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1 0.9 0.8 0.7 0.6 CDF 0.5 0.4 0.3 0.2 0.1 0 pl plpe plfo
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Figure 17.19 Results from Monte Carlo simulation of settlement problem with 1000 points and strati ed sampling combined with the Latin hypercube. pl = simulation, plpe = point-estimate, plfo = FOSM.
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The technique has the advantage that it is relatively easy to implement on a computer and can deal with a wide range of functions, including those that cannot be expressed conveniently in explicit form. The major disadvantage is that it can converge slowly. Several techniques are available to accelerate convergence or, equivalently, to reduce variance. Each can be effective for some problems and counter-productive for others. The choice of which method to employ depends on knowledge of the problem and its components. Sometimes a preliminary calculation with a limited number of simulation points will indicate which variance reduction method can be expected to work best. In many cases two or more techniques can be combined effectively. Finally, accurate Monte Carlo simulation depends on reliable random numbers. Generating random numbers is an art, and one method will not work for all circumstances. There is a substantial literature on the subject, and a person contemplating an important study involving random numbers would be well advised to be satis ed that the random number generators are appropriate for the job.
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Load and Resistance Factor Design
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Most of this book discusses conceptual issues of uncertainty analysis, statistics, and reliability theory and deals with design examples on their own merits, independent of building codes and other aspects of professional practice. In recent years, however, these concepts of uncertainty, statistics, and reliability have begun to enter the public debate over how new structural and geotechnical building codes ought to be written. An important result of this debate is the evolution of building codes based on reliability considerations. The most important of these developments at present is the appearance of Load and Resistance Factor Design (LRFD) as the basis for new codes. This chapter discusses the evolution of LRFD-based codes and how reliability theory is used to calibrate and optimize these new codes.
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18.1 Limit State Design and Code Development
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Allowable Stress Design (ASD) sometimes called Working Stress Design (WSD) has been the traditional design basis in civil and mechanical engineering for over a century. Working stress design attempts to ensure that loads acting upon a structure or foundation do not exceed some allowable limit, often taken to be the limit of elastic resistance. Typically, the level of assurance that loads do not exceed this allowable limit is re ected in a factor of safety on the ratio of allowable to predicted loads, stresses, or other demands. The safety factor commonly used in ASD is not the central safety factor discussed in earlier chapters that uses the ratio of expected resistance to expected load, but the nominal safety factor that uses some higher than expected value of load and some lower than expected value of resistance. That is, the load might be taken as that value with an exceedance probability of, say, 0.05; while the resistance might be taken as that value with an exceedance probability of, say, 0.95.
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Reliability and Statistics in Geotechnical Engineering Gregory B. Baecher and John T. Christian 2003 John Wiley & Sons, Ltd ISBN: 0-471-49833-5
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LOAD AND RESISTANCE FACTOR DESIGN
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The geological uniqueness of individual construction sites, along with the demand for economical design, caused the geotechnical community at a very early stage in the development of the eld to adopt Limit State Design (LSD). Limit state design rather than being based on allowable stresses, is based on predictions how designs actually perform near failure. Failure in this meaning is typically taken either as ultimate failure (collapse) or as conditions affecting serviceability (e.g. excessive deformation). Although limit state design has become widespread in modern structural codes, in fact, geotechnical design led the civil engineering profession in the move toward performance-based design. Limiting equilibrium approaches to the design of slopes, deformation-based approaches to the design of underground openings, and plasticity criteria for the foundations of offshore structures are all examples of limit state design in traditional geotechnical practice. With limit state design, the relation between uncertainties in loads and resistances can be more directly related to the probabilities of failure than they can with ASD. This has led to new directions in North American and European building codes. In the 1970s and 1980s, the eld of structural engineering was dramatically changed by the rapid development of structural reliability theory (Melchers 1987), and the resulting incorporation of probabilistic concepts in structural codes (AASHTO 1994; Ellingwood et al. 1980).1 This was most notable in the development and implementation of load and resistance factor design (LRFD) as the basis for new code development in the 1980s and 1990s (Ravindra and Galambos 1978). Among the new structural codes using the LRFD approach are those of the American Institute of Steel Construction (AISC 1994), the American Concrete Institute (ACI 2002), the American Association of State Highway and Transportation Of cials (AASHTO 1994), and the American Forest and Paper Association. LRFD replaces single factors of safety on the ratio of total resistance to total load with a set of partial safety factors on individual components of resistance and load and uses limiting states as the checking points for design. The partial safety factors can be chosen to re ect differing uncertainties associated with the individual components of resistance and load and thus to improve upon the undifferentiated approach of simple factors of safety. This approach is not new. Freudenthal (1951, 1956) proposed partial safety factors in his seminal early papers on structural safety, and Taylor (1948) discusses partial safety factors (speci cally with respect to the soil strength parameters c and for analysis of the stability of embankments) in his classic soil mechanics text.
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