Modern statistical analysis and optimal estimation of geotechnical data

Abstract

A common problem in geotechnical engineering is to estimate the parameters of a soil deposit from scattered measurements for use in deterministic models, finite elements for example. In this article two major sources of soil uncertainty are considered: measurement errors and spatial variability. A stochastic framework is then developed, in terms of the theory of random functions, to clarify dependencies and interactions between these uncertainties and the expected soil behaviour. This improves the engineering judgement leading to optimum design decisions. Spatial multivariable models describing geological processes in terms of covariances, parameter increments, recursive equations, empirical relationships or combinations thereof, improve the statistical inferences of the underlying random functions, and are of use both qualitatively and quantitatively. “Best” estimators in a well-established stochastic sense are derived from easily programmed procedures, and are tested in a number of common geotechnical applications, in an attempt to understand their properties and investigate their potential uses.