New FORM algorithm with example applications

B. K. Low
School of Civil and Structural Engineering, Nanyang Technological University (NTU), Singapore

Wilson H. Tang
Department of Civil Engineering, Hong Kong University of Science and Technology, Hong Kong

A new algorithm for the first-order reliability method (FORM) is used to illustrate efficient structural and geotechnical reliability-based design involving correlated non-normal random variables and explicit and implicit performance functions. The new approach differs from the authors’ 2004 algorithm in that it does not require computations of equivalent normal means and equivalent normal standard deviations. It is more efficient and succinct than the 2004 approach. Advantages include ease of randomizing initial points for checking robustness, and fewer required constraints during optimization search for the design point. The new algorithm is illustrated in the Excel spreadsheet platform by FORM analyses of three examples involving correlated nonnormals, namely a case with simple nonlinear performance function, an anchored sheet pile wall, and stochastic analysis of a Norway slope accounting for spatial variation.

References

Der Kiureghian, A. & Liu, P.L. (1986). Structural reliability under incomplete probability information. J. Engineering Mechanics, ASCE, 112(1), 85-104.
Der Kiureghian, A., Lin, H.Z., Hwang, S.J. (1987). Secondorder reliability approximations. J. Engineering Mechanics, ASCE, 113(8), 1208-1225.

Ang, H. S. & Tang, W. H. (1984). Probability concepts in engineering planning and design, vol. 2-Decision, risk, and reliability. John Wiley, New York.
Baecher, G.B., and Christian, J.T. (2003). Reliability and Statistics in Geotechnical Engineering. Wiley; Hoboken, N.J.

Haldar, A., and Mahadevan, S. (1999). Probability, Reliability and Statistical Methods in Engineering Design. Wiley, N.Y.
Kerisel, J. and Absi, E. 1990. Active and Passive Earth Pressure Tables, 3rd ed., A.A. Balkema, Rotterdam.
Low, B. K. (2003). Practical probabilistic slope stability analysis. Proceedings, Soil and Rock America, M.I.T., Massachusetts, June 2003, Verlag Glückauf GmbH Essen, Vol. 2, 2777-2784.
Low, B.K. (2005). Reliability-based design applied to retaining walls. Geotechnique, Vol. 55, No. 1, pp.63-75.

Low, B.K. and Wilson H. Tang (2004). Reliability analysis using object-oriented constrained optimization. Structural Safety, Elsevier Science Ltd., Amsterdam, Vol. 26, No. 1, pp.69-89.
Low, B.K. and Wilson H. Tang (2007). Efficient spreadsheet algorithm for first-order reliability method. Journal of Engineering Mechanics, ASCE, Vol. 133, No. 12, pp.1378-1387.
Low, B. K., Gilbert, R. B. & Wright, S. G. (1998). Slope reliability analysis using generalized method of slices. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, New York, 124(4), 350-362.
Low, B.K., Lacasse, S. and Nadim, F. (2007). Slope reliability analysis accounting for spatial variation. Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, Taylor & Francis, London, Vol. 1, No. 4, pp.177-189.
Rackwitz, R. (2001). Reliability Analysis—A Review and Some Perspectives. Structural Safety, 23, pp. 365-395, Elsevier Science Ltd.
Xu, B. and Low, B.K. (2006). Probabilistic stability analyses of embankments based on finite-element method. Journal Geotechnical and Geoenvironmental Engineering, ASCE, 132(11), 1444-1454.

Tandjiria, V., Teh, C.I., and Low, B.K. (2000). Reliability analysis of laterally loaded piles using response surface methods. Structural Safety, Elsevier Science Ltd., Amsterdam, Vol. 22, No. 4, pp.335-355.

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