Probabilistic characterization of soil properties based on the maximum entropy method from fractional moments: Model development, case study, and application

Abstract

In probabilistic reliability analysis for geotechnical engineering applications, determining 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 probability distribution is dictated by subjective familiarity with a classical (e.g., normal or lognormal) distribution. This paper proposes an objective and unbiased method to estimate probability distributions of a soil property using the maximum entropy method from fractional moments of observed data. The probability distribution is based on the concept of maximum entropy and is free from the assumptions of classical distributions. A case study is presented for the undrained shear strength of soil in the Nipigon River landslide area, Ontario, Canada. The maximum entropy distributions of the soil property from fractional moments are compared to the frequency histogram, normal and lognormal distributions, and maximum entropy distributions from integral moments. The maximum entropy distribution with two-order fractional moments, almost equivalent to that with four-order integral moments, is verified with the chi-square goodness-of-fit test. Issues related to overfitting/underfitting, minimum sample size, fractional orders, negative moments, and limitations are discussed. Application of the method to geotechnical reliability analysis is illustrated.