On the estimation of scale of fluctuation in geostatistics

Abstract

Describing how soil properties vary spatially is of particular importance in stochastic analyses of geotechnical problems, because spatial variability has a significant influence on local material and global geotechnical response. In particular, the scale of fluctuation θ is a key parameter in the correlation model used to represent the spatial variability of a site through a random field. It is, therefore, of fundamental importance to accurately estimate θ in order to best model the actual soil heterogeneity. In this paper, two methodologies are investigated to assess their abilities to estimate the vertical and horizontal scales of fluctuation of a particular site using in situ cone penetration test (CPT) data. The first method belongs to the family of more traditional approaches, which are based on best fitting a theoretical correlation model to available CPT data. The second method involves a new strategy which combines information from conditional random fields with the traditional approach. Both methods are applied to a case study involving the estimation of θ at three twodimensional sections across a site and the results obtained show general agreement between the two methods, suggesting a similar level of accuracy between the new and traditional approaches. However, in order to further assess the relative accuracy of estimates provided by each method, a second numerical analysis is proposed. The results confirm the general consistency observed in the case study calculations, particularly in the vertical direction where a large amount of data are available. Interestingly, for the horizontal direction, where data are typically scarce, some additional improvement in terms of relative error is obtained with the new approach.

Influence of heterogeneity on 3D slope reliability and failure consequence

“…Note that the vertical scale of fluctuation is generally much smaller than the height of a slope and may easily be determined from in situ (e.g. CPT) data [4,5,15], whereas the horizontal scale of fluctuation is generally much larger than the vertical scale of fluctuation and more difficult to quantify [26,27]: hence the reason for keeping h v constant and varying h h in this investigation.…”

Determining an appropriate finite element size for modelling the strength of undrained random soils

“…Conversely, two points separated by a distance greater than h are largely uncorrelated. Many studies have been undertaken in recent years to develop probabilistic methods that address spatial variability in a systematic way (e.g., [9,19,11,13,14,16,1,21,18,17,20]). Of particular importance has been the development of the random finite element method (RFEM) for modelling the spatial variability of geomaterials (e.g., [7]).…”

Slope failure analysis using the random material point method

“…Note that some reduction of the distribution width may be possible, by constraining the spatial variability using site-specific data to condition the random fields (Lloret-Cabot et al, 2014).…”