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Uncertainty and risk are central features of geotechnical and geological engineering. Engineers can deal with uncertainty by ignoring it, by being conservative, by using the observational method, or by quantifying it. In recent years, reliability analysis and probabilistic methods have found wide application in geotechnical engineering and related fields. The tools are well known, including methods of reliability analysis and decision trees. Analytical models for deterministic geotechnical applications are also widely available, even if their underlying reliability is sometimes suspect. The major issues involve input and output. In order to develop appropriate input, the engineer must understand the nature of uncertainty and probability. Most geotechnical uncertainty reflects lack of knowledge, and probability based on the engineer's degree of belief comes closest to the profession's practical approach. Bayesian approaches are especially powerful because they provide probabilities on the state of nature rather than on the observations. The first point in developing a model from geotechnical data is that the distinction between the trend or systematic error and the spatial error is a modeling choice, not a property of nature. Second, properties estimated from small samples may be seriously in error, whether they are used probabilistically or deterministically. Third, experts generally estimate mean trends well but tend to underestimate uncertainty and to be overconfident in their estimates. In this context, engineering judgment should be based on a demonstrable chain of reasoning and not on speculation. One difficulty in interpreting results is that most people, including engineers, have difficulty establishing an allowable probability of failure or dealing with low values of probability. The F-N plot is one useful vehicle for comparing calculated probabilities with observed frequencies of failure of comparable facilities. In any comparison it must be noted that a calculated probability is a lower bound because it must fail to incorporate the factors that are ignored in the analysis. It is useful to compare probabilities of failure for alternative designs, and the reliability methods reveal the contributions of different components to the uncertainty in the probability of failure. Probability is not a property of the world but a state of mind; geotechnical uncertainty is primarily epistemic, Bayesian, and belief based. The current challenges to the profession are to make use of probabilistic methods in practice and to sharpen our investigations and analyses so that each additional data point provides maximal information. CE Database subject headings: Failures: Geotechnical engineering; Probability; Reliability; Statistics; Uncertainty analysis; Risk analysis.

Rosenblueth's point-estimate method for approximating the low-order moments of functions of random variables is widely used in geotechnical reliability analyses. It is a special case of numerical quadrature based on orthogonal polynomials. For normal variables, it corresponds to Gauss-Hermite quadrature, but Rosenblueth's procedure automatically generates the weights and abscissas of Gauss-Legendre and Gauss-Laguerre quadrature as well. Despite beliefs to the contrary, the method is not a form of Monte Carlo simulation or FOSM Taylor series expansion. The method is reasonably robust and can be satisfactorily accurate for a wide range of practical problems, although the computational requirements increase rapidly with the number of uncertain quantities. Caution should be exercised in applying the method when transformation of the uncertain quantities severely changes the form of the distributions or when moments of order greater than the two are involved. Examples with closed-form solutions serve to illustrate the use and accuracy of the method.

Formally probabilistic methods for the analysis of slope stability have had relatively little impact on practice. Many engineers are not familiar with probabilistic concepts, and it has been difficult to incorporate concepts of reliability into practice. Also, there is confusion over what reliability and probability of failure mean. The most effective applications of probabilistic methods are those involving relative probabilities of failure or illuminating the effects of uncertainties in the parameters. Attempts to determine the absolute probability of failure are much less successful. The paper describes how probabilistic descriptions of soil parameters can be derived from field and laboratory data and applied in stability anlysis. The first-order, second-moment approach is explored and applied to the design of embankment dams. The example illustrates the relative contributions of uncertainties about different parameters to the reliability of the embankment. Reliability analysis is especially useful in establishing design values of factors of safety representing consistent risks for different types of failure.

