Reliability-Based Optimization of Geotechnical Systems
Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 137, Issue 12
Abstract
Reliability-based optimization (RBO) intends to minimize the cost involved in a design while satisfying all technical requirements specified by using reliability theory. Although this idea is attractive, its implementation is generally difficult because an accurate evaluation of the reliability constraints is often computationally prohibitive when it is coupled with the minimization of a cost function. This paper suggests an indirect method for RBO of geotechnical systems initially on the basis of the mean first-order reliability method (MFORM). Because reliability analysis with MFORM is very efficient, the computational work involved in RBO is greatly reduced. The major concern about MFORM is that it is not an accurate reliability method. A reliability index mapping function was used to relate the reliability index calculated by MFORM to that calculated by a more accurate method. When the mapping function perfectly reflects the relationship between MFORM reliability index and that from an accurate reliability method, the RBO from MFORM and the original RBO problem are equivalent. When a perfect mapping function cannot be built, a procedure has been suggested to fine-tune the optimal design such that accurate reliability constraints can be maintained in the final optimal design. The proposed method is illustrated with two geotechnical examples: the optimal design of a shallow foundation and a gravity retaining wall.
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Acknowledgments
This research was substantially supported by the Program for Young Excellent Talents in Tongji University, Natural Science Foundation of China (UNSPECIFIEDNo. 41102174), Program for Changjiang Scholars and Innovative Research Team in University (UNSPECIFIEDPCSIRT, IRT1029), National 973 Basic Research Program of China (UNSPECIFIED2011CB013800), and Research Grants Council (RGC) of the Hong Kong SAR UNSPECIFIED(No. HKUST9/CRF/09 and 622308).
References
Ang, A. H.-S., and Tang, W. (1984). Probability concepts in engineering planning and design: Decision, risk, and reliability, Vol. 2, Wiley, New York.
Ang, A. H.-S., and Tang, W. H. (2007). Probability concepts in engineering: Emphasis on applications to civil and environmental engineering, 2nd Ed., Vol. 1, Wiley, New York.
Aoues, Y., and Chateauneuf, A. (2010). “Benchmark study of numerical methods for reliability-based design optimization.” Struct. Multidiscip. Optim., 41(2), 277–294.
Babu, G. L. S., and Basha, B. M. (2008). “Optimum design of cantilever sheet pile walls in sandy soils using inverse reliability approach.” Comput. Geotech., 35(2), 134–143.
Baecher, G. H. (1987). “Geotechnical risk analysis user’s guide.” FHWA/RD-87-011, Federal Highway Administration, McLean, VA.
Baecher, G. B., and Christian, J. T. (2003). Reliability and statistics in geotechnical engineering, Wiley, Chichester, UK.
Basha, B. M., and Babu, G. L. S. (2008). “Target reliability based design optimization of anchored cantilever sheet pile walls.” Can. Geotech. J., 45(4), 535–548.
Becker, D. E. (1996). “Eighteenth Canadian geotechnical colloquium: Limit states design for foundations. Part II: Development for the national building code of Canada.” Can. Geotech. J., 33(6), 984–1007.
Bhatti, M. A. (2000). Practical optimization methods, Springer-Verlag, New York.
Chalermyanont, T., and Benson, C. H. (2004). “Reliability-based design for internal stability of mechanically stabilized earth walls.” J. Geotech. Geoenviron. Eng., 130(2), 163–173.
Chan, C. M., Zhang, L. M., and Ng, J. T. M. (2009). “Optimization of pile groups using hybrid genetic algorithms.” J. Geotech. Geoenviron. Eng., 135(4), 497–505.
Chandra, S., Jayadeva, and Mehra, A. (2009). Numerical optimization with applications, Alpha Science, Oxford, UK.
Ching, J. (2009). “Equivalence between reliability and factor of safety.” Prob. Eng. Mech., 24(2), 159–171.
Ching, J., and Hsu, W. C. (2008). “Transforming reliability limit-state constraints into deterministic limit-state constraints.” Struct. Saf., 30(1), 11–33.
Cornell, C. A. (1969a). “A first-order reliability theory for structural design.” Study No. 3: Structural reliability and codified design, Univ. of Waterloo, Ontario, Canada.
Cornell, C. A. (1969b). “A probability-based structural code.” J. Am. Concr. Inst., 66(12), 974–985.
Craig, R. F. (1997). Soil mechanics, 6th Ed., Chapman & Hall, New York.
