A Comparative Assessment of the Methods-of-Moments for Estimating the Correlation Length of One-Dimensional Random Fields

Abstract

Due to geological processes, soil properties vary in vertical and horizontal directions which is defined as inherent uncertainty of soil. This type of uncertainty may seriously affect the reliability of, among others, deep and shallow foundations (and in turn, of structures, such as, buildings and bridges) and earth retention and shoring systems. The inherent uncertainty of soil properties is modelled as a random field, which is described by the mean, standard deviation and scale of fluctuation (also known as correlation length, θ) of soil properties. In this paper, the effectiveness of eight methods-of-moments for estimating the correlation length θ is investigated. This is done by generating samples of one-dimensional random fields for pre-defined values of the correlation length, which is then estimated by the different methods. For each method, the influence of the sampling domain length D and sampling interval dx on the estimation of θ were investigated, and the results are quantified in the form of errors over the parameter space, defined by the dimensionless ratios D/θ and θ/dx. Through the present analysis, one is able to assess the reliability of θ estimations obtained in practice, by mapping the conditions of any given experiment i.e., sampling domain, interval and estimated correlation length, onto the parameter space. The expected error associated with each method used is also quantified. Through this analysis a comparative assessment of the methods is also obtained.