Scale of Fluctuation for Spatially Varying Soils: Estimation Methods and Values

Spatial variability is one of the major sources of uncertainty in geotechnical applications. This variability is characterized customarily by the scale of fluctuation. Scale of fluctuation describes the distance over which the parameters of a soil or rock are similar or correlated. The scale of fluctuation is required in order to best characterize and to simulate a spatially variable field. This paper first provides an overview of the various methods available for estimating the scale of fluctuation from cone penetration test (CPT) data, along with two examples for comparing the methods. The first part reveals some issues with two popular estimation methods, namely the method of moments and the maximum-likelihood method (MLE). The method of moments is less sensitive to the choice of the autocorrelation function (ACF), but it could be less precise and may be based on a correlation estimator that does not produce a positive definite autocorrelation matrix. MLE can be very sensitive to the choice of the classical one-parameter ACF. It is not uncommon to assume such an ACF, rather than to identify the ACF from actual soil data with a more general two-parameter Whittle–Matérn (WM) model. This practice may not be robust. Nonetheless, a literature survey is useful if these caveats are kept in mind. The second part of this paper provides a database table of horizontal and vertical scale of fluctuation values in different locations and for different materials, collected from published case studies, which can be used as a reference when field data are not readily available. The probable range of values as a function of soil type is provided to inform sensitivity analysis and to guide the selection of a prior distribution for Bayesian analysis.