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5 gested by the dashed curve. The mean resistance for this Calibration" (Siu et al., 1975) for the National Building other predictive method remains unchanged, but the varia- Code of Canada (National Research Council of Canada, tion (i.e., uncertainty) is increased. 1977), Development of a Probability-Based Load Criterion In calculating the prescribed probability of failure (Pf), a for American National A58 (Ellingwood et al., 1980) for the derived probability density function is calculated for the mar- National Bureau of Standards, and the Rationalization of gin of safety (R,Q), and reliability is expressed using the "reli- Safety and Serviceability Factors in Structural Codes: CIRIA ability index", , which is the number of standard deviations Report 63 (Construction Industry Research and Information of the derived PDF of R - Q separating the mean safety mar- Association, 1977). The AASHTO LRFD Bridge Design Spec- gin from the nominal failure value of zero (Figure 2). Further ifications (AASHTO, 1994), resulting from work in NCHRP discussion of the relationship of pf to are given in section Project 12-33 (Nowak, 1999), provide design guidance for 2.7.1. For computational reasons, the margin of safety is girders. taken as R - Q when the resistances and load effects have normally distributed uncertainty, but as ln(R) - ln(Q) when the uncertainties are logNormally distributed. 1.3.3 LRFD Performance and Advantages 1.3.2 Background Information Experience has shown that adopting a probability-based design code can result in cost savings and efficient use of The concept of using the probability of failure as a crite- materials. Reliability improvements are still under evaluation rion for structural design is generally credited to the Russians even though the new LRFD codes are designed to yield reli- N. F. Khotsialov and N. S. Streletskii who presented it in the abilities equal to or higher than those of earlier codes. Expe- late 1920s, and it was introduced in the United States by riences are not yet well documented; but anecdotal evidence Freudenthal (1947). The recent development of LRFD in from naval architecture suggests that, relative to conventional civil engineering was initiated in structural engineering (see, WSD, the new AISC-LRFD requirements may save 5% to e.g., Ellingwood et al., 1980). Reliability-Based Design codes 30% of steel weight in ships (Ayyub, 1999). This may or may using LRFD have been published by the American Institute not be the case for civil engineering applications. Specific of Steel Construction (AISC, 1994; Galambos and Ravindra benefits for pile design include at least the following: 1978) and the American Concrete Institute (American Con- crete Institute, 1995). An effort was made by the National 1. Cost savings and improved reliability because of more Standards Institute (ANSI) to develop probability-based load efficiently balanced design. criteria for buildings (Ellingwood et al., 1982a, b) and ASCE 2. More rational and rigorous treatment of uncertainties in 7-93 (ASCE, 1993). The American Petroleum Institute (API) the design. extrapolated LRFD technology for use in fixed offshore plat- 3. Improved perspective on the overall design and con- forms (API, 1989; Moses 1985, 1986). Comprehensive sum- struction processes (sub- and superstructures); and the maries of the implementation of probabilistic design theory development of probability-based design procedures in design codes include those by "Practical Approach to Code can stimulate advances in pile analysis and design. Figure 2. An illustration of a combined probability density function (g(R,Q)) representing the margin of safety and the reliability index, . (g = Standard deviation of g(R,Q)).