Blasting can cause damage at some distance from the blast site, creating, for example, a stress wave that loosens glacial or rock formations causing a landslide. Although recent decades have seen significant advances, the variability of geologic properties, ignorance of the field geometry, and uncertainty about the stress wave patterns make it clear that their interaction is best addressed probabilistically. Measurements of blasting vibrations combined with probability theory for lognormally distributed variables provide a method to express the probability that the strength of the glacial-rock interface will be exceeded. A figure is plotted to show the relation between the probability of catastrophic sliding displacement, the scaled blast distance, and the interface strength. All parameters are described in terms of their means and standard deviations. [ABSTRACT FROM AUTHOR]

A widely used procedure for solving the problem of vertical consolidation of layers with different properties is to transform the thicknesses of the layers in proportion to the square root of their coefficients of consolidation. However, the Gray--Barber closed-form solution shows that this procedure is not correct except under a restrictive set of conditions. The transformation method should not be used. When solutions are needed for layered systems, the Gary--Barber solution or numerical methods should be employed. CE Database keywords: Consolidation, soils; Numerical models; Layered soils.

When there is an estimate of the probability of static failure for a set of slopes, based on historical records, maps, and subjective judgment, it is often necessary to estimate the additional hazard presented by earthquakes. Combining the procedures of reliability analysis with conventional recurrence relations for horizontal earthquake accelerations leads to a simple formulation that is easily implemented on a spreadsheet. For simple failure modes the dynamic factor of safety is a simple function of the static factor of safety, the amplified acceleration, the slope of the failure surface, and the friction angle. Application of the technique to the slopes of the Montes de Caneja in Puerto Rico indicates that the additional risk due to earthquakes is about one tenth of the static probability of failure, but other sets of input parameters can give probabilities of failure during earthquakes that are comparable to the static values.

Following disastrous earthquakes in Alaska and in Niigata, Japan in 1964, Professors H. B. Seed and I. M. Idriss developed and published a methodology termed the 'simplified procedure' for evaluating liquefaction resistance of soils. This procedure has become a standard of practice throughout North America and much of the world. The methodology which is largely empirical, has evolved over years, primarily through summary papers by H. B. Seed and his colleagues. No general review or update of the procedure has occurred, however, since 1985, the time of the last major paper by Professor Seed and a report from a National Research Council workshop on liquefaction of soils. In 1996 a workshop sponsored by the National Center for Earthquake Engineering Research (NCEER) was convened by Professors T. L. Youd and I. M. Idriss with 20 experts to review developments over the previous 10 years. The purpose was to gain consensus on updates and augmentations to the simplified procedure. The following topics were reviewed and recommendations developed: (1) criteria based on standard penetration tests; (2) criteria based on cone penetration tests; (3) criteria based on shear-wave velocity measurements; (4) use of the Becker penetration test for gravelly soil; (4) magnitude scaling factors; (5) correction factors for overburden pressures and sloping ground; and (6) input values for earthquake magnitude and peak acceleration. Probabilistic and seismic energy analyses were reviewed but no recommendations were formulated.

Uncertainties in observed data and in processing field and laboratory tests are major concerns. Assigning reasonable coefficients of variation to the parameters in the conventional analyses indicates that a site with deterministic factors of safety of 1.5 can actually have liquefaction triggering probability above 20%. About a third of the variance comes from uncertainty in the load, which is independent of the resistance. Researchers have traditionally presented the results of case studies in the form of charts showing instances in which liquefaction did and did not occur and have developed relations to separate the two. Although the original researchers developed the separations informally, recent work has applied statistical methods. These give the sampling distributions of the observed data rather than the probability of triggering given the data. Researchers have addressed this issue using Bayesian methods, adopting non-informative priors. Published curves of liquefaction probabilities can be interpreted as likelihood ratios. Other independent work demonstrates that geological, meteorological, and historical data can be used to develop prior probabilities, so it may not be necessary to assume a non-informative prior. The actual prior can then be combined with the likelihood ratios to provide rational probabilities of liquefaction. We recommend that researchers publish their likelihood ratios and allow engineers faced with particular sites to use those to update their own priors. [ABSTRACT FROM PUBLISHER]

A discussion is presented on the role of peak horizontal acceleration as a measure of ground motion amplitude. It is posited that location and definition of acceleration values are key in determining the accuracy of the model.