Der Kiureghian, A., and Polak, E. (1998). “Reliability-based optimal design: A decoupled approach.” Proc., 8th IFIP WG7.5 Working Conf. on Reliability and Optimization of Structural Systems, A. S. Nowak, ed., Book Crafters, Chelsea, MI, 197–205.
European Committee for Standardization (CEN). (2001). “Eurocode: Basis of structural design.” Final Draft prEN 1990:2001, Brussels, Belgium.
Foye, K. C., Salgado, R., and Scott, B. (2006). “Resistance factors for use in shallow foundation LRFD.” J. Geotech. Geoenviron. Eng., 132(9), 1208–1218.
Gasser, M., and Schuëller, G. (1997). “Reliability-based optimization of structural systems.” Math. Meth. Oper. Res., 46(3), 287–307.
Griffiths, D. V., and Fenton, G. A., eds. (2007). Probabilistic methods in geotechnical engineering, Springer, New York.
Guo, X., Bai, W., Zhang, W., and Gao, X. (2009). “Confidence structural robust design and optimization under stiffness and load uncertainties.” Comput. Methods Appl. Mech. Eng., 198(41–44), 3378–3399.
Hasofer, A. M., and Lind, N. C. (1974). “Exact and invariant second-moment code format.” J. Eng. Mech., 100(1), 111–121.
Kuschel, N., and Rackwitz, R. (1997). “Two basic problems in reliability-based structural optimization.” Math. Meth. Oper. Res., 46(3), 309–333.
Li, D., Zhou, C., Lu, W., and Jiang, Q. (2009). “A system reliability approach for evaluating stability of rock wedges with correlated failure modes.” Comput. Geotech., 36(8), 1298–1307.
Low, B. K., and Tang, W. H. (1997). “Efficient reliability evaluation using spreadsheet.” J. Eng. Mech., 123(7), 749–752.
Melchers, R. E. (1999). Structural reliability analysis and prediction, Wiley, New York.
Peck, R. P., Hanson, W. E., and Thornburn, T. H. (1974). Foundation engineering, 2nd Ed., Wiley, New York.
Phoon, K. K., ed. (2008). Reliability-based design in geotechnical engineering: Computations and applications, Taylor & Francis, London.
Poulos, H. G., and Davis, E. H. (1974). Elastic solutions for soil and rock mechanics, Wiley, New York.
Reddy, M. V., Granhdi, R. V., and Hopkins, D. A. (1994). “Reliability based structural optimization: A simplified safety index approach.” Comput. Struct., 53(6), 1407–1418.
Royset, J. O., Kiureghian, A. D., and Polak, E. (2001). “Reliability-based optimal design of series structural systems.” J. Eng. Mech., 127(6), 607–614.
Rżanicyn, A. R. (1947). “Opriedelenie zapasa procznosti soorużenii.” Stroit. Prom., 8 (in Russian).
Rżanicyn, A. R. (1949). “Statsticzeskoje obosnowanije rasczotnych koefficientow, matieriały k tieorii rasczota po predielnomu sostojaniju.” Strojizdat, Moscow (in Russian).
Shan, S., and Wang, G. G. (2008). “Reliability design space and complete single-loop reliability-based design optimization.” Reliab. Eng. Syst. Saf., 93(8), 1218–1230.
Tsompanakis, Y., Lagaros, N. D., and Papadrakakis, M. (2008). Structural design optimization considering uncertainties, Taylor & Francis, London.
Tung, Y. K., Yen, B. C., and Melching, C. S. (2006). Hydrosystems engineering reliability assessment and risk analysis, McGraw-Hill, New York.
Valdebenito, M. A., and Schuëller, G. I. (2010). “A survey on approaches for reliability-based optimization.” Struct Multidisc Optim., 42(5), 645–663.
Vesic, A. S. (1975). “Bearing capacity of shallow foundations.” Foundation engineering handbook, H. Winterkorn and H. Y. Fang, eds., Van Nostrand Reinhold, New York.
Wang, Y. (2009). “Reliability-based economic design optimization of spread foundations.” J. Geotech. Geoenviron. Eng., 135(7), 954–959.
Wang, Y., and Kulhawy, F. H. (2008). “Economic design optimization of foundations.” J. Geotech. Geoenviron. Eng., 134(8), 1097–1105.
Whitman, R. V., and Richart, F. E. (1967). “Design procedures for dynamically loaded foundations.” J. Soil Mech. Found. Div., 93(SM6), 169–193.
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© 2011 American Society of Civil Engineers.
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Received: Oct 16, 2009
Accepted: Apr 12, 2011
Published online: Apr 14, 2011
Published in print: Dec 1, 2011
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