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On the estimation of scale of fluctuation in geostatistics

Lloret-Cabot, Martí; Fenton, Gordon A.; Hicks, Michael A.

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Gordon A. Fenton

Michael A. Hicks


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 two-dimensional 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.


Lloret-Cabot, M., Fenton, G. A., & Hicks, M. A. (2014). On the estimation of scale of fluctuation in geostatistics. Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, 8(2), 129-140.

Journal Article Type Article
Acceptance Date Nov 28, 2013
Online Publication Date Jan 2, 2014
Publication Date Apr 3, 2014
Deposit Date Oct 2, 2018
Publicly Available Date Oct 5, 2018
Journal Georisk
Print ISSN 1749-9518
Electronic ISSN 1749-9526
Publisher Taylor and Francis Group
Peer Reviewed Peer Reviewed
Volume 8
Issue 2
Pages 129-140


Accepted Journal Article (3.2 Mb)

Copyright Statement
This is an Accepted Manuscript of an article published by Taylor & Francis in Georisk on 02 Jan 2014, available online:

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