Glenn Department of Civil Engineering, Clemson University, through the Aniket Shrikhande Graduate Fellowship. The last author acknowledges the financial support provided by Tongji University, China, for his sabbatical leave at Clemson University.
References
Ang, A. H. S., and Tang, W. H. (2007). Probability concepts in engineering: Emphasis on applications to civil and environmental engineering, 2nd Ed., Wiley, New York.
Baecher, G. B., and Christian, J. T. (2003). Reliability and statistics in geotechnical engineering, Wiley, New York.
Beyer, H.-G., and Sendhoff, B. (2007). “Robust optimization—A comprehensive survey.” Comput. Meth. Appl. Mech. Eng., 196(33–34), 3190–3218.
Bishop, A. W. (1955). “The use of the slip circle in the stability analysis of slopes.” Géotechnique, 5(1), 7–17.
Branke, J., Deb, K., Dierolf, H., and Osswald, M. (2004). “Finding knees in multi-objective optimization.” Proc., Parallel Problem Solving from Nature VIII, Springer, Berlin, 722–731.
Ching, J., Phoon, K.-K., and Hu, Y.-G. (2009). “Efficient evaluation of reliability for slopes with circular slip surfaces using importance sampling.” J. Geotech. Geoenviron. Eng., 768–777.
Christian, J. T. (2004). “Geotechnical engineering reliability: How well do we know what we are doing?” J. Geotech. Geoenviron. Eng., 985–1003.
Christian, J. T., Ladd, C. C., and Baecher, G. B. (1994). “Reliability applied to slope stability analysis.” J. Geotech. Engrg., 2180–2207.
Deb, K., and Gupta, S. (2011). “Understanding knee points in bicriteria problems and their implications as preferred solution principles.” Eng. Optim., 43(11), 1175–1204.
Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T. (2002). “A fast and elitist multiobjective genetic algorithm: NSGA-II.” IEEE Trans. Evol. Comput., 6(2), 182–197.
Dodagoudar, G. R., and Venkatachalam, G. (2000). “Reliability analysis of slopes using fuzzy sets theory.” Comput. Geotech., 27(2), 101–115.
Dong, W. M., and Wong, F. S. (1987). “Fuzzy weighted averages and implementation of the extension principle.” Fuzzy Sets Syst., 21(2), 183–199.
Duncan, J. M. (2000). “Factors of safety and reliability in geotechnical engineering.” J. Geotech. Geoenviron. Eng., 307–316.
El-Ramly, H., Morgenstern, N. R., and Cruden, D. M. (2005). “Probabilistic assessment of stability of a cut slope in residual soil.” Géotechnique, 55(1), 77–84.
Fellenius, W. (1936). “Calculation of the stability of earth dams.” Proc., 2nd Congress on Large Dams, International Commission on Large Dams, Washington, DC, 445–462.
Giasi, C. I., Masi, P., and Cherubini, C. (2003). “Probabilistic and fuzzy reliability analysis of a sample slope near Aliano.” Eng. Geol., 67(3–4), 391–402.
Gong, W., Wang, L., Juang, C. H., Zhang, J., and Huang, H. (2014). “Robust geotechnical design of shield-driven tunnels.” Comput. Geotech., 56(Mar), 191–201.
Greco, V. R. (1996). “Efficient Monte Carlo technique for locating critical slip surface.” J. Geotech. Engrg., 517–525.
Griffiths, D. V., and Lane, P. A. (1999). “Slope stability analysis by finite elements.” Géotechnique, 49(3), 387–403.
Harr, M. E. (1987). Reliability-based design in civil engineering, McGraw Hill, New York.
Juang, C. H., Huang, X. H., and Elton, D. J. (1992). “Modeling and analysis of non-random uncertainties—Fuzzy set approach.” Int. J. Numer. Anal. Methods Geomech., 16(5), 335–350.
