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Applications of Probabilistic Methods in Geotechnical Engineering. Part 1. Simplified Reliability Analyses for Geotechnical Problems,
STANFORD UNIV CALIF DEPT OF CIVIL ENGINEERING
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In this report, several approximate methods for determining the first and second moments of the probability density function of a random design variable have been presented. Once these moments are known, the probability of failure or reliability of the system can be calculated by assuming a distribution shape and using standard probability tables. This technique can be used on a variety of geotechnical problems to transform existing deterministic analyses into probabilistic design analyses. Examples of the application of the methodology developed herein are presented in the areas of shear strength, bearing capacity, and slope stability. The examples are used to illustrate how a reliability type of design analyses might be performed, the influence of the choice of distribution on calculated results, and the contrasts between conventional factor of safety analyses and probabilistic analyses. The point estimate method presented in this report is a simple and powerful tool that can be used in conjunction with any numerical analysis. By identifying the N random variables in a design analysis and assigning to them one sigma bounds to reflect subjective uncertainty or parameter variability, the mean and variances of the design parameters can be estimated from 2 to the nth point estimates. The primary obstacle to successful implementation of the techniques presented in this report is the lack of information on appropriate distribution shapes for various geotechnical design parameters.
APPROVED FOR PUBLIC RELEASE