Probabilistic reliability analysis of slopes with truncated random variables from censored samples

Abstract

Probabilistic reliability analysis and design have been a research topic of intense interest in geotechnical engineering in recent decades due to the inherent uncertainty in soil property data obtained from field or laboratory testing. Determination of the underlying probability distributions of soil properties and corresponding parameters from observed data is a critical initial step because subsequent risk and reliability analyses depend upon these evaluations. Conventionally, the choice of a probability distribution is dictated by subjective familiarity with a classical distribution, such as Normal or Lognormal. Furthermore, only censored/truncated samples can sometimes be obtained due to technical and environmental limitations. This research presents an objective and unbiased method to estimate truncated probability distributions of soil parameters using the MaxEnt method constrained by moments of censored/truncated samples and the Akaike information criterion (AIC). This method is described as "objective" because it relies solely on data and constraints rather than subjective choices, and "unbiased" because it avoids assumptions that could skew the distribution, thereby providing a more accurate and representative model of the soil parameters' probability distribution. The probability distribution is based on the concept of MaxEnt and is free from the assumptions of classical distributions. A first-order reliability method (FORM) is presented based on truncated MaxEnt distributions. The new method is applied to the probabilistic reliability analysis and design of Nipigon River slopes including parameters such as unit weight, friction angle, and cohesion of various soil types, to perform the probabilistic reliability analysis. The accuracy of these parameter estimations, drawn from field measurements and reported studies, is crucial for the reliability assessments conducted in this research.