Juang, C. H., Jhi, Y.-Y., and Lee, D.-H. (1998). “Stability analysis of existing slopes considering uncertainty.” Eng. Geol., 49(2), 111–122.
Juang, C. H., Wang, L., Atamturktur, S., and Luo, Z. (2012). “Reliability-based robust and optimal design of shallow foundations in cohesionless soil in the face of uncertainty.” J. Geoeng., 7(3), 75–87.
Juang, C. H., Wang, L., Hsieh, H.-S., and Atamturktur, S. (2014). “Robust geotechnical design of braced excavations in clays.” Struct. Saf., 49(Jul), 37–44.
Juang, C. H., Wang, L., Khoshnevisan, S., and Atamturktur, S. (2013a). “Robust geotechnical design—Methodology and applications.” J. Geoeng., 8(3), 71–81.
Juang, C. H., Wang, L., Liu, Z., Ravichandran, N., Huang, H., and Zhang, J. (2013b). “Robust geotechnical design of drilled shafts in sand: New design perspective.” J. Geotech. Geoenviron. Eng., 2007–2019.
Kim, J. Y., and Lee, S. R. (1997). “An improved search strategy for the critical slip surface using finite element stress fields.” Comput. Geotech., 21(4), 295–313.
Lovell, C. W., Sharma, S., and Carpenter, J. R. (1985). “Introduction to slope stability analysis with STABL4.” Rep. No. FHWATS-85-212, Federal Highway Administration, Washington, DC.
MATLAB 7.10.0 [Computer software]. MathWorks, Natick, MA.
Oka, Y., and Wu, T. H. (1990). “System reliability of slope stability.” J. Geotech. Engrg., 1185–1189.
Park, H. J., Um, J.-G., Woo, I., and Kim, J. W. (2012). “Application of fuzzy set theory to evaluate the probability of failure in rock slopes.” Eng. Geol., 125(Jan), 92–101.
Phadke, M. S. (1989). Quality engineering using robust design, Prentice Hall, Englewood Cliffs, NJ.
Shrestha, B., and Duckstein, L. (1997). “A fuzzy reliability measure for engineering applications.” Chapter 7, Uncertainty modeling and analysis in civil engineering, B. M. Ayyub, ed., CRC Press, Boca Raton, FL, 121–135.
Spencer, E. (1967). “A method of analysis of the stability of embankments assuming parallel inter-slice forces.” Géotechnique, 17(1), 11–26.
StablPro3 [Computer software]. Austin, TX, Ensoft.
Taguchi, G. (1986). Introduction to quality engineering: Designing quality into products and processes, Quality Resources, White Plains, NY.
Tsui, K.-L. (1992). “An overview of Taguchi method and newly developed statistical methods for robust design.” IIE Trans., 24(5), 44–57.
Turnbull, W. J., and Hvorslev, M. J. (1967). “Special problems in slope stability.” J. Soil Mech. and Found. Div., 93(4), 499–528.
Wang, L., Juang, C. H., Atamturktur, S., Gong, W., Khoshnevisan, S., and Hsieh, H. S. (2014). “Optimization of design of supported excavations in multi-layer strata.” J. Geoeng., 9(1), 1–12.
Wang, L., Hwang, J. H., Juang, C. H., and Atamturktur, S. (2013). “Reliability-based design of rock slopes—A new perspective on design robustness.” Eng. Geol., 154(Feb), 56–63.
Wu, T. H., Gale, S. M., Zhou, S. Z., and Geiger, E. C. (2011). “Reliability of settlement prediction—Case history.” J. Geotech. Geoenviron. Eng., 312–322.
Zadeh, L. A. (1965). “Fuzzy sets.” Inf. Control, 8(3), 338–353.
Information & Authors
Information
Published In
Journal of Geotechnical and Geoenvironmental Engineering
Volume 141 • Issue 1 • January 2015
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jul 25, 2013
Accepted: Aug 25, 2014
Published online: Sep 24, 2014
Published in print: Jan 1, 2015
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.