Summary
A new spreadsheet-based algorithm for the first-order reliability method (FORM) is illustrated for a two-dimensional rock slope of Hong Kong. The new algorithm combines inverse distribution functions and a refined Newton method with the automatic constrained-optimization search of the design point in the original space of the random variables; it obviates the need for computations of equivalent normal means and equivalent normal standard deviations. In the rock slope analysis, the versatile 4-parameter beta distribution is used in lieu of a truncated normal distribution. Probabilities of failure inferred from reliability indices are compared with those from Monte Carlo simulations. The effects of parametric correlations on the required reinforcing force for a target reliability index value are studied. The intuitive perspective of an expanding equivalent dispersion ellipsoid in the original space of the basic random variables is also described as it is the basis from which the new approach evolved.
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H. S. Ang W. H. Tang (1984) Probability concepts in engineering planning and design SeriesTitleDecision, risk, and reliability NumberInSeries2 John Wiley New York
G. B. Baecher J. T. Christian (2003) Reliability and statistics in geotechnical engineering J. Wiley, Hoboken, NJ Chichester, West Sussex, England
X. Chen N. C. Lind (1983) ArticleTitleFast probability integration by three-parameter normal tail approximations Struct. Saf. 1 IssueID4 269–276 Occurrence Handle10.1016/0167-4730(82)90003-0
A. Der Kiureghian P. L. Liu (1986) ArticleTitleStructural reliability under incomplete probability information J. Eng. Mech. ASCE 112 IssueID1 85–104
A. Der Kiureghian H. Z. Lin S. J. Hwang (1987) ArticleTitleSecond-order reliability approximations J. Eng. Mech. ASCE 113 IssueID8 1208–1225
O. Ditlevsen (1981) Uncertainty modeling: with applications to multidimensional civil engineering systems McGraw-Hill New York
A. Haldar S. Mahadevan (1999) Probability, reliability and statistical methods in engineering design John Wiley New York
A. M. Hasofer N. C. Lind (1974) ArticleTitleExact and invariant second-moment code format J. Eng. Mech. ASCE, New York 100 111–121
Hoek, E. (2006): Practical rock engineering. Chapter 7: A slope stability problem in Hong Kong; and Chapter 8: Factor or safety and probability of failure. In: http://www.rocscience.com/hoek/PracticalRockEngineering.asp
B. K. Low W. H. Tang (1997) ArticleTitleEfficient reliability evaluation using spreadsheet J. Eng. Mech. ASCE, New York 123 IssueID7 749–752 Occurrence Handle10.1061/(ASCE)0733-9399(1997)123:7(749)
B. K. Low W. H. Tang (1997) ArticleTitleReliability analysis of reinforced embankments on soft ground Can. Geotech. J. 34 IssueID5 672–685 Occurrence Handle10.1139/cgj-34-5-672
Low, B. K., Tang, W. H. (2004): Reliability analysis using object-oriented constrained optimization. Struct. Saf. 26(1), 69–89 (An Excel file for hands-on is downloadable from http://alum.mit.edu/www/bklow)
B. K. Low (2005) ArticleTitleReliability-based design applied to retaining walls Geotechnique 55 IssueID1 63–75 Occurrence Handle10.1680/geot.55.1.63.58585
B. K. Low (2007) ArticleTitleReliability analysis of rock slopes involving correlated nonnormals Int. J. Rock Mech. Min. Sci. 44 IssueID6 922–935 Occurrence Handle10.1016/j.ijrmms.2007.02.008
Low, B. K., Tang, W. H. (2007): Efficient spreadsheet algorithm for first-order reliability method. J. Engrg. Mechanics ASCE (Accepted)
R. E. Melchers (1999) Structural reliability analysis and prediction EditionNumber2 SeriesTitleAppendix B2 John Wiley New York
R. Rackwitz B. Fiessler (1978) ArticleTitleStructural reliability under combined random load sequences Comput. Struct. 9 IssueID5 484–494 Occurrence Handle10.1016/0045-7949(78)90046-9
R. Rackwitz (2001) ArticleTitleReliability analysis – a review and some perspectives Struct. Saf. 23 IssueID4 365–395 Occurrence Handle10.1016/S0167-4730(02)00009-7
M. Shinozuka (1983) ArticleTitleBasic analysis of structural safety J. Struct. Eng. ASCE 109 IssueID3 721–740 Occurrence Handle10.1061/(ASCE)0733-9445(1983)109:3(721)
Veneziano, D. (1974): Contributions to second moment reliability. Research Report No. R74-33. Department of Civil Engng., MIT, Cambridge, Masachusetts
Y. T. Wu P. H. Wirsching (1987) ArticleTitleNew algorithm for structural reliability estimation J. Eng. Mech. ASCE 113 IssueID9 1319–1335
Zha Yan-Gan Ono Tetsuro (2001) ArticleTitleMoment methods for structural reliability Struct. Saf. 23 IssueID1 47–75 Occurrence Handle10.1016/S0167-4730(00)00027-8
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Author’s address: Dr. Bak Kong Low, School of Civil and Environmental Engineering, Nanyang Technological University, Block N1 #1b-40, 50 Nanyang Avenue, 639798 Singapore
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Low, B. Efficient Probabilistic Algorithm Illustrated for a Rock Slope. Rock Mech Rock Eng 41, 715–734 (2008). https://doi.org/10.1007/s00603-007-0146-7
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DOI: https://doi.org/10.1007/s00603-007-0146-7