Limit State Imprecise Probabilistic Analysis in Geotechnical Engineering

Abstract

The treatment of imprecision attracted continuous interest since the origin of probability as the science of uncertainty. As a matter of fact, probability has been developed to deal with uncertainty and the first argument supporting precise rather than imprecise probability counts on the nature of ordinary measurements. Starting from only a few papers wherein imprecise probability has been explored as a marginal alternative to precise probability, a number of devoted works appeared with intensified frequency in the second half of the 20th century. From first developments, imprecise probability emerged in the field of engineering by different approaches. The key feature consists in the identification of probability bounds for scenarios of interest with extended application in model validation, provided the ingredients for a systematic investigation of sensitivities. In this way, regardless of the increased interest in probabilistic methods within the geotechnical engineering community, unresolved issues may comprehend a discrepancy in reliability studies regarding the frequency of failure whereas enough tests are very seldom available for a definite choice of the best statistical model. A mixed approach that admits imprecise information as well as probabilistic information is therefore desirable. In this paper the conventional probabilistic approach to uncertainty is extended to include imprecise information in the form of intervals. For demonstration, results are provided for a strip spread foundation designed by the Eurocode 7 methodology, wherein the shear strength parameters of the foundation soil are implemented as intervals and then combined with other uncertain parameters in the form of random variables under dependence.