Investigation of the reduction in uncertainty due to soil variability when conditioning a random field using Kriging

Abstract

Spatial variability of soil properties is inherent in soil deposits, whether as a result of natural geological processes or engineering construction. It is therefore important to account for soil variability in geotechnical design in order to represent more realistically a soil's in situ state. This variability may be modelled as a random field, with a given probability density function and scale of fluctuation. A more convenient way to deal with the uncertainty of a soil property due to spatial variability, by constraining the generated random field at the locations of actual field measurements, is presented in this article. Conditioning the random field at known locations is a powerful tool, not only because it more accurately represents the observed variability on site, but also because it uses the available field information more efficiently. In situ cone penetration test (CPT) data from a particular test site are used to determine the input statistics for generating random fields, which are later constrained (conditioned) at the locations of actual CPT measurements using the Kriging interpolation method. The results from the conditional random fields are then analysed, to quantify how the number of field measurements used influences the reduction of uncertainty. It is shown that the spatial uncertainty relative to the original (unconditional) random field reduces with the number of CPTs used in the conditioning.