Abstract
A geotechnical structure’s reliability index calculated using identical input parameters and assumptions can significantly vary as a function of the used method. The different approaches to solving the reliability problem could result in an error which depends on many factors. The most important error sources are the complexity of the performance function, the number of random variables, their mutual correlations, and marginal statistical distributions. A review of relevant literature in the field of reliability in geotechnical engineering revealed a lack of information on the errors of individual reliability methods for geotechnical problems and general criteria for assessing their suitability concerning the error size. The paper defines the reliability method error and proposes criteria for assessing the suitability of reliability methods in geotechnical engineering. Based on the proposed criteria, the suitability of common reliability methods was evaluated in the example of a shallow foundation, analysed according to Eurocode 7, DA 3, such that Ed=Rd. It is shown that due to the mathematically complex expression of the reliability integral, methods that are easier to use result in a larger error and are not suitable for a reliability analysis of shallow foundations. Sophisticated methods are more accurate but require specific knowledge and resources that are not often used in daily engineering practice.
Highlights
The value of the reliability index of a geotechnical structure, calculated using identical input parameters and assumptions, can vary significantly as a function of the applied method
The paper shows that the factor of safety (FS) for the ultimate limit state (ULS) of shallow foundation is neither lognormally nor normally distributed (Figures 5–7), i.e., its actual probability density function (PDF) is unknown
Due to the similarity of the lognormal PDF and the actual PDF of FS, the claim from [1,2,3,4,5,6] according to which it is reasonable to assume a lognormal distribution of FS may be acceptable for use in everyday engineering practice, under certain conditions—e.g., when used in combination with the Monte Carlo method or Analytical First Order Second Moment (FOSM) method (Figures 8 and 9)
Summary
The value of the reliability index of a geotechnical structure, calculated using identical input parameters and assumptions, can vary significantly as a function of the applied method. It is necessary to evaluate the reliability methods accuracies, i.e., research their suitability for application in different types of problem. Because of the differences in the mathematical expressions of the limit state definition among various geotechnical tasks, i.e., different forms of the performance function, it is not possible to give a generalized assessment of the suitability of a particular method of reliability to all geotechnical problems. It can be done on a case-by-case basis. The other possibility could be that a single method is suitable for application to a group of mathematically similar problems
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