Estimation for stochastic soil models

Although considerable theory exists for the probabilistic treatment of soils, the ability to identify the nature of spatial stochastic soil variation is almost nonexistent. We all know that we could excavate an entire site and there would be no doubt about the soil properties. However, there would no longer be anything to rest our structure on, and so we must live with uncertainty and attempt to quantify it rationally. Twenty years ago the mean and variance was sufficient. Clients are now demanding full reliability studies, requiring more sophisticated models, so that engineers are becoming interested in rational soil correlation structures. Knowing that soil properties are spatially correlated, what is a reasonable correlation model? Are soils best represented using fractal models or finite-scale models? What is the difference? How can this question be answered? Once a model has been decided upon, how can its parameters be estimated? These are questions that this paper addresses by looking at a number of tools that aid in selecting appropriate stochastic models. These tools include the sample covariance, spectral density, variance function, variogram, and wavelet variance functions. Common models, corresponding to finite scale and fractal models, are investigated, and estimation techniques are discussed.