Simulation of Random Fields via Local Average Subdivision

Abstract

A fast and accurate method of generating realizations of a homogeneous Gaussian scalar random process in one, two, or three dimensions is presented. The resulting discrete process represents local averages of a homogeneous random function defined by its mean and covariance function, the averaging being performed over incremental domains formed by different levels of discretization of the field. The approach is motivated first by the need to represent engineering properties as local averages (since many properties are not well defined at a point and show significant scale effects), and second to be able to easily condition the realization to incorporate known data or change resolution within sub-regions. The ability to condition the realization or increase the resolution in certain regions is an important contribution to finite element modeling of random phenomena. The Ornstein-Uhlenbeck and fractional Gaussian noise processes are used as illustrations.

Bearing Capacity of Spatially Random Cohesive Soil Using Numerical Limit Analyses

“…The study by Popescu et al (2005) uses the mid-point method for representing spatial variability of clays with non-Gaussian undrained shear strength properties (beta and gamma distribution), while Griffiths and Fenton (2001) has used a more rigorous method of Local Area Subdivision to represent spatial variability in the finite element model (FEM-LAS; after Fenton & Vanmarcke, 1990) assuming log-normally distributed undrained shear strengths.…”

Random analysis of bearing capacity of square footing using the LAS procedure

“…For arbitrary cell 1 2  i j Z generated in i + 1 step these conditions are: correct variance according to local averaging theory and appropriate correlation with cells in the neighborhood of the parent. As has been shown in the works by Fenton and Vanmarcke (1990) and Samy (1998) for the process with exponential covariance functions a neighborhood of the size 3 (…”

Calibration of Factors of Safety for Slope Stability of Dikes

“…Hicks & Spencer, 2010). Independent random fields for both shear strength variables were generated using local average subdivision (LAS) (Fenton & Vanmarcke, 1990), which requires only the mean, standard deviation and scales of fluctuation in the three dimensions (θ x , θ y and θ z ), where θ z is the vertical scale of fluctuation (θ v ) and θ x = θ y = θ h . Random fields were generated based on the covariance function, β, i.e.,…”