Random Field Generation and the Local Average Subdivision Method

Abstract

The use of multi-dimensional random fields to model real soils is becoming ever more important, simply because soils are spatially random. Such random field models allow the rational quantification of the behaviour of spatially variable soils, which are inherently uncertain, and lead to reliability estimates, decision analysis, and. ultimately, optimal designs. Random models are commonly used either in analytical studies employing theoretical results or in Monte Carlo simulations. Since theoretical results do not exist for many problems of interest to geotechnical engineers, the Monte Carlo approach is often the practical choice.

In that the accuracy of such models depends directly on the accuracy of the algorithm used to generate realizations of the representative random fields, there is a need to evaluate and compare various random field generators. To address this issue, three common random field generators are considered in this chapter: 1) the FFT method. 2) the Turning Bands Method (TBM). and 3) the Locai Average Subdivision (LAS) method. For each, an ensemble of realizations of a two-dimensional homogeneous Gauss-Markov process is generated and the field mean, variance, and covariance structures are checked for statistical accuracy. Concerns such as ease of use and efficiency are also considered. It is shown that all three methods have distinct advantages and disadvantages, and the choice of algorithm will depend on the particular application. A number of guidelines and suggestions are made to help avoid or minimize problems associated with each method.